Testing the ﬂavour sector of SUSY models @ LHCific.uv.es/~flasy2011/Porod.pdf · ΦTP2 Testing...

ΦTP2

Testing the flavour sector of

SUSY models LHC

Werner Porod

Universitat Wurzburg

FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 1

ΦTP2Overview

Flavour Generalities

LFV signals in models with

Dirac neutrinos

Majorana neutrinos

General MSSM + extensions

Squark flavour at LHC

Conclusions

More in F del Aguila et al EPJC 57 (2008) 183 [arXiv08011800]


ΦTP2Supersymmetry 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 conserved R-Parity (minus1)(3(BminusL)+2s)

(γ z0 h0d h

0u) rarr χ0

i (wplusmn hplusmn) rarr χplusmnj


ΦTP2Flavour Generalities

SM Higgs doublet + Yukawa couplings

rArr after EWSB CKM- and PMNS matrices

rArr excellent agreement with data eg

BR(brarr sγ) BR(B+u rarr τ+ν) BR(Bs rarr micro+microminus) BR(B rarr Dτν)

BR(brarr smicro+microminus) BR(Bd rarr micro+microminus) BR(Bd rarr micro+microminus) ∆MBs ∆MBd

BR(Ds rarr τν) BR(Ds rarr microν) ∆MD

BR(K rarr microν) BR(K0L rarr π0νν) BR(K+ rarr π+νν) ∆mK ǫK

BR(τ rarr eγ) BR(τ rarr microγ) BR(τ rarr lllprime) (l lprime = e micro)

BR(microrarr eγ) BR(microminus rarr eminuse+eminus)

electric dipolemoments eg dn de

However no clue what determines sizes of masses and mixing angles

Supersymmetry eg MSSM

WMSSM = HdLYeEC + HdQYdD

C + HuQYuUC minus microHdHu

Vsoft = HdLTeelowast +HdQTdd

lowast +HuQTuulowast

+X

f=LeQdu

flowastM2ff +M2

Hd|Hu|2 +M2

Hu|Hu|2 minusBmicroHdHu



Pragmatic approach Minimal Flavour Violationdagger

express all additional flavour structures in terms of rsquoknownrsquo Yukawas

eg at some (high) scale

Tf = A0fYf M2f

= M20f13 + αY dagger

f Yf

where A0f and M20f are scalars

generic prediction for squarkslowast FV decays are governed by |VCKMij |2 eg

BR(trarr χ+1 s) ≃ |VCKMts|2BR(trarr χ+

1 s)

BR(trarr χ012c) ltsim 10minus7

Sleptons depend on mechanism for neutrino masses

dagger AJ Buras et al PLB 500 (2001) 161 G DrsquoAmbrosio et al NPB 645 (2002) 155lowast E Lunghi WP O Vives PRD 74 (2006) 075003



more ambitious new symmetries eg Abelian or non-Abelian gauge or discrete

SU(3) flavour examplelowast

WY = Hψiψcj

h

θi3θ

j3 + θi

23θj23

ldquo

θ3θ3rdquo

+ ǫiklθ23kθ3lθj23

ldquo

θ23θ3rdquo

+ i

Yd prop

0

B

B

0 xd12 ε

3 xd13 ε

3

xd12 ε

3 ε2 xd23 ε

2

xd13 ε

3 xd23 ε

2 1

1

C

C

A

Yu prop

0

B

B

0 xu12 ε

3 xu13 ε

3

xu12 ε

3 ε2 xu23 ε

2

xu13 ε

3 xu23 ε

2 1

1

C

C

A

(M2f)ji = m2

0

bdquo

δji

+1

M2f

raquo

θdagger3iθj3 + θ3iθ

dagger3

j+ θdagger23i

θj23 + θ23iθ

dagger23

j+ θdagger123i

θj123 + θ123iθ

dagger123

jndash

+1

M4f

(ǫiklθdagger3

kθdagger23

l)(ǫjmnθ3mθ23n) +

laquo

LHC similar to MFV approach although somewhat larger effects

lowast GG Ross L Velasco-Sevilla O Vives NPB 692 50 (2004) L Calibbi J Jones-Perez

O Vives PRD 78 (2008) 075007 L Calibbi et al NPB 831 (2010) 26


ΦTP2Lepton 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


ΦTP2Dirac neutrinos MFV scenario

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 JCAP 0605 (2006) 005 JHEP 0611 (2006) 050


