Measurement of Dark Measurement of Dark Matter Content at the LHCMatter Content at the LHC

Bhaskar DuttaCollaborators: R. Arnowitt, A. Gurrola, T. Kamon, A. Krislock, D. Toback

Texas A&M University

Measurement of Dark Matter Content at the LHC 118th August’ 08

OUTLINEOUTLINE

DM Relic Density (DM Relic Density (hh22 ) in SUSY ) in SUSY mSUGRA Co-annihilation (CA) Region at the LHCmSUGRA Co-annihilation (CA) Region at the LHC Prediction of DM Relic Density (Prediction of DM Relic Density (hh22 ) ) SummarySummary

Arnowitt, Dutta, Kamon, Kolev, Toback, PLB 639 (2006) 46Arnowitt, Dutta, Kamon, Kolev, Toback, PLB 639 (2006) 46Arnowitt, Arusano, Dutta, Kamon, Kolev, Simeon, Toback, Wagner, PLB 649 (2007) 73Arnowitt, Arusano, Dutta, Kamon, Kolev, Simeon, Toback, Wagner, PLB 649 (2007) 73Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, Phys. Rev. Lett. 100, (2008) 231802 Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, Phys. Rev. Lett. 100, (2008) 231802 Crockett, Dutta, Flanagan, Gurrola, Kamon, Kolev, VanDyke, ‘08;Crockett, Dutta, Flanagan, Gurrola, Kamon, Kolev, VanDyke, ‘08;

2Measurement of Dark Matter Content at the LHC

3

011

~~ MMM Δ011

~~ MMM Δ

2

1CDM

+ ….

fTMe k/Δ

2

01~

1~+ + ….

Co-annihilation (CA) Process

Co-annihilation (CA) ProcessGriest, Seckel ’91

A near degeneracy occurs naturally for light stau in mSUGRA.A near degeneracy occurs naturally for light stau in mSUGRA.

Anatomy of Anatomy of annann

Precision Cosmology at the LHC

pbM

vann 1~~2

2

2GeV) 37(21/2

15020

2cE

m.m~m

In mSUGRA model the lightest stau seems to be naturally close to the lightest neutralino mass especially for large tan

For example, the lightest selectron mass is related to the lightest neutralino mass in terms of GUT scale parameters:

For larger m1/2 the degeneracy is maintained by increasing m0 and we get a corridor in the m0 - m1/2

plane.

The coannihilation channel occurs in most SUGRA models with non-universal soft breaking,

21/2

160201

m.~

m

Thus for m0 = 0, becomes degenerate with at m1/2 = 370 GeV, i.e. the coannihilation region begins at

0

1

~2

cE~

m1/2 = (370-400) GeV

Coannihilation, GUT Scale

Arnowitt, Dutta, Santoso’ 01

Measurement of Dark Matter Content at the LHC 4

DM Allowed Regions in mSUGRABelow is the case of mSUGRA model.

However, the results can be generalized.

[Stau-Neutralino CA region]

[Focus point region]the lightest neutralino has a larger Higgsino component[A-annihilation funnel region]This appears for large values of m1/2

[Bulk region] almost ruled out

5Measurement of Dark Matter Content at the LHC

CA Region at tanCA Region at tan = 40 = 40

GeV 155011

~MMM ~~ GeV 155011

~MMM ~~

Can we measure M at colliders?Can we measure M at colliders?

