Testing supersymmetric

neutrino mass models

at the LHCWerner Porod

Universitat Wurzburg

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 1

Overview

rdquoWhy supersymmetryrdquo or

rdquoWhy do we want to extend the Standard Modelrdquo

Neutrinos amp lepton flavour violation

Signals in models with

Dirac neutrinos

Majorana neutrinos

Neutrino masses via R-parity violation

Conclusions

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 2

Why supersymmetry

How to combine gravity with the SM

rArr local Supersymmetry (SUSY) implies gravity

SM particles can be put in multiplets of larger gaugegroups

in SU(5) 1 = νcR 5 = (dc

αR νlL lL)

10 = (uαL ucαR dαL lR)

in SO(10) 16 = (uαL ucαR dαL dc

αR lL lR νlL νcR)

However there are two problems in the SM but not inSUSY

proton decay (also in SUSY SU(5) a problem)

gauge coupling unification

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 3

Evolution of gauge couplings SM versus SUSY

SM MSSM

102 104 106 108 1010 1012 1014 1016

Interaction Energy in GeV

0

10

20

30

40

50

60

1-1

2-1

3-1

102 104 106 108 1010 1012 1014 1016

Interaction Energy in GeV

0

10

20

30

40

50

60

1- 1

2- 1

3- 1

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 4

Why supersymmetry

What is the nature of dark matter

What is the origin of the observed baryon asymmetry

Why three generations

Why do have neutrinos so tiny masses

rdquoWhy does electroweak symmetry breakrdquo or

rdquoWhy is micro2 lt 0 in the SMrdquo

Hierarchy problem

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 5

Supersymmetry MSSM

Standard Model MSSM

mattere d d d

νe u u uhArr

e d d d

νe u u u

gauge sector hArrγ Z0 Wplusmn g γ z0 wplusmn g

Higgs sector hArrH0 h0hArrh0 H0 A0 Hplusmn h0d h0

u hplusmn

assume for the moment conserved R-Parity (minus1)(3(BminusL)+2s)

(γ z0 h0d h

0u) rarr χ0

i (wplusmn hplusmn) rarr χplusmnj

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 6

Experimental information

Mass bounds from LEPTevatron

Higgs gtsim 100 GeV

charginossleptons gtsim 100 GeV

squarks (except t b) gluinos gtsim 300 GeV

rare decays

bounds on flavour violation beyond CKM

Cold dark matter Ωh2 ltsim 012

high precision measurments of gauge couplings

rArr unification if SUSY is present

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 7

Lepton flavour violation experimental data

Neutrinos tiny masses

∆m2atm ≃ 3 middot 10minus3 eV2

∆m2sol ≃ 7 middot 10minus5 eV2

3H decay mν ltsim 2 eV

Neutrinos large mixings

| tan θatm|2 ≃ 1

| tan θsol|2 ≃ 04

|Ue3|2 ltsim 005

strong bounds for charged leptons

BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12

BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8

BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)

|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm

SUSY contributions to anomalous magnetic moments

|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 8

Dirac neutrinos

analog to leptons or quarks

Yν H νL νR rarr Yν v νL νR = mν νL νR

requires Yν ≪ Ye

rArr no impact for future collider experiments

Exception νR is LSP and thus a candidate for dark matter

rArr long lived NLSP eg t1 rarr l+bνR

Remark mνRhardly runs rArr eg mνR

≃ m0 in mSUGRA

mνR ≃ 0 in GMSB

S Gopalakrishna A de Gouvea and W P JHEP 0611 (2006) 050

S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007

D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 9

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Why supersymmetry

How to combine gravity with the SM

rArr local Supersymmetry (SUSY) implies gravity

SM particles can be put in multiplets of larger gaugegroups

in SU(5) 1 = νcR 5 = (dc

αR νlL lL)

10 = (uαL ucαR dαL lR)

in SO(10) 16 = (uαL ucαR dαL dc

αR lL lR νlL νcR)

However there are two problems in the SM but not inSUSY

proton decay (also in SUSY SU(5) a problem)

gauge coupling unification

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 3

Evolution of gauge couplings SM versus SUSY

SM MSSM

102 104 106 108 1010 1012 1014 1016

Interaction Energy in GeV

0

10

20

30

40

50

60

1-1

2-1

3-1

102 104 106 108 1010 1012 1014 1016

Interaction Energy in GeV

0

10

20

30

40

50

60

1- 1

2- 1

3- 1

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 4

Why supersymmetry

What is the nature of dark matter

What is the origin of the observed baryon asymmetry

Why three generations

Why do have neutrinos so tiny masses

rdquoWhy does electroweak symmetry breakrdquo or

rdquoWhy is micro2 lt 0 in the SMrdquo

Hierarchy problem

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 5

Supersymmetry MSSM

Standard Model MSSM

mattere d d d

νe u u uhArr

e d d d

νe u u u

gauge sector hArrγ Z0 Wplusmn g γ z0 wplusmn g

Higgs sector hArrH0 h0hArrh0 H0 A0 Hplusmn h0d h0

u hplusmn

assume for the moment conserved R-Parity (minus1)(3(BminusL)+2s)

