Measurement of Relic Measurement of Relic Density at the LHCDensity at the LHCyy

Arxiv: 0802 2968Arxiv: 0802.2968Phys. Lett.B: 649:73, 2007;639:46 2006

Bhaskar DuttaBhaskar DuttaTexas A&M UniversityTexas A&M University

Bhaskar DuttaBhaskar DuttaTexas A&M UniversityTexas A&M University

639:46, 2006

Measurement of Relic Density at the LHC 1

e as & U ve s tye as & U ve s tye as & U ve s tye as & U ve s tyCollaborators: R. Arnowitt, A. Gurrola, T. Kamon, A. Krislock, D. Toback

SUSY in Early Stage at the LHCLHC

The signal to look for: 4 jet + missing E

(or l+l-, τ+τ−)

Measurement of Relic Density at the LHC

2The signal to look for: 4 jet + missing ET

Example AnalysisKinematical Cuts and Event Selection

ETj1 > 100 GeV, ET

j2,3,4 > 50 GeVT , TMeff > 400 GeV (Meff ≡ ET

j1+ETj2+ET

j3+ETj4+ ET

miss)ET

miss > Max [100, 0.2 Meff]T [ , eff]Hinchliffe et al. Phys. Rev. D 55 (1997) 5520

Measurement of Relic Density at the LHC

3

Relic Density and MeffSUSY scale is measured with an accuracy of 10-20%

Thi d ll h h hThis measurement does not tell us whether themodel can generate the right amount of darkmatter

The dark matter content is measured with anaccuracy of around 6% at WMAPaccuracy of around 6% at WMAP

Question:

To what accuracy can we calculate the relic density based on the measurements at the LHC?

Measurement of Relic Density at the LHC

4

based on the measurements at the LHC?

Analysis Strategy

We establish the dark matter allowed regionsWe establ sh the da k atte allowed eg onsfrom the detailed features of the signals.

We accurately measure the masses and model( ll f SUGRA )parameters (all four mSUGRA parameters).

We calculate the relic density and comparethat with WMAP observation.

Measurement of Relic Density at the LHC

5

Minimal Supergravity (mSUGRA)Minimal Supergravity (mSUGRA)4 parameters + 1 sign

m1/2 Common gaugino mass at MG

m0 Common scalar mass at MG

A0 Trilinear couping at MG

tanβ <Hu>/<Hd> at the electroweak scalesign(µ) Sign of Higgs mixing parameter (W(2) = µ Hu Hd)

Experimental Constraintsi. MHiggs > 114 GeV Mchargino > 104 GeV

2 2 10 4 B (b ) 4 5 10 4

Experimental Constraints

ii. 2.2x10−4 < Br (b → s γ) < 4.5x10−4

iii. 12900940 201

.h. ~ <<χ

Ω

Measurement of Relic Density at the LHC 6

iv. (g−2)µ

1χ

: 3 σ descripency

Dark Matter Allowed RegionsWe choose mSUGRA model. However, the results can begeneralized.g

Focus point region – the lightestneutralino has a larger higgsinog ggcomponent

A-annihilation funnel region –gThis appears for large values ofm1/2

Neutralino-stau coannihilation

Measurement of Relic Density at the LHC

7

Neutralino stau coannihilationregion

Relic Density Calculation2

⎥⎤

⎢⎡

( ) 1CDM

⎥⎥⎥⎥

⎢⎢⎢⎢

∝−Ω +…( )CDM

⎥⎥⎥

⎦⎢⎢⎢

⎣ ⎦⎣

In the stau-neutralino coannihilation region

01χ~

2⎥⎤

⎢⎡

1χ20∆ /Me −

⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢

011 ~~ MMM

χτ −≡∆

Measurement of Relic Density at the LHC

81τ~ ⎥

⎥⎦⎢

⎢⎣ Griest, Seckel ’91

Our Reference PointOur Reference Point

m1/2 = 351, m0 = 210, tanβ = 40, µ >0, A0 = 0 [ISAJET version 7.69][ISAJET version 7.69]

Measurement of Relic Density at the LHC 9

SUSY Anatomy

g~u

Lu~u

es

M(j )Ma

sse

M(jττ)02χ~

u

SU

SY

M

MM(ττ)

1τ~τ

01χ~2χS

Meff

pT(τ)τ1χ

(CDM)

E miss + jets + >2Measurement of Relic Density at the

LHC 10

ETmiss + jets + >2τ

ppTTsoftsoft Slope and Slope and MMττττ

/ 2 G

eV

pT and Mττ distributions in truedi-τ pairs from neutralino decaywith |η| < 2 5

of C

ount

s with |η| < 2.5

Num

ber

Slope of pT distribution of “softτ” contains ∆M information

GeV 0

1102 →→ ~~~ χττττχ

Low energy τ’s are an enormous challengefor the detectors

Cou

nts /

1

ETvis(true) > 20, 20 GeV

GeV) 5.7( =M∆

umbe

r of

C ETvis(true) > 40, 20 GeV

ETvis(true) > 40, 40 GeV

Measurement of Relic Density at the LHC 11

N

(GeV) visττM

180180

Measurement of Relic Density at the LHC 12

Measurement of Relic Density at the LHC 12

MMττττ DistributionDistribution

Clean peak even for low ∆M

(GeV) visττM (GeV) vis

ττM

Measurement of Relic Density at the LHC 13

We choose the peak position as an observable.

