Sup ersymmetry , da rk matter and the LHC GGI Conference ... · Th e se regions c ou ld p ossibly...

Supersymmetry, dark matter and the LHC

GGI Conference: The Dark Matter connection:Theory & Experiment

May 20, 2010[PN]

Outline

Connection of DM to LHC with LSP= !0

Other LHC and dark matter related talks: By Dutta, Kraml, Polesello, Su

Gaugino-Higgsino content of the neutralino and LHCsignatures

Multicomponent dark matter.

SUSY breaking mechanisms

Gravity mediation (1982)

Chamseddine, Arnowitt, PN (1982)Barbieri, Ferrara, Savoy (1982)

Hall, Lykken, Weinberg (1983)

Gauge mediation (1994)Dine, Nelson, Shirman, · · ·

Anomaly mediation (1999)Randall, Sundrum, · · ·

Mixed gravity, anomaly, gauge mediation such as mirage,deflected mirage etc.

Connection of DM to LHC with LSP= !

Typically the satisfaction of the relic density constraints aresatisfied in four broad regions of the SUGRA parameter space.

Bulk regions

Pole regions

Coannihilation regionsWino, stau, stop, gluino · · · coannihilation

Hyperbolic Branch/Focus Point regionChan, Chattopadhyay, PN (1998), Feng, Matchev, Moroi (2000); Baer, Tata

et.al. (2003)

These regions could possibly lead to distinguishable signatures atthe LHC. We explore this possibility specifically for the staucoannihilation region and for for the HB/FP region.

Some Prominent SUSY signatures

In pp collisions at the LHC one will produce gg, gq, qq. The g, qthat are produced will decay producing many signatures

g ! qq, qq!0i , qq!!±

j

q ! qg, q!0i , q!!±

j

!0i , !±

j will decay producing in general multi-leptons and the LSPneutralino will carry large missing energy.

Typical SUSY signals: Jets + leptons+ EmissT .

1 One lepton+jets+EmissT .

2 Opposite sign (OS) dileptons +jets+EmissT .

3 Same sign (SS) dileptons +jets+EmissT .

4 3leptons + jets+EmissT .

5 Tagged b jets and tau jets with and without missing ET .

At the LHC:

Post Trigger Level Cuts

1 In an event, we only select photons, electrons, and muons that have transversemomentum Pp

T > 10 GeV and |!p| < 2.4, p = (", e, µ).

2 Taus which satisfy P!T > 10 GeV and |!! | < 2.0 are selected.

3 For hadronic jets, only those satisfying P jT > 60 GeV and |!j | < 3 are selected.

4 We require a large amount of missing transverse momentum, PmissT > 200 GeV.

5 There are at least two jets that satisfy the PT and ! cuts.

The default post trigger level cuts are standard and are designed to suppress the

Standard Model background, and highlight the SUSY events over a broad class of

models.

Stau Coannihilation and Hyperbolic/Focus point region andDecay Chains

On HB/FP the squarks are generally heavy and thus thegluinos are produced more profusely in this region thansquarks. The gluinos have longer decay chains and thusmissing PT associated with this region is smaller.

g ! qq!0i , qq!!±

j

Also a larger multiplicity of quarks, specfically b quarks,produced in the HB/FP region.

On the Stau co-annihilation branch squarks are light and theyare more profusely produced than gluinos. The squarks haveshorter decay chains, and thus missing PT associated withthis region is larger.

q ! q!0i , q!!±

j

What can we learn from the LHC regarding theorigin of Dark matter?

Feldman, Liu, PN: Phys. Rev. D 78, 083523 (2008), arXiv:0808.1595 [hep-ph]

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and HB. !P missT " acts as an indicator of Stau-Co and HB regions.


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SM(nb) vs nb for the Stau-Co and HB regions where N(nb)(SM(nb)) is the number of SUSY (SM) events that contain n b-tagged jets. A sharpdiscrimination between the Stau-Co and the HB by b-tagging is observed. Thenumber n!

jet is fixed at 2. Here meg ! 1.1 TeV.

Direct detection and NLSPFeldman, Liu, PN, arXiv:0711.4591 [hep-ph]; PLB 662,190(2008)

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The Wall: Chattopadhyay, Corsetti, PN (2003); Baer, Balazs, Belyaev, O,Farril(2003); Roszkowski, Ruiz de Austri, Trotta (2007).