(γ z0 h0d h

0u) rarr χ0

i (wplusmn hplusmn) rarr χplusmnj

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 6

Experimental information

Mass bounds from LEPTevatron

Higgs gtsim 100 GeV

charginossleptons gtsim 100 GeV

squarks (except t b) gluinos gtsim 300 GeV

rare decays

bounds on flavour violation beyond CKM

Cold dark matter Ωh2 ltsim 012

high precision measurments of gauge couplings

rArr unification if SUSY is present

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 7

Lepton flavour violation experimental data

Neutrinos tiny masses

∆m2atm ≃ 3 middot 10minus3 eV2

∆m2sol ≃ 7 middot 10minus5 eV2

3H decay mν ltsim 2 eV

Neutrinos large mixings

| tan θatm|2 ≃ 1

| tan θsol|2 ≃ 04

|Ue3|2 ltsim 005

strong bounds for charged leptons

BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12

BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8

BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)

|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm

SUSY contributions to anomalous magnetic moments

|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 8

Dirac neutrinos

analog to leptons or quarks

Yν H νL νR rarr Yν v νL νR = mν νL νR

requires Yν ≪ Ye

rArr no impact for future collider experiments

Exception νR is LSP and thus a candidate for dark matter

rArr long lived NLSP eg t1 rarr l+bνR

Remark mνRhardly runs rArr eg mνR

≃ m0 in mSUGRA

mνR ≃ 0 in GMSB

S Gopalakrishna A de Gouvea and W P JHEP 0611 (2006) 050

S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007

D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 9

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Evolution of gauge couplings SM versus SUSY

SM MSSM

102 104 106 108 1010 1012 1014 1016

Interaction Energy in GeV

0

10

20

30

40

50

60

1-1

2-1

3-1

102 104 106 108 1010 1012 1014 1016

Interaction Energy in GeV

0

10

20

30

40

50

60

1- 1

2- 1

3- 1

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 4

Why supersymmetry

What is the nature of dark matter

What is the origin of the observed baryon asymmetry

Why three generations

Why do have neutrinos so tiny masses

rdquoWhy does electroweak symmetry breakrdquo or

rdquoWhy is micro2 lt 0 in the SMrdquo

Hierarchy problem

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 5

Supersymmetry MSSM

Standard Model MSSM

mattere d d d

νe u u uhArr

e d d d

νe u u u

gauge sector hArrγ Z0 Wplusmn g γ z0 wplusmn g

Higgs sector hArrH0 h0hArrh0 H0 A0 Hplusmn h0d h0

u hplusmn

assume for the moment conserved R-Parity (minus1)(3(BminusL)+2s)

(γ z0 h0d h

0u) rarr χ0

i (wplusmn hplusmn) rarr χplusmnj

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 6

Experimental information

Mass bounds from LEPTevatron

Higgs gtsim 100 GeV

charginossleptons gtsim 100 GeV

squarks (except t b) gluinos gtsim 300 GeV

rare decays

bounds on flavour violation beyond CKM

Cold dark matter Ωh2 ltsim 012

high precision measurments of gauge couplings

rArr unification if SUSY is present

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 7

Lepton flavour violation experimental data

Neutrinos tiny masses

∆m2atm ≃ 3 middot 10minus3 eV2

∆m2sol ≃ 7 middot 10minus5 eV2

3H decay mν ltsim 2 eV

Neutrinos large mixings

| tan θatm|2 ≃ 1

| tan θsol|2 ≃ 04

|Ue3|2 ltsim 005

strong bounds for charged leptons

BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12

BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8

BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)

|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm

SUSY contributions to anomalous magnetic moments

|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 8

Dirac neutrinos

analog to leptons or quarks

Yν H νL νR rarr Yν v νL νR = mν νL νR

requires Yν ≪ Ye

rArr no impact for future collider experiments

Exception νR is LSP and thus a candidate for dark matter

rArr long lived NLSP eg t1 rarr l+bνR

Remark mνRhardly runs rArr eg mνR

≃ m0 in mSUGRA

mνR ≃ 0 in GMSB

S Gopalakrishna A de Gouvea and W P JHEP 0611 (2006) 050

S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007

D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 9

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Why supersymmetry

What is the nature of dark matter

What is the origin of the observed baryon asymmetry

Why three generations

Why do have neutrinos so tiny masses

rdquoWhy does electroweak symmetry breakrdquo or

rdquoWhy is micro2 lt 0 in the SMrdquo

Hierarchy problem

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 5

Supersymmetry MSSM

Standard Model MSSM

mattere d d d

νe u u uhArr

e d d d

νe u u u

gauge sector hArrγ Z0 Wplusmn g γ z0 wplusmn g

Higgs sector hArrH0 h0hArrh0 H0 A0 Hplusmn h0d h0

u hplusmn

assume for the moment conserved R-Parity (minus1)(3(BminusL)+2s)