6Measurement of Dark Matter Content at the LHC

Smoking Gun of CA RegionSmoking Gun of CA Region

100%1~

Lu~

01χ~

02χ~

g~

97%

u

u

SU

SY

Mass

es

(CDM)

2 quarks+2 ’s+missing energy

Uni

que

kine

mat

ics

7

Low energy taus exist in theCA regionHowever, one needs to measure the model Parameters to predict theDark matter content in this scenario

Measurement of Dark Matter Content at the LHC

Nu

mb

er o

f C

oun

ts /

1 G

eV

ETvis(true) > 20, 20 GeV

ETvis(true) > 40, 20 GeV

ETvis(true) > 40, 40 GeV

GeV) 5.7(

011

02

M

~~~

Nu

mb

er o

f C

oun

ts /

2 G

eVppTT

softsoft Slope and Slope and MM

Slope of pT distribution of “soft ” contains ΔM information

Low energy ’s are an enormous challenge for the detectors

pT and M distributions in true di- pairs from neutralino decay

Measurement of Dark Matter Content at the LHC 8

9

We use ISAJET + PGS4 PLB 639 (2006) 46PLB 639 (2006) 46Measurement of Dark Matter Content at the LHC

MM Distribution Distribution

Clean peak even for low M

We choose the peak position as an observable.We choose the peak position as an observable.

(GeV) visM (GeV) vis

M

10Measurement of Dark Matter Content at the LHC

SUSY Anatomy

Mj

M

pT()

100%1~

Lu~

01χ~

02χ~

g~

97%

u

u

SU

SY

Mass

es

(CDM)

Measuring Relic Density at the LHC 11

Meff

4 j+E4 j+ETTmissmiss: M: Meffeff Distribution Distribution

At Reference PointMeff

peak = 1274 GeV

Meffpeak = 1220 GeV

(m1/2 = 335 GeV)Meff

peak = 1331 GeV(m1/2 = 365 GeV)

ETj1 > 100 GeV, ET

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

j1+ETj2+ET

j3+ETj4+ ET

miss [No b jets; b ~ 50%]) ET

miss > max [100, 0.2 Meff]

12Measurement of Dark Matter Content at the LHC

3 j+1b+E3 j+1b+ETTmissmiss :M :Meffeff

((bb)) DistributionDistribution

At Reference PointMeff

(b)peak = 1026 GeV

Meff(b)peak = 933 GeV

(m1/2 = 335 GeV)Meff

(b)peak = 1122 GeV(m1/2 = 365 GeV)

ETj1 > 100 GeV, ET

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

(b) > 400 GeV (Meff

(b) ET

j1=b+ETj2+ET

j3+ETj4+ ET

miss [j1 = b jet]) ET

miss > max [100, 0.2 Meff]

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

without measuring stop and sbottom masses

13Phys. Rev. Lett. 100, (2008) 231802Phys. Rev. Lett. 100, (2008) 231802

Measurement of Dark Matter Content at the LHC

Observables

SM+SUSY Background gets reduced

NN

•Ditau invariant mass: M

• Jet-- invariant mass: Mj

• Jet- invariant mass: Mj

• PT of the low energy • Meff : 4 jets +missing energy• Meff(b) : 4 jets +missing energy

Since we are using 7 variables, we can measure the model parameters and the grand unified scale symmetry (a major ingredient of this model)

1.Sort ’s by ET (ET1 > ET

2 > …)• Use OSLS method to extract pairs from the

decays

All these variables depend on masses => model parameters

Measurement of Dark Matter Content at the LHC 14

7 Eqs (as functions of SUSY parameters)

)~,~(

)~,~,,~(

)~,~,,~ (

)~,~,~(

)~,(

)~,~,(

6peakeff

01

025

(2)peak2

01

024

(2)peak1

01

023

(2)peak

012

01

021

peak

L

Lj

Lj

Lj

qgfM

MqfM

MqfM

qfM

MfSlope

MfM

Invert the equations to Invert the equations to determine the massesdetermine the masses

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

1 ellipse

)91.5( 8.09.5/

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theoryMM