ΦTP2Dirac neutrinos NLSP life times

m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

general signature two long lived particles + multi jets andor multi lepton

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

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


ΦTP2Majorana 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


ΦTP2The Setup GUT scale

Relevant SU(5) invariant parts of the superpotentials at MGUT

Type-I

WRHN = YIN Nc 5M middot 5H +

1

2MR NcNc

Type-II

W15H =1radic2Y

IIN 5M middot 15 middot 5M +

1radic2λ15H middot 15 middot 5H +

1radic2λ25H middot 15 middot 5H

+M1515 middot 15

Type-III

W24H = 5H24MY IIIN 5M +

1

224MM2424M


ΦTP2The SU(5)-broken phase

Under SU(3) times SUL(2) times U(1)Y

The 5 10 and 5H contain

5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)

The 15 decomposes as

15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)


24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5

6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I

Postulate very heavy right-handed neutrinos yielding the following superpotential below

MGUT

WI =WMSSM +Wν

Wν = bNcYνbL middot bHu +

1

2bNcMR

bNc

Neutrino mass matrix

mν = minusv2u

2Y T

ν Mminus1R Yν

Inverting the seesaw equation gives Yν a la Casas amp Ibarra

Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger

mν MR diagonal matrices containing the corresponding eigenvalues

U neutrino mixing matrix

R complex orthogonal matrix


ΦTP2Seesaw II

Below MGUT the superpotential reads

WII = WMSSM +1radic2(YT

bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2

fields with index 1 (2) originate from the 15-plet (15-plet)

The effective mass matrix is

mν = minusv2u

2

λ2

MTYT

Note that

YT = UT middot YT middot U


ΦTP2Seesaw III

In the SU(5) broken phase the superpotential becomes

WIII = WMSSM + bHu(cWMYN minusr

3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW

last step valid if MB ≃ MW and YB ≃ YW

rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45


ΦTP2Effect of heavy particles on MSSM parameters

MSSM (b1 b2 b3) = (335 1minus3)

per 15-plet ∆bi = 72 rArr type II model ∆bi = 7

per 24-plet ∆bi = 5 rArr type III model ∆bi = 15



MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016

Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0

Full lines seesaw type I dashed lines type II dash-dotted lines type III

degenerate spectrum of the seesaw particles

J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003


ΦTP2Effect on heavy particles on MSSM spectrum IM

h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016

m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0





ΦTP2rdquoInvariantsrdquo

1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155

(solution of 1-loop RGEs)

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

J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003


ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models

1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3

light blue lines m0 = 500 GeV and M12 = 1 TeV

red lines m0 = M12 = 1 TeV

black line analytical approximation

full (dashed) lines 2-loop (1-loop) results


ΦTP2LFV in the slepton sector approximate formulas I

one-step integration of the RGEs assuming mSUGRA boundary

∆M2Lij ≃ minus ak

8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij

∆Alij ≃ minus ak3

16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0

Lij = ln(MGUT Mi)δij

for i 6= j with Ye diagonal

aI = 1 aII = 6 and aIII =9

5


ΦTP2LFV in the slepton sector approximate formulas II

(∆M2L)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 |2

em8tan2 β

Br(τ2 rarr e+ χ01)

Br(τ2 rarr micro+ χ01)

≃ldquo (∆M2

L)13

(∆M2L)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


ΦTP2Seesaw 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


ΦTP2Seesaw 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 νR

SPS1arsquo (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


ΦTP2Seesaw 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(


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(


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)



ΦTP2Seesaw I

Texture models hierarchical νR

real textures rdquocomplexificationrdquo of one texture


F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004


ΦTP2Seesaw II with a pair of 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




ΦTP2Seesaw III in comparisonB

r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π

degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV

J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003


ΦTP2Masses 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 008

rArr mass determination within 2-5

For background suppression

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


ΦTP2Seesaw 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 rarr P

ij lilj rarr microplusmnτ∓χ01)

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

JN Esteves et al JHEP 0905 003 (2009)


ΦTP2Low scale Seesaw

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

However dim-5 operator might be forbidden due to symmetries

eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37

solves at the same time the micro-problem


C + HuQYuUC minus λHdHuS +

κ

3S3

flavour symmetries + extra SU(2) doublets + singletts

or linear or inverse seesaw rArr see talk by M Krauss

dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235


ΦTP2NMSSM phenomenology in a nut-shell

Higgs sector h0i (i=123) a0

i (i=12)

non-standard Higgs decayslowast

h0i rarr a0

1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus

Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg

Γ(τ1 rarr χ01τ) prop λ2

r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs

lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041

dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723

S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140


ΦTP2arbitrary 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


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)