(γ z0 h0d h

0u) rarr χ0

i (wplusmn hplusmn) rarr χplusmnj

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 6

Experimental information

Mass bounds from LEPTevatron

Higgs gtsim 100 GeV

charginossleptons gtsim 100 GeV

squarks (except t b) gluinos gtsim 300 GeV

rare decays

bounds on flavour violation beyond CKM

Cold dark matter Ωh2 ltsim 012

high precision measurments of gauge couplings

rArr unification if SUSY is present

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 7

Lepton flavour violation experimental data

Neutrinos tiny masses

∆m2atm ≃ 3 middot 10minus3 eV2

∆m2sol ≃ 7 middot 10minus5 eV2

3H decay mν ltsim 2 eV

Neutrinos large mixings

| tan θatm|2 ≃ 1

| tan θsol|2 ≃ 04

|Ue3|2 ltsim 005

strong bounds for charged leptons

BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12

BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8

BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)

|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm

SUSY contributions to anomalous magnetic moments

|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 8

Dirac neutrinos

analog to leptons or quarks

Yν H νL νR rarr Yν v νL νR = mν νL νR

requires Yν ≪ Ye

rArr no impact for future collider experiments

Exception νR is LSP and thus a candidate for dark matter

rArr long lived NLSP eg t1 rarr l+bνR

Remark mνRhardly runs rArr eg mνR

≃ m0 in mSUGRA

mνR ≃ 0 in GMSB

S Gopalakrishna A de Gouvea and W P JHEP 0611 (2006) 050

S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007

D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 9

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Supersymmetry MSSM

Standard Model MSSM

mattere d d d

νe u u uhArr

e d d d

νe u u u

gauge sector hArrγ Z0 Wplusmn g γ z0 wplusmn g

Higgs sector hArrH0 h0hArrh0 H0 A0 Hplusmn h0d h0

u hplusmn

assume for the moment conserved R-Parity (minus1)(3(BminusL)+2s)

(γ z0 h0d h

0u) rarr χ0

i (wplusmn hplusmn) rarr χplusmnj

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 6

Experimental information

Mass bounds from LEPTevatron

Higgs gtsim 100 GeV

charginossleptons gtsim 100 GeV

squarks (except t b) gluinos gtsim 300 GeV

rare decays

bounds on flavour violation beyond CKM

Cold dark matter Ωh2 ltsim 012

high precision measurments of gauge couplings

rArr unification if SUSY is present

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 7

Lepton flavour violation experimental data

Neutrinos tiny masses

∆m2atm ≃ 3 middot 10minus3 eV2

∆m2sol ≃ 7 middot 10minus5 eV2

3H decay mν ltsim 2 eV

Neutrinos large mixings

| tan θatm|2 ≃ 1

| tan θsol|2 ≃ 04

|Ue3|2 ltsim 005

strong bounds for charged leptons

BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12

BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8

BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)

|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm

SUSY contributions to anomalous magnetic moments

|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 8

Dirac neutrinos

analog to leptons or quarks

Yν H νL νR rarr Yν v νL νR = mν νL νR

requires Yν ≪ Ye

rArr no impact for future collider experiments

Exception νR is LSP and thus a candidate for dark matter

rArr long lived NLSP eg t1 rarr l+bνR

Remark mνRhardly runs rArr eg mνR

≃ m0 in mSUGRA

mνR ≃ 0 in GMSB

S Gopalakrishna A de Gouvea and W P JHEP 0611 (2006) 050

S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007

D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 9

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Experimental information

Mass bounds from LEPTevatron

Higgs gtsim 100 GeV

charginossleptons gtsim 100 GeV

squarks (except t b) gluinos gtsim 300 GeV

rare decays

bounds on flavour violation beyond CKM

Cold dark matter Ωh2 ltsim 012

high precision measurments of gauge couplings

rArr unification if SUSY is present

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 7

Lepton flavour violation experimental data

Neutrinos tiny masses

∆m2atm ≃ 3 middot 10minus3 eV2

∆m2sol ≃ 7 middot 10minus5 eV2

3H decay mν ltsim 2 eV

Neutrinos large mixings

| tan θatm|2 ≃ 1

| tan θsol|2 ≃ 04

|Ue3|2 ltsim 005

strong bounds for charged leptons

BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12

BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8

BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)

|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm

SUSY contributions to anomalous magnetic moments

|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 8

Dirac neutrinos

analog to leptons or quarks

Yν H νL νR rarr Yν v νL νR = mν νL νR

requires Yν ≪ Ye

rArr no impact for future collider experiments

Exception νR is LSP and thus a candidate for dark matter

rArr long lived NLSP eg t1 rarr l+bνR

Remark mνRhardly runs rArr eg mνR

≃ m0 in mSUGRA

mνR ≃ 0 in GMSB

S Gopalakrishna A de Gouvea and W P JHEP 0611 (2006) 050

S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007

D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 9

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Lepton flavour violation experimental data