theoryMM

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MM

MM

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15

Phys. Rev. Lett. 100, (2008) 231802Phys. Rev. Lett. 100, (2008) 231802

Meff(b) = f7(g, qL, t, b)~ ~ ~ ~

Measurement of Dark Matter Content 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., Peak(M) = f (Mgluino, Mstau, M , M )

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

DM Relic Density in mSUGRADM Relic Density in mSUGRA

01~0

2~

16Measurement of Dark Matter Content at the LHC

Determining mSUGRA ParametersDetermining mSUGRA Parameters

),tan,,()(

),(

),tan,,(

),(

002/14eff

02/13eff

002/12

02/11

AmmXbM

mmXM

AmmXM

mmXM j

?tan

?

?

?

0

2/1

0

A

m

m

),tan,( 02/102

~01

AmmZh

)fb (??? ???/ 12~

2~ 0

101

hh

17Measurement of Dark Matter Content at the LHC

Mass Measurements Mass Measurements mSUGRAmSUGRA

M peak, Meff(b)peak …. Sensitive to A0 , tanmandm1/2

Mjpeak, Meff

peak …. Sensitive to m0, m1/2

18Measurement of Dark Matter Content at the LHC

Determining mSUGRA ParametersDetermining mSUGRA Parameters

),tan,,(

),(

002/14)(

eff

02/13eff

AmmfM

mmfMb

),tan,,(

),(

002/12

02/11

AmmfM

mmfM j

Solved by inverting the following functions:

140tan

160

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5210

0

2/1

0

A

m

m

10 fb-1

),tan,( 02/102

~01

AmmZh

1fb 10 L

1fb 50

)fb 30( %6/ 12~

2~ 0

101

hh

19

Phys. Rev. Lett. 100, (2008) 231802Phys. Rev. Lett. 100, (2008) 231802

Measurement of Dark Matter Content at the LHC

Focus Point (FP)Focus Point (FP)m0 is large, m1/2 can be small, e.g., m0= 3550 GeV, m1/2=314 GeV, tan=10, A0=0

20Measurement of Dark Matter Content at the LHC

M(gluino) = 889 GeV, ΔM(χ3

0- χ10) = 81 GeV,

ΔM(χ20- χ1

0) = 59 GeV, ΔM(χ3

0- χ20) = 22 GeV

Br(g → χ20 tt) = 10.2%

Br(g → χ20 uu) = 0.8%

Br(g → χ30 tt) = 11.1%

Br(g → χ30 uu) = 0.009%

~~

~~

---

-

)( OSDFOSSF eee )( OSDFOSSF eee

)( OSDF e )( OSDF e

)OSSF( ee )OSSF( ee

M(ll) (GeV)

Eve

nts

/GeV

GeV 59)()( 01

02 ~M~M GeV 59)()( 0

102 ~M~M GeV 81)()( 0

103 ~M~M GeV 81)()( 0

103 ~M~M

Measurement of Dark Matter Content at the LHC 21

Dilepton Mass at FP

Baer, Barger, Salughnessy, Summy, Wang , PRD, 75, 095010 (2007),Crockett, Dutta, Flanagan, Gurrola, Kamon, Kolev, VanDyke, 08;

Measurement of Dark Matter Content at the LHC 22

Determination of masses: FP

Relic density calculation depends on , tan and m1/2

All other masses are heavy

m1/2 and tan can be solved from M(gluino), ΔM (χ3

0- χ10) and ΔM (χ2

0- χ10)

M(gluino), ΔM (χ30- χ1

0) and ΔM (χ20- χ1

0) can be measuredwith an accuracy of ~ 10%

Higher jet, b-jet, lepton multiplicity requirement increase the signal over background rate

[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., Peak(M) = f (Mgluino, Mstau, M , M ) 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)

SummarySummary

01~0

2~

23

)fb 30( %6/ 12~

2~ 0

101

hh

Measurement of Dark Matter Content at the LHC

Summary…[4] For large m0, when staus are not present, the mSUGRA parameters can still be extracted, but with less accuracy

[6] It will be interesting to determine nonuniversal model Parameters, e.g., (Higgs sector nonuniversality)

work in progress…

[5] This analysis can be applied to any SUSY model

Measurement of Dark Matter Content at the LHC