Chargino Wall: Feldman, Liu, PN (2008)

Chargino -NLSP

Higgs -NLSP

Stau -NLSP

Stop -NLSP

Combined LHC and dark matter dataFeldman, Liu, PN: Phys. Rev. D 78, 083523 (2008), arXiv:0808.1595 [hep-ph]

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Feldman, Liu, PN: JHEP 0804:054,2008.40 counting signatures for each parameter point.

40 Signatures Description 40 Signatures Description(1) ! 0L 0 Lepton (22)!0T 0 !(2)!1L 1 Lepton (23)!1T (23)!1 !(3)!2L 2 Lepton (24)!2T (24)!2 !(4)!3L 3 Lepton (25)!3T (25)!3 !(5)!4L 4 Lepton and more (26)!4T 4 ! and more

(6)!0L1b 0 Lepton + 1 b-jet (27)!0T1b 0 ! + 1 b-jet(7)!1L1b 1 Lepton + 1 b-jet (28)!1T1b 1 ! + 1 b-jet(8)!2L1b 2 Lepton + 1 b-jet (29)!2T1b 2 ! + 1 b-jet(9)!0L2b 0 Lepton + 2 b-jet (30)!0T2b 0 ! + 2 b-jet(10)!1L2b 1 Lepton + 2 b-jet (31)!1T2b 1 ! + 2 b-jet(11)!2L2b 2 Lepton + 2 b-jet (32)!2T2b 2 ! + 2 b-jet(12)!ep e+ in 1L (33)!em e− in 1L(13)!mp µ+ in 1L (34)!mm µ− in 1L(14)!tp !+ in 1T (35)!tm !− in 1T(15)!OS Opposite Sign Di-Lepton (36)!0b 0 b-jet(16)!SS Same Sign Di-Lepton (37)!1b 1 b-jet

(17)!OSSF Opp Sign Same Flavor Di-Lepton (38)!2b 2 b-jet(18)!SSSF Same Sign Same Flavor Di-Lepton (39)!3b 3 b-jet(19)!OST Opposite Sign Di-! (40)!4b 4 b-jet and more(20)!SST Same Sign Di-!((21)!TL 1 ! plus 1 Lepton

Feldman, Liu, PN: JHEP 0804:054,2008.

Kinematical signatures1. P miss

T2. PT peak value

3. Effective Mass = P missT +

!j P j

T

4.Invariant Mass of all jets5.. Invariant Mass of e+e! pair6. Invariant Mass of µ+µ! pair7. Invariant Mass of !+!! pair

A list of the kinematical signatures analyzed for each point in the SUGRA modelparameter space. L = e, µ signifies only electrons and muons.

OSSF Di-leptonFeldman, Liu, PN: JHEP 0804:054,2008.

0 50 100 150 2000

20

40

60

80

100

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Feldman, Liu, PN: arXiv:0808.1595 [hep-ph].

Hyperbolic Branch

Stau Coannihilation

Signatures and backgrounds for mSPsFeldman, Liu, PN: JHEP 0804:054,2008.

0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0L/N

1L/N

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SM

mSP1

mSP2

mSP3

mSP4

mSP5

mSP6

mSP7

mSP8

mSP11

mSP12

mSP13

mSP14

mSP16

SM

0.3 0.5 0.7 0.9

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0.2

0.3

0.4

0b/N

1b/N

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SUP

CP

HP

SM

mSP1

mSP2

mSP3

mSP4

mSP5

mSP6

mSP7

mSP8

mSP11

mSP12

mSP13

mSP14

mSP16

SM

0.1 0.2 0.3 0.40

0.1

0.2

1b/N

2b/N

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SUP

HP

CP

SM

mSP1

mSP2

mSP3

mSP4

mSP5

mSP6

mSP7

mSP8

mSP11

mSP12

mSP13

mSP14

mSP16

SM

0.1 0.3 0.5 0.7 0.9200

400

600

800

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SM

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HB

Stau Co

HB

Stau Co

Stau Co

Stau Co

HB

HB

SUSY: like-sign dileptons

40

Similar sensitivity seen in like-sign dilepton analysis

1 fb-1

0.1 fb-1

Very soon the LHC will surpass

the Tevatron in the search for SUSY

From Conway’s talk at Pheno 2010

(GeV)0

m500 1000 1500 2000 2500

(G

eV)

1/2

m

100

200

300

400

500

600

500 GeV

600 GeV

800 GeV

1 TeV

1.2 TeV

111 GeV

114 GeV

LHC7 - All Channels

LS

P!"