Neutrinos tiny masses

∆m2atm ≃ 3 middot 10minus3 eV2

∆m2sol ≃ 7 middot 10minus5 eV2

3H decay mν ltsim 2 eV

Neutrinos large mixings

| tan θatm|2 ≃ 1

| tan θsol|2 ≃ 04

|Ue3|2 ltsim 005

strong bounds for charged leptons

BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12

BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8

BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)

|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm

SUSY contributions to anomalous magnetic moments

|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 8

Dirac neutrinos

analog to leptons or quarks

Yν H νL νR rarr Yν v νL νR = mν νL νR

requires Yν ≪ Ye

rArr no impact for future collider experiments

Exception νR is LSP and thus a candidate for dark matter

rArr long lived NLSP eg t1 rarr l+bνR

Remark mνRhardly runs rArr eg mνR

≃ m0 in mSUGRA

mνR ≃ 0 in GMSB

S Gopalakrishna A de Gouvea and W P JHEP 0611 (2006) 050

S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007

D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 9

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Dirac neutrinos

analog to leptons or quarks

Yν H νL νR rarr Yν v νL νR = mν νL νR

requires Yν ≪ Ye

rArr no impact for future collider experiments

Exception νR is LSP and thus a candidate for dark matter

rArr long lived NLSP eg t1 rarr l+bνR

Remark mνRhardly runs rArr eg mνR

≃ m0 in mSUGRA

mνR ≃ 0 in GMSB

S Gopalakrishna A de Gouvea and W P JHEP 0611 (2006) 050

S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007

D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 9

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Majorana neutrinos Seesaw mechanismlowast

Neutrino masses due tof

Λ(HL)(HL)

lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)

M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315

RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich

Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181

(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)

R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 10

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw I

Supersymmetry

W = Y jiebLibHdbEc

j + Y jiνbLibHubNc

j +MRibNc

ibNc

i

neutrino masses

mν ≃ minus(Y Tν v)Mminus1

R (Yνv) rArr mν = UT middotmν middot U

convenient parameterizationdagger

Yν =radic

2 ivU

q

MR middotR middotradicmν middot Udagger

RGE running

(∆M2

L)ij = minus 1

8π2(3m2

0 +A20)(Y dagger

ν LYν)ij

(∆Al)ij = minus 38π2

A0Yli(Ydaggerν LYν)ij

(∆M2

E)ij = 0

Lkl = log`MX

Mk

acute

δkl

daggerJ A Casas and A Ibarra Nucl Phys B618 171 (2001) [hep-ph0103065]

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 11

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw I

(∆M2

L)ij and (∆Al)ij induce

lj rarr liγ lil+k l

minusr

lj rarr liχ0s

χ0s rarr li lk

Neglecting L-R mixing

Br(li rarr ljγ) prop α3m5li

|(δm2L)ij |2em8

tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2

L)23

rdquo2

Moreover in most of the parameter space

Br(li rarr 3lj)

Br(li rarr lj + γ)≃ α

3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 12

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw I

take all parameters real

U = UTBM =

0

B

B

B

q

23

1radic3

0

minus 1radic6

1radic3

1radic2

1radic6

minus 1radic3

1radic2

1

C

C

C

A

R =

0

B

B

1 0 0

0 1 0

0 0 1

1

C

C

A

Use 2-loop RGEs and 1-loop corrections including flavour effects

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 13

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw I

(GeV)1M

1010 1210 1410

1610

)j

3 l

rarr i)B

r(l

γ j

lrarr i

Br(l

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(

)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(

=0 eV1

νm

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νRSPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 14

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw I

(GeV)1M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

(GeV)2M

1010 1110 1210

1310 1410

1510

1610

)χ

micro rarr

τsim) B

r(

χ e

rarr

τsimB

r(

-610

-510

-410

-310

-210

-110

1

)χ e rarr τsimBr(

)χ micro rarr τsimBr(

Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR hierarchical νR(M1 = M3 = 1010 GeV)

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch et al Phys Rev D 78 (2008) 013006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 15

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)

F Deppisch F Plentinger W P R Ruumlckl G Seidl in preparation

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 16

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw II

include SU(2) Triplet Higgs

W = WMSSM +1radic2

ldquo

Y ijT LiT1Lj + λ1HdT1Hd + λ2HuT2Hu

rdquo

+MT T1T2

mν =v222

λ2

MTYT

MT

λ2

≃ 1015GeVldquo005 eV

mν

rdquo

Gauge coupling unification rArr use 15

15 = S + T + Z

S sim (6 1minus2

3) T sim (1 3 1) Z sim (3 2

1

6)