ΦTP2Flavour 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


ΦTP2Phases special cancelation regions

1024 de 108 BR(τ rarr eγ)

Variations around SPS3

see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005


ΦTP2Squarks variations around SPS1arsquo

δDRR23

δLL23

δDLR32

δDLR23

27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1

δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087


ΦTP2Edge variables in the squark sector

x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]

100 dBr(g rarr ujukχ0

1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt

mg = 800 GeV mujgtsim 560 GeV

δLLij = 006 δRRuij = 006

σ(pprarr gg) ≃ 2 pb

mg = 1300 GeV mu1= 470 GeV muj

gtsim 1 TeV


σ(pprarr gg) ≃ 40 fb

A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380


ΦTP2Conclusions

MSSM extensions in view of neutrino physics

SUSY flavour problem orginates in the SM flavour problem

Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM

t1 rarr lbνχ01)

Seesaw models

most promising τ2 decays

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

in case of seesaw II or III different mass ratios

NMSSM

potenitally larger LFV signals due to lower seesaw scale

modified Higgsneutralino sector

modified phenomenology h01 rarr a1a1 andor displace vertices

Squarks similar techniques for flavour violating signals as for sleptons but technically

more challanging

general MSSM larger effects require special parameter combinations

rArr hint of hidden symmetries


ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T


MGUT = 2 times 1016 GeV

black lines seesaw type-II

green lines seesaw type-III with three 24-plets with degenerate mass spectrum



ΦTP2Seesaw 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 Phys Rev D 78 (2008) 116013


small hspace 2cm Overview

small hspace 2cm Supersymmetry MSSM

small hspace 2cm Flavour Generalities



small hspace 2cm Lepton flavour violation experimental data

small hspace 2cm Dirac neutrinos MFV scenario

small hspace 2cm Dirac neutrinos NLSP life times

small hspace 2cm Majorana neutrinos Seesaw mechanism$^$

small hspace 2cm The Setup GUT scale

small hspace 2cm The $SU(5)$-broken phase

small hspace 2cm Seesaw I

small hspace 2cm Seesaw II

small hspace 2cm Seesaw III

small hspace 2cm Effect of heavy particles on MSSM parameters


small hspace 2cm Effect on heavy particles on MSSM spectrum I

small hspace 2cm Invariants

small hspace 2cm Invariants limits for seesaw type-III models

small hspace 2cm LFV in the slepton sector approximate formulas I

small hspace 2cm LFV in the slepton sector approximate formulas II





small hspace 2cm Seesaw II with a pair of $15$-plets

small hspace 2cm Seesaw III in comparison

small hspace 2cm Masses at LHC

small hspace 2cm Seesaw I + II signal at LHC

small hspace 2cm small Low scale Seesaw

small hspace 2cm small NMSSM phenomenology in a nut-shell

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 Phases special cancelation regions

small hspace 2cm Squarks variations around SPS1a

small hspace 2cm Edge variables in the squark sector

small hspace 2cm small Conclusions

small hspace 2cm Landau Poles

small hspace 2cm small Seesaw special kinematics$^dagger $

ΦTP2Overview

Flavour Generalities

LFV signals in models with

Dirac neutrinos

Majorana neutrinos

General MSSM + extensions

Squark flavour at LHC

Conclusions

More in F del Aguila et al EPJC 57 (2008) 183 [arXiv08011800]



Standard Model MSSM

mattere d d d

νe u u uhArr

e d d d

νe u u u



u hplusmn


(γ z0 h0d h

0u) rarr χ0




















+X

f=LeQdu

flowastM2ff +M2

Hd|Hu|2 +M2







Tf = A0fYf M2f


f Yf




1 s)