LEP excluded

(G

eV)

g~m

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

(GeV)0

m500 1000 1500 2000 2500

(G

eV)

1/2

m

100

200

300

400

500

600

-12 fb-11 fb

-10.33 fb-10.1 fb

g~m

hm

= 172.6 GeVt

> 0, m! = 45, # = 0, tan0A

Baer, Barger, Lessa, Tata arXiv:1004.3594 [hep-ph] mSUGRA

Gaugino -Higgsino Content of the Neutralino and LHCSignatures

The signatures at the LHC will be dependent on the gaugino vshiggsino content of the neutralino. Thus the neutralino wavefunction can be expanded as

χ = αλB + βλW + γh1 + δh2

For illustration we consider two models.

Model 1: A pure Wino model (PWM) where the neutralino isalmost 100% wino. Models of this type arise in anomalymediated breaking. One characteristic of such models is thatthe lighter chargino and the neutralino are essentiallydegenerate.Model 2: As second example we consider a mixedHiggino-Wino model (HWM) which has a substantial higgsinocomponent.

These models lead to distinguishable signatures at the LHC.

Pure Wino and Higgsino-Wino model examples

Pure Wino Model (PWM)

(m0, m1/2, A0, tan !) = (1000, 850, 0, 10),

("1,2,3, signµ) = (0, !.7, 0, +).

#0 = .009$B!0.996$W + .081h1 ! .023h2

Higgsino-wino model (HWM)

(m0, m1/2, A0, tan !) = (800, 558, 0, 5),

("1,2,3, signµ) = (!0.09, !.5, !.51, +).

#0 = .726$B!0.616$W + .26h1 ! .16h2

Sparticle masses in mixed Higgsino-Wino and Pure Winomodels

Feldman, Liu, PN, Nelson, PRD D 80, 075001 (2009)

Mass HWM PWM Mass HWM PWMme!0

1198.9 195.2 mt1

648.5 1516

me!02

217.0 357.0 mt2866.8 1749

me!03

429.9 1025 mb1841.4 1729

me!04

451.3 1029 mb2970.2 1902

me!±1

208.8 195.5 m"1 817.7 1011

me!±2

448.6 1036 m"2 822.8 1041

mg 707.1 1929

Relevant sparticle mass spectra for the HWM and PWM as calculated from the

high-scale boundary conditions. All masses are in GeV.

E!ective mass distribution


Effective Mass (GeV)0 500 1000 1500 2000 2500 3000

-1

Even

ts/3

0 G

eV

/5 f

b

0

50

100

150

200

250

300 Data Set

-1Background: 5 fb

-1Model HWM: 5 fb

-1Model PWM: 100 fb

DistributioneffM

Meff is defined as the scalar sum of the transverse momenta of four hardest jets

PT ! (200,150,50,50) GeV in the event plus missing energy (EmissT ! 200

GeV).The plot is of events for the Higgsino-Wino model (for 5fb!1 yellow) and for

Pure Wino model (100 fb!1 blue).

The invariant mass distribution of two b-jets events inHiggsino-Wino model.


0 200 400 600 800 10000

10

20

30

40

50

60

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5,'+()678$2'3698$:%!9

LHC @ 14 TeV

0 200 400 600 800 10000

50

100

150

200

250

300

350SUSY

SM

In HWM gluino is light and will be produced in significant amounts at the LHC. Now

g ! bb + !0, and so mg " (Mbbinv)kink + m!0 . Embedded window shows mass

distributions for SUSY and SM with a 200 GeV EmissT cut. To suppress SM

background take (i) a 400 GeV EmissT cut, (ii) two more jets besides 2 b-tagged jets.

Monojet SignaturesFeldman, Liu, PN, Nelson, PRD 80, 075001 (2009)

HWM PWM

Object Cuts (GeV) Events S/√

B Events S/√

B

pjetT ≥ 150, #ET ≥ 150 1994 2.13 3442 3.68

pjetT ≥ 200, #ET ≥ 150 1302 2.52 1983 3.84

pjetT ≥ 150, #ET ≥ 200 1334 2.53 2147 4.08

pjetT ≥ 200, #ET ≥ 200 1241 2.58 1904 3.95

pjetT ≥ 150, #ET ≥ 300 659 3.57 771 4.17

Table: Monojet signature for the HWM and the PWM: Event counts are after100 fb!1 of integrated luminosity for various choices of cuts on total !ET and jet pT .All signatures involve a lepton veto and require no other jets in the event with

pjetT " 20 GeV. No transverse sphericity cut was applied in any of these signatures.