W sub 1radic2(YT LT1L+ YSD

cSDc) + YZDcZL+ YdD

cQHd + YuUcQHu + YeE

cLHd

+1radic2(λ1HdT1Hd + λ2HuT2Hu) +MT T1T2 +MZ Z1Z2 +MS S1S2 + microHdHu

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 17

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw II with 15-plets

1011

1012

1013

1014

1015

1016

15

2

3

5

1 10(m

2 Qminus

m2 E)M

2 1

1 10(m

2 Dminus

m2 L)M

2 1

(m

2 Lminus

m2 E)M

2 1

(m

2 Qminus

m2 U)M

2 1

M15 = MT [GeV]

(b1 b2 b3)MSSM = (33

5 1minus3)

(b1 b2 b3)T1+T2 = (18

5 4 0)

(b1 b2 b3)15+15 = (7 7 7)

Seesaw I (≃ MSSM)

m2Qminusm2

E

M21

≃ 20m2

Dminusm2L

M21

≃ 18

m2Qminusm2

U

M21

≃ 16m2

Dminusm2L

M21

≃ 155

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 18

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 19

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Masses at LHC

~q lnear ~01q~02 ~lR lfar0

500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello

5 kinematical observables depending on 4 SUSY masses

eg m(ll) = 7702 plusmn 005 plusmn 008rArr mass determination within 2-5

For background suppression

N(e+eminus) + N(micro+microminus) minus N(e+microminus) minus N(micro+eminus)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 20

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw I + II signal at LHC

200 400 600 800

M12

[GeV]

10-5

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

400 600 800

M12

[GeV]

10-4

10-3

10-2

10-1

100

101

σ(χ

20) times

BR

[fb

]

m0=100 GeV

m0=200 GeV

m0=300 GeV

m0=500 GeV

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 21

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw special kinematicsdagger

mSugra stau co-annihilation for DM in particular mτ1 minus mχ01

ltsim mτ

τ1

(a)

χ01

τ

(b)

χ01

τ1

τ

π

ντ

χ01

ντ

νl

lW

τ

τ1

(c)

(a)

lα

χ01

1Me 2

Rτ minusMe 2Rα

lαRτR ≃ l1

∆M 2 eRRατ

χ01

lα

(b)

1Me 2

Rτ minusMe 2Lα

M 2 eLRττ ∆M 2 e

LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

τ1 life times up to 104 sec

dagger S Kaneko et al arXiv08110703 (hep-ph)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 22

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

NMSSM + Seesaw

general problem up to now mν ≃ 01 eV rArr Y 2M fixed

forbid dim-5 operator eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)

2S2

M37

solves at the same time the micro-problem

dagger I Gogoladze N Okada Q Shafi Phys Lett B 672 (2009) 235

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 23

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

arbitrary M 2Eij M 2

Lij Alij χ02 rarr lilj rarr lkljχ

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

1middot 10-12 1middot 10-10 1middot 10-8

00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0

1 microplusmn τ∓)

BR(τ rarr microγ)

Variations around SPS1a

(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 24

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Flavour mixing and edge variables

0 20 40 60 800

002

004

006

008

100Γtot

dΓ(χ02rarrlplusmni l

∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓

m(lplusmni l∓j ) [GeV]0 20 40 60 80

0

001

002

003

004

005

100Γtot

dΓ(χ02rarrl+lminusχ0

1)dm(l+lminus)

e+eminus(= micro+microminus) [LFC]

micro+microminus

e+eminus

m(l+lminus) [GeV]

A Bartl et al Eur Phys J C 46 (2006) 783

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 25

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Introduction to explicit R-parity violation

The most general superpotential allowed by SU(3) times SU(2) times U(1)

W = WRP+WRp

rArr MSSM part

WRP= Y ij

e HdLiECj + Y ij

d HdQiDCj + Y ij

u HuQiUCj minus microHdHu

rArr R-parity violating part

WRp = λijkLiLjECk + λprimeijkLiQjD

Ck + λprimeprimeijkU

Ci D

Cj D

Ck + ǫiLiHu

rArr λijk λprimeijk and ǫi violate lepton number

rArr λprimeprimeijk violate baryon number

rArr lepton number and baryon number violation shouldnrsquot be present at the same time

because

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 26

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Proton decay

rArr Consider for example

d

u e+

u

macrsλprimeprime112 λ

prime112

Estimated decay width

Γ(P rarr e+π0) asymp (λprime11k)2(λprimeprime

11k)2

16π2m4dk

M5proton

Given that τ(P rarr eπ) gt 1032 yr

λprime11k middot λprimeprime

11kltsim 2 middot 10minus27

(mdk

100GeV

)2

rArr For this reason the MSSM assumes R-parity

RP = (minus1)3(BminusL)+2S

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 27

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Alternatives to RP

rArr An alternative is matter parity (all λ λprime λprimeprime and ǫ forbidden)

(Li Ei Qi Ui Di) rarr minus(Li Ei Qi Ui Di) (Hd Hu) rarr (Hd Hu)

rArr Sufficient to forbid baryon number violation for example via baryon-paritydagger