WY = Hψiψcj

h

θi3θ

j3 + θi

23θj23

ldquo

θ3θ3rdquo


ldquo

θ23θ3rdquo

+ i

Yd prop

0

B

B

0 xd12 ε

3 xd13 ε

3

xd12 ε

3 ε2 xd23 ε

2

xd13 ε

3 xd23 ε

2 1

1

C

C

A

Yu prop

0

B

B

0 xu12 ε

3 xu13 ε

3

xu12 ε

3 ε2 xu23 ε

2

xu13 ε

3 xu23 ε

2 1

1

C

C

A

(M2f)ji = m2

0

bdquo

δji

+1

M2f

raquo


dagger3

j+ θdagger23i

θj23 + θ23iθ

dagger23

j+ θdagger123i

θj123 + θ123iθ

dagger123

jndash

+1

M4f

(ǫiklθdagger3

kθdagger23


laquo











| tan θatm|2 ≃ 1


|Ue3|2 ltsim 005












requires Yν ≪ Ye





≃ m0 in mSUGRA

mνR ≃ 0 in GMSB




m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)







Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































Standard Model MSSM

mattere d d d

νe u u uhArr

e d d d

νe u u u



u hplusmn


(γ z0 h0d h

0u) rarr χ0




















+X

f=LeQdu

flowastM2ff +M2

Hd|Hu|2 +M2







Tf = A0fYf M2f


f Yf




1 s)








WY = Hψiψcj

h

θi3θ

j3 + θi

23θj23

ldquo

θ3θ3rdquo


ldquo

θ23θ3rdquo

+ i

Yd prop

0

B

B

0 xd12 ε

3 xd13 ε

3

xd12 ε

3 ε2 xd23 ε

2

xd13 ε

3 xd23 ε

2 1

1

C

C

A

Yu prop

0

B

B

0 xu12 ε

3 xu13 ε

3

xu12 ε

3 ε2 xu23 ε

2

xu13 ε

3 xu23 ε

2 1

1

C

C

A

(M2f)ji = m2

0

bdquo

δji

+1

M2f

raquo


dagger3

j+ θdagger23i

θj23 + θ23iθ

dagger23

j+ θdagger123i

θj123 + θ123iθ

dagger123

jndash

+1

M4f

(ǫiklθdagger3

kθdagger23


laquo











| tan θatm|2 ≃ 1


|Ue3|2 ltsim 005












requires Yν ≪ Ye





≃ m0 in mSUGRA

mνR ≃ 0 in GMSB




m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)







Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ




























































+X

f=LeQdu

flowastM2ff +M2

Hd|Hu|2 +M2







Tf = A0fYf M2f


f Yf




1 s)








WY = Hψiψcj

h

θi3θ

j3 + θi

23θj23

ldquo

θ3θ3rdquo


ldquo

θ23θ3rdquo

+ i

Yd prop

0

B

B

0 xd12 ε

3 xd13 ε

3

xd12 ε

3 ε2 xd23 ε

2

xd13 ε

3 xd23 ε

2 1

1

C

C

A

Yu prop

0

B

B

0 xu12 ε

3 xu13 ε

3

xu12 ε

3 ε2 xu23 ε

2

xu13 ε

3 xu23 ε

2 1

1

C

C

A

(M2f)ji = m2

0

bdquo

δji

+1

M2f

raquo


dagger3

j+ θdagger23i

θj23 + θ23iθ

dagger23

j+ θdagger123i

θj123 + θ123iθ

dagger123

jndash

+1

M4f

(ǫiklθdagger3

kθdagger23


laquo











| tan θatm|2 ≃ 1


|Ue3|2 ltsim 005












requires Yν ≪ Ye





≃ m0 in mSUGRA

mνR ≃ 0 in GMSB




m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)







Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ















































Tf = A0fYf M2f


f Yf




1 s)








WY = Hψiψcj

h

θi3θ

j3 + θi

23θj23

ldquo

θ3θ3rdquo


ldquo

θ23θ3rdquo

+ i

Yd prop

0

B

B

0 xd12 ε

3 xd13 ε

3

xd12 ε

3 ε2 xd23 ε

2

xd13 ε

3 xd23 ε

2 1

1

C

C

A

Yu prop

0

B

B

0 xu12 ε

3 xu13 ε

3

xu12 ε

3 ε2 xu23 ε

2

xu13 ε

3 xu23 ε

2 1

1

C

C

A

(M2f)ji = m2

0

bdquo

δji

+1

M2f

raquo


dagger3

j+ θdagger23i

θj23 + θ23iθ

dagger23

j+ θdagger123i

θj123 + θ123iθ

dagger123

jndash

+1

M4f

(ǫiklθdagger3

kθdagger23


laquo











| tan θatm|2 ≃ 1


|Ue3|2 ltsim 005












requires Yν ≪ Ye





≃ m0 in mSUGRA

mνR ≃ 0 in GMSB




m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)







Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ














































WY = Hψiψcj

h

θi3θ

j3 + θi

23θj23

ldquo

θ3θ3rdquo


ldquo

θ23θ3rdquo

+ i

Yd prop

0

B

B

0 xd12 ε

3 xd13 ε

3

xd12 ε

3 ε2 xd23 ε

2

xd13 ε

3 xd23 ε

2 1

1

C

C

A

Yu prop

0

B

B

0 xu12 ε

3 xu13 ε

3

xu12 ε

3 ε2 xu23 ε

2

xu13 ε

3 xu23 ε

2 1

1

C

C

A

(M2f)ji = m2

0

bdquo

δji

+1

M2f

raquo


dagger3

j+ θdagger23i

θj23 + θ23iθ

dagger23

j+ θdagger123i

θj123 + θ123iθ

dagger123

jndash

+1

M4f

(ǫiklθdagger3

kθdagger23


laquo











| tan θatm|2 ≃ 1


|Ue3|2 ltsim 005












requires Yν ≪ Ye





≃ m0 in mSUGRA

mνR ≃ 0 in GMSB




m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)







Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

















































| tan θatm|2 ≃ 1


|Ue3|2 ltsim 005












requires Yν ≪ Ye





≃ m0 in mSUGRA

mνR ≃ 0 in GMSB




m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)







Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ














































requires Yν ≪ Ye





≃ m0 in mSUGRA

mνR ≃ 0 in GMSB




m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)







Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































m (GeV)12

βtan = 10

tan =30β

Lif

e t

ime (

seco

nd

s)

10

800 1000 1200 1400

100

600

1

τ1

m0 = 100 GeV

A0 = 100 GeV

sgn(micro) = 1

m (GeV)ν~1

t~

1

t~

1

m =300 GeV

t~

1

m =250 GeV

m =350 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)

m (GeV)t~1

ν~

1

ν~

1

m =200 GeV

ν~

1

m =100 GeV

m =300 GeV

100

10000

1e+06

1e+08

1e+10

1e+12

1e+14

100 150 200 250 300 350

Lif

eminus

tim

e (

secon

ds)







Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ













































Λ(HL)(HL)










Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ













































Type-I


1

2MR NcNc

Type-II

W15H =1radic2Y




+M1515 middot 15

Type-III


1

224MM2424M







15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ
















































15 =bS(6 1minus2

3) + bT (1 3 1) + bZ(3 2

1

6)



6)

+ bXM (3 25

6) + bGM (8 1 0)


ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Seesaw I


MGUT

WI =WMSSM +Wν


1

2bNcMR

bNc


mν = minusv2u

2Y T

ν Mminus1R Yν


Yν =radic

2i

vu

q

MR middotR middotp

mν middot Udagger





ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Seesaw II



bL bT1bL+ YS

bDcbS1

bDc) + YZbDc

bZ1bL

+1radic2(λ1

bHdbT1

bHd + λ2bHu

bT2bHu) +MT

bT1bT2 +MZ

bZ1bZ2 +MS

bS1bS2



mν = minusv2u

2

λ2

MTYT

Note that



ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Seesaw III



3

10bBMYB)bL+ bHu

bXMYXbDc

+1

2bBMMB

bBM +1

2bGMMG

bGM +1

2cWMMW

cWM + bXMMXbXM

giving

mν = minusv2u

2

bdquo

3

10Y T

B Mminus1B YB +

1

2Y T

WMminus1W YW

laquo

≃ minusv2u4

10Y T

WMminus1W YW





MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































MSSM (b1 b2 b3) = (335 1minus3)





MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































MSSM (b1 b2 b3) = (335 1minus3)



M1M

2M

3 (

Ge

V)

MSeesaw (GeV)

M1

M2

M3

0

500

1000

1500

2000

2500

1012

1013

1014

1015

1016

|MQ

||M

L||M

E| (G

eV

)MSeesaw (GeV)

|ME|

|ML|

|MQ|

750

1000

1250

1500

1750

2000

2250

1012

1013

1014

1015

1016







h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































h

mχ

0 1

mχ

+ 1 (

Ge

V)

MSeesaw (GeV)

Mh

mχ01

mχ+1

0

200

400

600

800

1000

1012

1013

1014

1015

1016

MA

mχ

0 2

mχ

+ 2 (

Ge

V)

MSeesaw (GeV)

