Measurement of Dark Matter Relic Density Measurement of Dark Matter Relic Density in the mSUGRA Co-annihilation Region in the mSUGRA Co-annihilation Region

at the LHCat the LHC

Teruki KamonIn collaboration with

Richard Arnowitt, Bhaskar Dutta, Alfredo Gurrola, Abram Krislock, and David Toback

Texas A&M UniversityThe 16th International Conference on Supersymmetry and the Unification of Fundamental Interactions

(SUSY2008), Seoul, Korea, June 16 - 21, 2008June 17, 2008

Measurement of Dark Matter Relic Density at the LHC 1

SUSY DM ≟ CDM

Dark Matter (DM) Particle in SUSY Dark Matter (DM) Particle in SUSY & Cosmological Connection & Cosmological Connection

Probing the SUSY Dark MatterProbing the SUSY Dark Matter

SUSY Signal in Co-annihilation (CA) RegionSUSY Signal in Co-annihilation (CA) RegionDM Density (DM Density (hh22 ) at the LHC ) at the LHC

Arnowitt, Dutta, Gurrola, Kamon, Krislock, TobackArnowitt, Dutta, Gurrola, Kamon, Krislock, TobackPRL100 (2008) 231802 PRL100 (2008) 231802 or arXiv:0802.2968 (hep-ph) or arXiv:0802.2968 (hep-ph)

For earlier studies, see Arnowitt For earlier studies, see Arnowitt et alet al., PLB 649 (2007) 73; Arnowitt ., PLB 649 (2007) 73; Arnowitt et alet al,, PLB 639 (2006) 46,, PLB 639 (2006) 46Measurement of Dark Matter Relic Density at the

LHC 2Teruki Kamon

DM Particle in SUSYDM Particle in SUSYSU

SYSU

SY

CDM CDM == Neutralino ( ) Neutralino ( )01~

Ast

roph

ysic

sA

stro

phys

ics

Measurement of Dark Matter Relic Density at the LHC 3

WMAP 5: 23.3% ( 1.3%)

Teruki Kamon

4 parameters + 1 sign

Choosing Benchmark Model …Choosing Benchmark Model …

(WMAP3) 12900940

SM from deviation 3 ~:)2(1054)(1022

GeV 104 GeV; 114

2

44

01

1

.h.

g.sbB.

MM

~

~Higgs

du

Zdu

HHWMA

MmMm

MH/H

in of Sign :)sign(at coupingTrilinear :

at massscalar Common :at mass gaugino Common :

at :tan

(2)GUT0

GUT0

GUT1/2

4

An accidental near degeneracy occurs naturally for light stau in many models. The mSUGRAmSUGRA model is one of them and chosen as our benchmark scenario.

Key experimentalconstraints

Teruki Kamon

Measurement of Dark Matter Relic Density at the LHC

DM Allowed RegionsDM Allowed Regions4

tan= 40A0 = 0, > 0

12

3

4

mSUGRAmSUGRA

R. Arnowitt et al., Phys. Lett. B538 (2002) 121

5

M (

GeV

)

(GeV) 21 /m

M = 5-15 GeV

Smoking Gun of CA Region?Smoking Gun of CA Region?

Excluded by1)Rare B decay b s 2)No CDM candidate3)Magnetic moment of muon

123 Measurement of Dark Matter Relic Density at the

LHC

R. Arnowitt et al., Phys. Lett. B639 (2006) 46

Teruki Kamon

Proving Proving SUSY DM SUSY DM in Inclusive Jets+Ein Inclusive Jets+ETTmissmiss

Nojiri, Polesselo, Tovey,Nojiri, Polesselo, Tovey, JHEP 0603 (2006) 063JHEP 0603 (2006) 063

Arnowitt Arnowitt et al.et al., to appear , to appear in PRL (2008)in PRL (2008)

Measurement of Dark Matter Relic Density at the LHC 6

Dilepton mass “edge” in the 20 ee/ 1

0 decays for reconstruction of SUSY Masses

LM1( Low Mass Case 1) LM1( Low Mass Case 1)

%.~~B

qq~qq~g~M

M

R

q~

g~

211)(

559

611pb 55

02

02

?SUSY DM ≟ CDM

Teruki Kamon

In the CA region, the ee and channels are almost absent.

Dilepton Endpoint in CA Region

Program:(1) Establish the “CA region” signal (2) Determine SUSY masses/mSUGRA parameters (3) Measure h2 and compare with CDMh2