( all λprimeprime forbidden)

(Qi Ui Di) rarr minus(Qi Ui Di) (Li Ei Hd Hu) rarr (Li Ei Hd Hu)

rArr Spontaneous R-parity violation (all λ λprime and λprimeprime forbidden)

W = WMSSM + Y νibLibHubNc + middot middot middot

rArr If 〈νc〉 6= 0 explicit bilinear RPV terms are generated effectively

ǫi = Y ijν 〈νc

j 〉

dagger complete list of possible discrete symmetries by H Dreiner et al

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 28

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Gauge Mediated SUSY Breaking (GMSB)

Basis idea transfer of SUSY breaking from hidden sector via

messenger fields using gauge interactions

Messenger scale Mi(MM ) sim g(x)αiΛG

M2j (MM ) sim f(x)

sumCiα

2iΛ

2G

x = ΛGMM f(x) g(x) = (n5 + 3n10)O(1)

Generic prediction light gravitino being the LSP

NLSP χ01 or lR (l = e micro τ )

add bilinear R-parity violating terms

W = WMSSM + ǫiLiHu Vsoft = V MSSMsoft + BiǫiLiHu

rArr sneutrino vevs vi

in the following take vi as free parameters instead Bi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 29

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

R-parity violation and neutrino massesmixings

basis ψ0T = (minusiλprimeminusiλ3 eH1d eH2

u νe νmicro ντ ) we get

MN =

2

6

6

4

Mχ0 mT

m 0

3

7

7

5

Mχ0 =

2

6

6

6

6

6

6

4

M1 0 minus 12gprimevd

12gprimevu

0 M212gvd minus 1

2gvu

minus 12gprimevd

12gvd 0 minusmicro

12gprimevu minus 1

2gvu minusmicro 0

3

7

7

7

7

7

7

5

m =

2

6

6

6

6

6

4

minus 12gprimev1 1

2gv1 0 ǫ1

minus 12gprimev2 1

2gv2 0 ǫ2

minus 12gprimev3 1

2gv3 0 ǫ3

3

7

7

7

7

7

5

Approximate diagonalization as in usual seesaw mechanism gives

mνeff =M1g2+M2gprime

2

4 det(Mχ0 )

0

B

B

Λ21 Λ1Λ2 Λ1Λ3

Λ1Λ2 Λ22 Λ2Λ3

Λ1Λ3 Λ2Λ3 Λ23

1

C

C

A

Λi = microvi + vdǫi

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 30

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

R-parity violation and neutrino massesmixings

second ν mass via loops

m1lpν ≃ 1

16π2

3h2b sin(2θb)mb log

m2

b2

m2

b1

+ h2τ sin(2θτ )mτ log

m2τ2

m2τ1

(ǫ21 + ǫ22)

micro2

ǫi = V νjiǫj

mixing angles

tan2 θatm ≃bdquo

Λ2

Λ3

laquo2

U2e3 ≃ |Λ1|

q

Λ22 + Λ2

3

tan2 θsol ≃bdquo

ǫ1

ǫ2

laquo2

experimental data require

|~Λ|q

detMχ0

sim O(10minus6) |~ǫ|micro

sim O(10minus4)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 31

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Neutrino masses

Two examples of neutrino masses as function of ~ǫ2|~Λ|(other parameters fixed)

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) gt 0

10-2 10-1 100 101 102 10310-5

10-3

10-1

101 mν1 mν2 mν3 [eV]

~ǫ2|~Λ|

ǫ2Λ2(ǫ3Λ3) lt 0

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 32

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Neutralino decays

dominant modes R-parity violating modes

Γ(χ01 rarr Wplusmnl∓i ) prop Λ2

i

detMχ0

Γ(χ01 rarr

sum

i

Zνi) ≃ 12

sum

i

Γ(χ01 rarr Wplusmnl∓i )

Γ(χ01 rarr ντ+lminusi ) prop ǫ2

i

micro2

R-parity conserving mode

Γ(χ01 rarr Gγ) ≃ 12 times 10minus6κ2

γ

( mχ01

100 GeV

)5(100 eV

m32

)2eV

total width

Γ ≃ (10minus4 minus 10minus2) eV

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 33

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Neutralino decays

BR(χ01 rarr

P

i Wli)

mχ0

1

[GeV]

100 200 300 400 500

005

0075

01

0125

015

0175

02

BR(χ01 rarr

P

ij νiτlj )

mχ0

1

[GeV]100 200 300 400 500

06

07

08

09

BR(χ01 rarr Gγ)

mχ0

1

[GeV]

100 200 300 400 500

10-1

5 10-2

2 10-2

10-2

5 10-3

2 10-3

10-3

m32 = 100 eV n5 = 1

mdash tan β = 10 micro gt 0 - - tan β = 10 micro lt 0 mdash tan β = 35 micro gt 0 - - tan β = 35 micro lt 0

M Hirsch W P und D Restrepo JHEP 0503 062 (2005)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 34