MMττττ DistributionDistribution

M k d d A d tMeasurement of Relic Density at the

LHC 14

Mpeakττ depends on m0, m1/2, A0 and tanβ

MMjjττττ DistributionDistribution

endj

peakj MM ττττ ∝2

2

2

2

02

01

02 11

χ

χχττ

~

~

q~

~

q~endj M

M

M

MMM −−=

2

Mττ < Mττendpoint

Jets with ET > 100 GeVJets with ET > 100 GeVJττ masses for each jetChoose the 2nd large value

k M 840 G V

Squark Mass = 660 GeV

Squark Mass = 840 GeVMpeak

jττ depends on

Peak value depends on squark mass

m0, m1/2

Measurement of Relic Density at the LHC 15

We choose the peak position as an observable.

MMjjττττ DistributionDistribution

Mpeak depends on m mMpeakjττ depends on m0, m1/2

Measurement of Relic Density at the LHC 16

MMeffeff DistributionDistributionET

j1 > 100 GeV, ETj2,3,4 > 50 GeV [No e’s, µ’s with pT > 20 GeV]

Meff > 400 GeV (Meff ≡ ETj1+ET

j2+ETj3+ET

j4+ ETmiss [No b jets; εb ~ 50%])

ETmiss > max [100, 0.2 Meff]

At Reference PointM ff

peak = 1274 GeVMeff

peak = 1220 GeV(m1/2 = 335 GeV)

Meffpeak = 1331 GeV

(m1/2 = 365 GeV)

ET > max [100, 0.2 Meff]

Meffp 1274 GeV

Measurement of Relic Density at the LHC 17

MMeffeffpeakpeak vs. vs. mm00, m, m1/21/2

m1/2 (GeV) m0 (GeV)

Meffpeak …. insensitive to A0 and tanβ.

1/2 ( ) 0 ( )

Measurement of Relic Density at the LHC 18

MMeffeff((bb)) DistributionDistribution

ETj1 > 100 GeV, ET

j2,3,4 > 50 GeV [No e’s, µ’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]

At Reference PointM ff

(b)peak = 1026 GeVMeff

(b)peak = 933 GeV(m1/2 = 335 GeV)

Meff(b)peak = 1122 GeV

(m1/2 = 365 GeV)

ET > max [100, 0.2 Meff]

Meff( )p 1026 GeV

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

without measuring stop and sbottom massesMeasurement of Relic Density at the

LHC 19

without measuring stop and sbottom masses

MMeffeff((bb)peak)peak vs. vs. XX

m1/2 m0

(b) k βA0 tanβ

Measurement of Relic Density at the LHC 20

Meff(b)peak …. sensitive to A0 and tanβ.

Determining Model ParametersDetermining Model Parameters

),tan,,( , ),( 002/1202/11 AmmfMmmfM j βττττ ==

The Model parameters are solved by inverting the following functions:

),tan,,( , ),( 002/14)(

02/13 AmmfMmmfM beffeff β==

m0=205 4; m1/2=350 4.2; A0=0 16; tanβ= 40 0.8± ± ± ± (10 fb-1)

We can also determine the sparticle masses using these observables and a few additional ones, e.g., M(peak)

jτ , etc

=748 25; =831 21; =10.6 2; =141 19; = 260 15;

q~M g~MM M

± ± M∆ ±± ±

Gaugino Universality can be checked!

141 19; 260 15; 01χ~

M 02

~Mχ± ±

Measurement of Relic Density at the LHC 21

Gaugino Universality can be checked!

Relic Density and LuminosityRelic Density and LuminosityHow does the uncertainty in the Dark

Matter relic density change with Luminosity?L 0 f 1L= 50 fb-1

L= 10 fb-1

δΩh2/Ωh2 ~ 6% (30 fb-1)

Measurement of Relic Density at the LHC 22

( )

ConclusionMeff will establish the existence of SUSY

Different observables are needed to establishDifferent observables are needed to establish the dark matter allowed regions in SUSY model at the LHC

Analysis with visible ETτ > 20 GeV establishes stau-

neutralino coannihilation region

The mSUGRA parameters are determined using :1) Meff

peak 2)Mjττpeak 3)Mττ

peak 4) Meffpeak(b)

δΩh2/Ωh2 ~ 6% (30 fb-1)m0=205 4; m1/2=350 4.2; A0=0 16; tanβ= 40 0.8± ± ± ± (10 fb-1)

( )Squark, Gluino, stau, neutralino(1,2) can be

determined without using mSUGRA assumptionsMeasurement of Relic Density at the

LHC 23

determined without using mSUGRA assumptionsGaugino universality can be checked at 15% level