MA

mχ02

mχ+2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1012

1013

1014

1015

1016







1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































1012

1013

1014

1015

1016

15

2

3

1 10(m

2 Qminus

m2 E)

M2 1

1 10(m

2 Dminus

m2 L)

M2 1

(m2 Lminus

m2 E)

M2 1

(m2 Qminus

m2 U)

M2 1

M15 = M24 [GeV]

Seesaw I (≃ MSSM)

m2

Qminusm2

E

M2

1

≃ 20m2

Dminusm2

L

M2

1

≃ 18

m2

Lminusm2

E

M2

1

≃ 16m2

Qminusm2

U

M2

1

≃ 155






1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































1013

1014

1015

1016

1

15

2

25

3

35

4

(m2 Lminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

1013

1014

1015

1016

1

2

3

4

5

1 10(m

2 Qminus

m2 E)

M2 1

M24 [GeV]

SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV

blue lines SPS3









8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ














































8π2

`

3m20 + A2

0

acute

ldquo

Y kdaggerN LY k

N

rdquo

ij


16π2A0

ldquo

YeYkdaggerN LY k

N

rdquo

ij

∆M2Eij ≃ 0




5





minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ














































minusr

lj rarr liχ0s

χ0s rarr li lk



|(δm2L)ij |2

em8tan2 β



≃ldquo (∆M2

L)13

(∆M2L)23

rdquo2


Br(li rarr 3lj)


3π

ldquo

log(m2

li

m2lj

) minus 11

4

rdquo


ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Seesaw I


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



ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Seesaw 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



=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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm

degenerate νR




ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Seesaw 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(


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(


Excluded by

)γ e rarr microBr(

=0 eV1

νm


(M1 = M3 = 1010 GeV)




ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Seesaw I







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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































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





r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































r(micro

rarr e

γ)

MSeesaw (GeV)

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-18

10-16

10-14

10-12

10-10

10-8

1010

1011

1012

1013

1014

1015

1016

III

II

I Br(

micro rarr

e γ

)

s213

m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-4

10-3

10-2

10-1

III δDirac = 0

III δDirac = π

I δDirac = 0

I δDirac = π




ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Masses at LHC


500

1000

1500

0 20 40 60 80 100

m(ll) (GeV)

Eve

nts

1 G

eV1

00 fb

-1

G Polesello








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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































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


2 rarr P








eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ














































eg Z3 + NMSSMdagger

(LHu)2S

M26

(LHu)2S2

M37




κ

3S3







i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ













































i (i=12)


h0i rarr a0




r

m2τ1

minusm2χ0

1

minusm2τ

Note micro = λvs







01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ













































01


00001

0001

001

01


00001

0001

001

01

BR(χ02 rarr χ0

1 eplusmn τ∓)

BR(τ rarr eγ)

BR(χ02 rarr χ0


BR(τ rarr microγ)




0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































0 20 40 60 800

002

004

006

008

100Γtot


∓j χ

01)

dm(lplusmni l∓j )

eplusmnτ∓

microplusmnτ∓

eplusmnmicro∓


0

001

002

003

004

005

100Γtot


1)dm(l+lminus)


micro+microminus

e+eminus

m(l+lminus) [GeV]









δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ

















































δDRR23

δLL23

δDLR32

δDLR23


δLLij =(M2

q LL)ij

m2

q

δqRRij =(M2

q RR)ij

m2

q

δqLRij =(M2

q LR)ij

m2

q

(i 6= j)

T Hurth WP JHEP 0908 (2009) 087



x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ












































x

x

200 300 400 500 600

0

01

02

Mujuk[GeV]


1)dMujuk

[GeVminus1]

tt

ct

x

x

100 300 500 700 900 1100

0

001

002

003

004

005

006

007

Mujuk[GeV]


1)dMujuk

[GeVminus1]

ct

tt





gtsim 1 TeV





ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Conclusions




t1 rarr lbνχ01)

Seesaw models




NMSSM





more challanging




ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































ΦTP2Landau Poles

8 10 12 14 16

08

10

12

14

16

18

20

log(MSeesawGeV)

g GU

T









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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ













































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


LL ατ

lαLτLτR ≃ l1

1Me 2

Rτ minusMe 2Lτ











































Testing the ﬂavour sector of SUSY models @ LHCific.uv.es/~flasy2011/Porod.pdf · ΦTP2 Testing...

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Transcript of Testing the ﬂavour sector of SUSY models @ LHCific.uv.es/~flasy2011/Porod.pdf · ΦTP2 Testing...