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Neutralino decays correlations

Correlations

01 02 05 1 2 5 1001

02

05

1

2

5

10

BR(χ01 rarrWmicro) BR(χ0

1 rarrWτ )

tan2(θatm)

01 02 05 1 2 5 10

01

02

05

1

2

5

10

BR(χ01 rarr νeτ ) BR(χ0

1 rarr νmicroτ )

tan2(θsol)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 35

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Comments

mτ1

mχ01

prop 1radicn5

rArr for n5 ge 3 hardly points with χ01 LSP

lR NLSPs BR(lν) ≫ BR(lG)

n5 = 2 BR(Gγ) reduced by a factor 2-3

G decays via R-parity violating couplings however

Γ(G) ≃ 35 middot 10minus16 mν [eV]

005eV

m332

M2Pl

rArr τ(G) sim O(1031)Hubbletimes

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 36

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Conclusions

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR

(but NMSSM t1 rarr lbνχ01)

Seesaw models

most promosing τ2 decays

very difficult to test at LHC signals of O(10 fb) or below

in case of Seesaw II different mass ratios

R-parity violation

interesting correlations between ν-physics and LSP decays

testable at LHC

displaced vertices

Can the model be pinned down

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 37

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw II with 15-plets

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrH Τ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1011 1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 005

SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 38

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw II with 15-plets

1012 1013 1014 1015 1016

M15 = MTGeVD

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Br H

li

reglj ΓL

BrHΤ reg ΜΓL

BrH Μ reg eΓL

BrH Τ reg eΓL

1012 1013 1014 1015 1016

M15 = MTGeVD

1

10-1

10-2

10-3

10-4

10-5

10-6

10-7

Br H

Τ

2reg

Χ1

eL

Br H

Τ

2reg

Χ1

ΜL

BrH Τ2 reg Χ1 eL

BrH Τ2 reg Χ1 ΜL

Excluded by

BrH Μ reg eΓL

λ1 = λ2 = 05

SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10) micro gt 0

M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 39

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Seesaw II signal at LHC

400 600 800

M12

[GeV]

10-3

10-2

10-1

100

101

σ(χ

20)

times B

R [

fb]

λ2=05

λ2=01

λ2=09

σ(pprarr χ02) timesBR(χ0

2 rarrP

ij lilj rarr microplusmnτ∓χ01)

m0 = 100 GeV A0 = 0 tan β = 10 micro gt 0 λ1 = 002

JN Esteves et al arXiv09031408

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 40

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Bilinear R-parity breaking extension of the MSSM

Connection to trilinear R-parity violation rotate (Hd Li) such that

ǫprimei = 0 gives in leading order of ǫimicro

λprimeijk =

ǫimicro

δjkhdk

and

λ121 = heǫ2micro λ122 = hmicro

ǫ1micro λ123 = 0

λ131 = heǫ3micro λ132 = 0 λ133 = hτ

ǫ1micro

λ231 = 0 λ232 = hmicroǫ3micro λ233 = hτ

ǫ2micro

λijk = minusλjik

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 41

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Solar angle

Approximation formula gives tan2 θ⊙ ≃(

ǫ1

ǫ2

)2

10-2 10-1 10010-2

10-1

100

(ǫ1ǫ2)2

tan2 θ⊙

10-2 10-1 100 101 10210-2

10-1

100

101

102

(ǫ1ǫ2)2

tan2 θ⊙

rArr Left figure Neutralino LSP bndashbi loop usually dominant

rArr Right figure Stau LSP both bndashbi and Splusmnj ndashχ∓

k

(j = 1 7 k = 1 5) equally important

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 42

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Gravitino Dark Matter

Standard thermal history of the universe

Ω32h2 ≃ 011

( m32

100 eV

) (100

glowast

)(glowast ≃ 90 minus 140)

Current data

ΩCDMh2 ≃ 0105 plusmn 0008

rArr m32 ≃ 100 eV if DM candidate warm dark matter

constraints from Lyman-α forest mWDM gtsim 550 eV

(M Viel et al arXivastro-ph0501562)

rArr assume additional entropy production eg non-standard decays

of messenger particles

(E Baltz H Murayama astro-ph0108172 M Fujii and T Yanagida hep-ph0208191)

does not work in practice F Staub W P J Niemeyer arXiv09070530

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 43

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

GMSB signals

10 20 50 102 2 102 5 102 103 2 103

100

10-1

10-2

10-3

10-4

10-5

BR(χ01 rarr Gγ)

m32 [eV]

10 20 50 102 2 102 5 102 103 2 103

100

10

102

103

104

105

106

BR(χ01 rarr Gγ)BR(χ0

1 rarr νγ)

m32 [eV]

mχ0 = 500 GeV

mχ0 = 400 GeV

mχ0 = 300 GeV

mχ0 = 200 GeV

mχ0 = 100 GeV

n5 = 1 tan β = 10

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 44

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Charged Scalar LSP

100 150 200 250 300 350 400

1

10-1

10-2

10-3

10-4

10-5

10-6

Decay length (e micro τ ) [cm]

ml [GeV]

rArr e micro τ can be separated

in this model

Moreover

Γ(τ)