Multicomponent dark matterFeldman, Liu, PN, Peim, arXiv:1004.0649

PRD to appear

Dark matter may be constituted of more than one component.

!CDM h2 =X

i

!CDM ih2.

U(1)X × U(1)C extension where U(1)X is hidden sector and U(1)C is theanomaly free combination Le − Lµ .

L = LMSSM + LU (1)2 + "L,

where LU (1)2 is the kinetic energy for the X and C multiplets and for LSt weassume the following form

"L =

Zd2!d2! [(M1C + M!

2X + S + S)2 + (M!1C + M2X + S! + S!)2].

A Dirac fermion is placed in the hidden sector. The new particles in this model consistof

spin 0 : ", "!, #, #!

spin1

2: $, %0

5, %06, %0

7, %08

spin 1 : Z!, Z!!.

Various other works on multicomponent DMJE Kim

Cirelli, Cline---

!! (Q

Y,Q

X)

U(1)X SU(3)

C X SU(2)

L X U(1)

Y

Connector

Sector

Visible

Sector

MSSM (B","

B, D

B) (C

","

C, D

C)

Stueckelberg

FI D Terms Hidden

Sector

U(1)n

Axions

Mixing between U_X(hidden) and U_Y (hypercharge) as a probe of the hidden sector was introduced in Kors, PN, Phys.Lett.B586:366-372,2004.

Hidden Sector and Leptophilic Couplings

The basic interaction of Xµ and of Cµ with matter is given by

Lint = gXQX!"µ!Xµ +∑

f

gCQfCf"µfCµ

where f runs over e and µ families and where QeC = !Qµ

C. Inthe mass diagonal basis the interaction assumes the form

Lint = (gXQX!"µ! cos #X !∑

f

gCQfCf"µf sin #X)Z!

µ

+(gXQX!"µ! sin #X +∑

f

gCQfCf"µf cos #X)Z!!

µ.

These interactions lead to the annihilation of !! into e+e" andµ+µ" via the Z!, Z!! poles for which we assume Breit-Wignerforms.

Z′ and Z′′ resonances

The partial Z′, Z′′ decay widths

Γ(Z′ → ff) = (gC QfC sin !X )2

MZ !

12",

Γ(Z′′ → ff) = (gC QfC cos !X )2

MZ !!

12",

Γ(Z′ → ##) = (gC QfC cos !X )2

MZ !

12"(1 +

2M2ψ

M2Z !

)(1 −4M2

ψ

M2Z !

)1/2Θ(MZ ! − 2Mψ ) (1)

and similarly for the partial decay width of the Z′′ into ## with MZ ! → MZ !! andcos !X → sin !X .

For small mixing angle !X Z′ decay width into ff is much smaller than theZ′′ decay width into ff.

If Mψ $ MZ !/2, the Z′ decay width into ## will be small due tokinematical suppression while the Z′′ decay width into ## will be small due tomixing angle.

The above results in Z′ to be a narrow resonance.

Constraints from gµ ! 2

Their exchange gives

∆(gµ ! 2) =g2

Cm2µ

24π2

[sin2 θX

M2Z!

+cos2 θX

M2Z!!

].

The current error is

∆(gµ ! 2) = 1.2 " 10!9

in the determination of gµ ! 2.Assuming θX is small, one finds the following constraint on αC,

αC ! 0.001(

MZ!!

300 GeV

)2

,

where αC = g2C/4π. Precision electroweak fits are una!ected.

Dark matter possibilities in the U(1)X ! U(1)C extension.

Two component dark matter: Dirac (!), Majorana (").

Three component dark matter: Dirac (!), scalars (#, #!).

Four component dark matter:Dirac (!), Majorana (")and scalars (#, #!, ).

Two component dark matter: ! and "

! + ! " Z, Z!, $ " SM + SM!,

" + " " (s : Z!, Z, h, H, A, %), (t/u : fa, "i, "±k )

" SM + SM! + plus coannihilations

Boltzmann equations for the two component model

dn!

dt= !3Hn! !

1

2"σv#!! (n2

! ! n2!,eq), (3)

dn"

dt= !3Hn" ! "σv#""(n2

" ! n2",eq) +

1

2"σv#!!!""(n2

! ! n2!,eq).

Here "σv#!! refers to ψψ $ ff, χχ, and "σv#"" stands for "σv#""!SM SM! .