7

Num

ber

of C

ount

s / 1

GeV

ETvis(true) > 20, 20 GeV

ETvis(true) > 40, 20 GeV

ETvis(true) > 40, 40 GeV

GeV) 5.7(

011

02

M

~~~

(GeV) )( visibleM

%~~B

%~~B

%~~B

qq~qq~g~M,M

L

R

q~g~

0)(

100)(

0)(

748831

1

102

02

02

pT

> 20 GeV is essential!

Teruki Kamon

Measurement of Dark Matter Relic Density at the LHC

SUSY Anatomy in the CA SUSY Anatomy in the CA RegionRegion

8

Mj

&Mj

M

pT()

100%1~

Lu~

01χ~

02χ~

g~

97%

u

u

SUSY

Mas

ses

(CDM)

pT > 40 GeV

pT > 20 GeV

ET jet > 100 G

eV

[Key Assumption] = 50% , fake rate 1%

for pTvis > 20 GeV

Measurement of Dark Matter Relic Density at the LHC

Teruki Kamon

OSOSLS MLS M Distribution Distribution

Clean peak even for low M

(GeV) visM

maxpeak MM

02~

M

g~M

Independent of thegluino masses!

Uncertainty Bands with 10 fb-1

Teruki Kamon 9

Measurement of Dark Matter Relic Density at the LHC

OSLS Slope(pTsoft )

Uncertainty Bands with 10 fb-1

(GeV) g~M

10

Independent of the gluino masses!

Measurement of Dark Matter Relic Density at the LHC

)( ),( 01

01

02

21peak

~~~ M,MfslopeM,M,MfM Teruki Kamon

MMjj Distribution Distributionendpeak jj MM 2

~

2~

2~

2~

~02

01

02 11

M

M

M

MMM

qq

endj

1) M < Mendpoint; Jets with ET > 100 GeV; Mj masses for each jet

2) Choose the 2nd large value Peak value ~ True Value

11

Mj(GeV)

Measurement of Dark Matter Relic Density at the LHC

)( 01

02

3(2)peak

~~q~j M,M,MfML

)( ), ( 01

02

01

02 5

(2)peak24

(2)peak1 ~~q~j~~q~j M,M,M,MfMM,M,M,MfM

LL

Teruki Kamon

Excess in ETmiss + Jets

SUSY scale measurement at 10-20%.

MMeffeff Distribution DistributionHinchliffe and Paige, Phys. Rev. D 55 (1997) 5520

ETj1 > 100, ET

j2,3,4 > 50; No e’s, ’s with pT > 20 GeV Meff > 400 GeV; ET

miss > max [100, 0.2 Meff]

Meff

g~g~pp Meff ET

j1+ETj2+ET

j3+ETj4+ ET

miss [No b jets; b ~ 50%]

12

)q~,g~(fM L6peakeff Teruki

Kamon

m1/2 = 335 GeVMeff

peak = 1220 GeV

m1/2 = 351 GeVMeff

peak = 1274 GeV

m1/2 = 365 GeVMeff

peak = 1331 GeV

e.g.,

Measurement of Dark Matter Relic Density at the LHC

)(

)(

) (

)(

)(

)(

6peakeff

01

025

(2)peak2

01

024

(2)peak1

01

023

(2)peak

012

01

021

peak

L

Lj

Lj

Lj

q~,g~fM

~,~,M,q~fM

~,~,M,q~fM

~,~,q~fM

~,MfSlope

~,~,MfM

Invert the equations to determine the masses

We test a gaugino univesality at 15% level.

)91.5( 8.09.5/

)19.3( 2.01.3/0.26.10

;19141;15260

;21831 ;25748

01

02

01

02

~~

~~

~~

~~

theoryMM

theoryMMM

MM

MM

g

g

gqL

10 fb-1

6 equations 6 equations for for 5 SUSY 5 SUSY massesmasses

14119 GeV

(GeV) 01~

M

Determining SUSY Masses (10 Determining SUSY Masses (10 fbfb11))

13Teruki Kamon

Measurement of Dark Matter Relic Density at the LHC

[1] Established the CA region by detecting low energy ’s (pT

vis > 20 GeV)

[2] Determined SUSY masses using:M, Slope, Mj, Mj, Meff

e.g., Gaugino universality test at ~15% (10 fb-1)

[3] Measure the dark matter relic density by determining m0, m1/2, tan, and A0

DM Relic Density in mSUGRADM Relic Density in mSUGRA

14

)( 01

02

1peak

~~ M,M,MfM

),tan,,(? ),(

),tan,,(),(

002/14

02/13peakeff

002/12peak

02/11peak

AmmXmmXM

AmmXMmmXM j

),tan,( 02/102

~01

AmmZh

Teruki Kamon

Measurement of Dark Matter Relic Density at the LHC

Introducing Introducing MMeffeff((bb))

Meff(b)

ETj1=b+ET

j2+ETj3+ET

j4+ ETmiss [j1 = b jet]

ETj1 > 100 GeV, ET

j2,3,4 > 50 GeV [No e’s, ’s with pT > 20 GeV]Meff

(b) > 400 GeV ; ET

miss > max [100, 0.2 Meff]

MMeffeff((bb)) can be used to probe A0 and tan even

without measuring stop and sbottom masses

Meff(b)peak (GeV)

15

m1/2 = 335 GeVMeff

(b)peak = 933 GeVm1/2 = 351 GeVMeff

(b)peak = 1026 GeVm1/2 = 365 GeVMeff

(b)peak = 1122 GeV

Teruki Kamon

Measurement of Dark Matter Relic Density at the LHC

Determining mSUGRA ParametersDetermining mSUGRA ParametersSolved by inverting the following functions:

140tan160

43505210

0

2/1

0

A

mm

),tan,( 02/102

~01

AmmZh

1fb 10 L1fb 50

)fb 70( %1.4)fb 30( %2.6/

1

12~

2~ 0

101

hh

),tan,,(),(

),tan,,(),(

002/14peak )(

eff

02/13peakeff

002/12peak

02/11peak

AmmXMmmXM

AmmXMmmXM

b

j

10 fb-1

16Teruki Kamon

Measurement of Dark Matter Relic Density at the LHC

[1] Established the CA region by detecting low energy ’s (pT

vis > 20 GeV)

[2] Determined SUSY masses using:M, Slope, Mj, Mj, Meff

e.g., Gaugino universality test at ~15% (10 fb-1)

[3] Measured the dark matter relic density by determining m0, m1/2, tan, and A0 using Mj, Meff, M, and Meff

(b)

[4] Working on non-minimal case...

SummarySummary

)fb 30( %6/ 12~

2~ 0

101

hh

17

)( 01

02

1peak

~~ M,M,MfM

Teruki Kamon

Measurement of Dark Matter Relic Density at the LHC

Backups

MeffMeff

Meff(b)peak (GeV)

m1/2 = 335 GeVMeff

(b)peak = 933 GeV

m1/2 = 351 GeVMeff

(b)peak = 1026 GeV

m1/2 = 365 GeVMeff

(b)peak = 1122 GeV

m1/2 = 335 GeVMeff

peak = 1220 GeV

m1/2 = 351 GeVMeff

peak = 1274 GeV

m1/2 = 365 GeVMeff

peak = 1331 GeV

Meffpeak (GeV)

Meffpeak /M(u_R)=1.75

Meff(b)peak /M(t_1)=1.84

Meff(b)peak /M(3rd)=1.7

Mas

s of

Squ

arks

and

Sle

pton

s

Mass of GauginosNo CDM Candidate

Excluded(Magnetic Moment of Muon)Excluded

(Rare B D

ecay b s )

Excluded

(Higgs m

ass)

CDM allowed region

Magnetic Moment of Muon

Higgs Mass (Mh)

Branching Ratio b s

DM Allowed Regions DM Allowed Regions (Illustration)(Illustration)

Co-annihilation Region

(GeV) )( M

Dilepton Endpoint DM content Measurements of the SUSY masses

[e.g., M.M. Nojiri, G. Polesselo, D.R. Tovey, JHEP 0603 (2006) 063]

Key: Dilepton “edge” in the 20 decay in dilepton (ee, , )

channels for reconstruction of decay chain.

[post-WMAP benchmark point B’] = 55 pb m1/2= 180, m0= 850

%~~B

%~~B

%.~~B

qq~qq~g~M,M

L

R

q~g~

36)(

46)(

211)(

559611

1

102

02

02

LM1( Low Mass Case 1): LM1( Low Mass Case 1):

Measuring Dark Matter Relic Density at the LHC 21

MM peak peak vs. vs. XX

Uncertainty Bandswith 10 fb-1

gMX ~MX

01

~MX

Measuring Dark Matter Relic Density at the LHC 22

)( 01

02

1peak

~~ M,M,MfM

02

~MX

MMjj Distribution Distributionendpeak jj MM 2

~

2~

2~

2~

~02

01

02 11

M

M

M

MMM

qq

endj

M < Mendpoint

Jets with ET > 100 GeVMj masses for each jet

Choose the 2nd large value Mj

“other” jet

Peak value ~ True Value

We choose the peak position as an observable.23

Mj(GeV)

qq~g~ q

Measuring Dark Matter Relic Density at the LHC

Excess in ETmiss + Jets

SUSY scale measurement at 10-20%.

Excess in Excess in EETTmissmiss + Jets + Jets

Hinchliffe and Paige, Phys. Rev. D 55 (1997) 5520

ETj1 > 100 GeV, ET

j2,3,4 > 50 GeV [No e’s, ’s with pT > 20 GeV] Meff > 400 GeV; ET

miss > max [100, 0.2 Meff]

HM1 ScenarioHM1 Scenario

m1/2= 250, m0= 60

= 45 fb

CMS

Meff

1721

1886

q~

g~

M

M

g~g~pp

Meff ETj1+ET

j2+ETj3+ET

j4+ ETmiss

[No b jets; b ~ 50%]

Measuring Dark Matter Relic Density at the LHC 24

Mass Measurements Mass Measurements mSUGRAmSUGRA

Meff(b)peak & M

peak …. Sensitive to A0 and tan

5/19/08 Measuring Dark Matter Relic Density at the LHC 25

Mjpeak & Meff

peak …. Insensitive to A0 and tan

SUSY Anatomy in the CA SUSY Anatomy in the CA RegionRegion

Mj

&Mj

M

pT()

100%1~

Lu~

01χ~

02χ~

g~

97%

u

u

SUSY

Mas

ses

(CDM)

q~g~pp

5/19/08 Measuring Dark Matter Relic Density at the LHC 26

ET jet > 100 G

eV

pT > 40 GeV

pT > 20 GeV