Γ(micro)≃

(YτYmicro

)2 mτ

mmicro

lj rarr lisum

k

νk qqprime

M Hirsch W Porod J C Romatildeo and J W F Valle Phys Rev D66 (2002) 095006

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 45

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Charged Scalar LSP

005 01 05 1 5

005

01

05

1

5BR(e1 rarr microνi) BR(e1 rarr τνi)

(ǫ2ǫ3)2001 01 1 10 100

001

01

1

10

100

BR(micro1 rarr eνi) BR(micro1 rarr τνi)

(ǫ1ǫ3)2

001 01 1 10 100001

01

1

10

100BR(τ1 rarr eνi) BR(τ1 rarr microνi)

(ǫ1ǫ2)2

Cross check possible (ǫ1ǫ3)2(ǫ1ǫ2)

2 equiv (ǫ2ǫ3)2

rArr Measure 2 ratios 3rd is fixed

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 46

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

bilinear R-parity violation reach in mSUGRA

3-lepton channel

m0 (GeV)

m12

(G

eV

)

multi-lepton channel

m0 (GeV)

m12

(G

eV

)

displaced vertex

m0 (GeV)

m12

(G

eV

)

L = 100 fbminus1 A0 = minus100 GeV tanβ = 10 micro gt 0

F de Campos et al JHEP 0805 048 (2008)

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 47

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Cosmology

No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

openflat

Knop et al (2003)Spergel et al (2003)Allen et al (2002)

Ω

ΩΛ

M

ΩB = (4 plusmn 04)

ΩDM = (23 plusmn 4)

ΩΛ = (73 plusmn 4)

RA Knopp et al Astrophys J 598 (2003) 102 L Roszkowski astro-ph0404052

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 48

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Running SUSY masses

sign(m2)|m|

G Kane C Kolda L Roszkowski J Wells PRD 1994

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 49

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

Hierarchy problem

f

f

φ φ

φf

φ φ

f

f

δm2 = minusN(f)λ2

f

8π2Λ2 +

δm2 = N(f)λ2

f

8π2Λ2 minus

exacte SUSY δm2 = 0

softly broken SUSY δm2 prop (m2

fminusm2

f ) log(m2

fm2

f )

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 50

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC

SUSY masses at LHC

talk by I Borjanovic at rsquoFlavour in the era of LHCrsquo Novrsquo05 CERN

Mass reconstruction

Fit results

Gjelsten Lytken Miller Osland Polesello ATL-PHYS-2004-007

ucircm($10)= 48 GeV ucircm($2

0)= 47 GeV

ucircm(lR) = 48 GeV ucircm(qL)= 87 GeV

m($10) = 96 GeV

m(lR ) = 143 GeV

m(qL) = 540 GeV

m($20) = 177 GeV

L=100 fb-1

5 endpoints measurements 4 unknown masses

MPI fur Kernphysik Heidelberg 3 May 2010 W Porod Uni Wurzburg ndash p 51

• small hspace 2cm Overview
• small hspace 2cm Why supersymmetry
• small hspace 2cm Evolution of gauge couplings SM versus SUSY
• small hspace 2cm Why supersymmetry
• small hspace 2cm Supersymmetry MSSM
• small hspace 2cm Experimental information
• small hspace 2cm Lepton flavour violation experimental data
• small hspace 2cm Dirac neutrinos
• small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw I
• small hspace 2cm small Seesaw II
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Masses at LHC
• small hspace 2cm small Seesaw I + II signal at LHC
• small hspace 2cm small Seesaw special kinematics$^dagger $
• small hspace 2cm small NMSSM + Seesaw
• small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
• small hspace 2cm small Flavour mixing and edge variables
• small hspace 2cm Introduction to explicit R-parity violation
• small hspace 2cm Proton decay
• small hspace 2cm Alternatives to $R_P$
• small hspace 2cm Gauge Mediated SUSY Breaking (GMSB)
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm R-parity violation and neutrino massesmixings
• small hspace 2cm Neutrino masses
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays
• small hspace 2cm Neutralino decays correlations
• small hspace 2cm Comments
• small hspace 2cm small Conclusions
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II with $15$-plets
• small hspace 2cm small Seesaw II signal at LHC
• small hspace 2cm Bilinear R-parity breaking extension of the MSSM
• small hspace 2cm Solar angle
• small hspace 2cm Gravitino Dark Matter
• small hspace 2cm GMSB signals
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm Charged Scalar LSP
• small hspace 2cm small bilinear R-parity violation reach in mSUGRA
• small hspace 2cm Cosmology
• small hspace 2cm Running SUSY masses
• small hspace 2cm Hierarchy problem
• small hspace 2cm small SUSY masses at LHC