Total relic density

(!h2)WMAP = (!!h2)0 + (!"h2)0 %C!

J!0

+C"

J"0

,

C" %1.07 & 109 GeV"1

pg#(χ)Mpl

, C! % 2 &1.07 & 109 GeV"1

pg#(ψ)Mpl

,

J"0 =

Z xχf

0"σv#"" dx , J!

0 =

Z xψf

0"σv#!! dx .

The local density of dark matter

ρ$,!/ρ$," ' (!!h2)0/(!"h2)0.

Multi-component Dark Matter

Feldman, Liu, PN, Peim arXiv:1004.0649000

Positron flux p flux

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&$'&&'()*$+(,*-./(01$"23*%2

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! = (50%)(Ωh2)!+"

456('0,

!!((U(1)X !U(1)C : Bhaloe = 2, Ωh2

! = (60%)(Ωh2)!+"

E GeV

e/(e

+e)

788

787

789

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+F!H

+F!I

+F!J

+F!K

+F!.

+F!+

Two-component Dark Matter Model

Feldman, Liu, PN, Peim arXiv:1004.0649000

Photon flux !SI

!"!!!#$%!

!"&!'!"!(!'"!!!)$%(*+&(,(,-

0

o < l < 360

o

10o < |b| < 20

o

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<=*>!?#@"#A

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Neutralino Component Mass (GeV)

!S

I (

cm

2)

!

!

"# $# %# &## &'# &"# &$#&#

!"(

&#!"$

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0.6-!3&"!0

'

0.6-!6G7H

0.6-!6G:8

0.6-!=A8F;7

How large a spin independent cross section in neutralinoproton scattering?

Explore the cross sections under the following set of constraints

Radiative electroweak symmetry breaking constraint (REWSB)

Relic density constraint

Experimental constraints on sparticle masses, FCNCconstraints etc.

One finds that REWSB constraints by themselves allow !SI aslarge as 10−40 cm−2 or even larger. However, the cross sectionsare cut down under the relic density and other experimentalconstraints. Specifically it is di!cult to get !SI ! 10−40 cm−2

at m! = 10 GeV with all the experimental constraints imposed.

COGENT Feldman, Liu, PN arXiv: 1003.0437,

PRD to appear

LSP Neutralino Mass (GeV)

!S

I c

m2

!

!

" #$ #" %$ %" &$ &" '$ '" "$#$

!''

#$!'&

#$!'%

#$!'#

#$!'$

CoGeNT 2010DAMA/LIBRA Interp.

Compatible

REWSB ONLY:

NO MASS LIMITS, NO WMAP,

NO FLAVOR CONSTRAINTS

LSP Neutralino Mass (GeV) !

SI c

m2

!

!

" #$ #" %$ %" &$ &" '$ '" "$#$

!''

#$!'&

#$!'%

#$!'#

#$!'$

CoGeNT 2010DAMA/LIBRA Interp.

Compatible

REWSB AND SPARTICLE

MASS LIMITS IMPOSED.

SQUARE IN WMAP RANGE.

Difficult to get 10−40 cm2 at m! = 10 GeV with REWSB andexperimental constraints.

Also: Kuflick, Pierce, Zurek

Conclusions

The LHC data will be very helpful in establishing the earlyhistory of the universe, e.g., whether dark matter originatedvia stau co-annihilation or on the hyperbolic branch, or bysome other mechanism.

Dark matter experiments along with LHC data will helpdecipher the nature of dark matter including if it isconstituted of one or more than one components.

Extra Transparencies

Positron excess vs WMAP

The basic issue: one needs < σv >∼ 10!24cm3/s for positronexcess and < σv >∼ 10!26cm3/s for relic density. Di!erentpossibilities

Breit-Wigner pole enhancement of < σv > in the galaxyFeldman, Liu, PN; Ibe, Murayama, Yanagida

The Boost from Coannihilation (BCo) mechanism to enhancerelic densityFeldman, Liu, PN, Nelson

Sommerfeld enhancement

Non-thermal processes to enhance relic density.

!!"!#$%!&"!"!$#$!

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!123!!#!$$!4567

89!:!!;</=>

!?%!@!A!!!;BCDEF>

$ % G D H I J K L M

%$!GJ

%$!GI

Enhancement of annihilation cross section in the galaxy

Feldman, Liu, PN, PRD 79, 063509 (2009)

Sup ersymmetry , da rk matter and the LHC GGI Conference ... · Th e se regions c ou ld p ossibly...

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