Measurement of Relic Density at the LHC 1

Bhaskar DuttaBhaskar DuttaTexas A&M UniversityTexas A&M University

Bhaskar DuttaBhaskar DuttaTexas A&M UniversityTexas A&M University

Measurement of Relic Density at the LHC

Measurement of Relic Density at the LHC

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

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

Measurement of Relic Density at the LHC

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The signal to look for: 4 jet + missing ET

SUSY in Early Stage at the LHC

(or l+l-, )

Measurement of Relic Density at the LHC

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Kinematical Cuts and Event Selection ET

j1 > 100 GeV, ETj2,3,4 > 50 GeV

Meff > 400 GeV (Meff ETj1+ET

j2+ETj3+ET

j4+ ETmiss)

ETmiss > Max [100, 0.2 Meff]

Hinchliffe et al. Phys. Rev. D 55 (1997) 5520

Example Analysis

Measurement of Relic Density at the LHC

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SUSY scale is measured with an accuracy of 10-20%

This measurement does not tell us whether the model can generate the right amount of dark matter

The dark matter content is measured with an accuracy of around 6% at WMAP Question:

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

Relic Density and Meff

Measurement of Relic Density at the LHC

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We establish dark matter allowed regions from the detailed features of the signals.

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

We calculate the relic density and compare that with WMAP observation.

Analysis Strategy

Measurement of Relic Density at the LHC 6

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

tan <Hu>/<Hd> at the electroweak scale

sign() Sign of Higgs mixing parameter (W(2) = Hu Hd)

4 parameters + 1 signm1/2 Common gaugino mass at MG

m0 Common scalar mass at MG

A0 Trilinear couping at MG

tan <Hu>/<Hd> at the electroweak scale

sign() Sign of Higgs mixing parameter (W(2) = Hu Hd)

i. MHiggs > 114 GeV Mchargino > 104 GeVii. 2.2x104 < Br (b s ) < 4.5x104

iii.

iv. (g2)

Experimental Constraints

12900940 201

.h. ~ : 3 descripency

Measurement of Relic Density at the LHC

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Dark Matter Allowed RegionsWe choose mSUGRA model. However, the

results can be generalized.

Neutralino-stau coannihilation region [In this talk]

Focus point region – the lightest neutralino has a larger higgsino componentA-annihilation funnel region – This appears for large values of m1/2

Measurement of Relic Density at the LHC

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2

1CDM

+…

In the stau-neutralino coannihilation region

01~

1~

20Δ

2

/Me

011

~~ MMM Δ

Griest, Seckel ’91

Relic Density Calculation

Measurement of Relic Density at the LHC 9

Our Reference PointOur Reference Point

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

Measurement of Relic Density at the LHC 10

SUSY Anatomy

Meff (4 jets + ETmiss)

M(j)

M()M()

pT()pT()

100%1~

Lu~

01χ~

02χ~

g~

97%

u

u

SU

SY

Mass

es

(CDM)

ETmiss

+ jets + >2

Measurement of Relic Density at the LHC 11

Nu

mb

er o

f C

oun

ts /

1 G

eV

(GeV) visM

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 with || < 2.5

Measurement of Relic Density at the LHC 12

180

Measurement of Relic Density at the LHC 12

Measurement of Relic Density at the LHC 13

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

Measurement of Relic Density at the LHC 14

MM Distribution Distribution

Mpeak depends on m0, m1/2, A0 and tan

Measurement of Relic Density at the LHC 15

MMjj Distribution Distribution

Squark Mass = 840 GeV

Squark Mass = 660 GeV

Peak value depends on squark mass

endj

peakj MM 2

2

2

2

02

01

02 11

~

~

q~

~

q~endj M

M

M

MMM

M < Mendpoint

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

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

Measurement of Relic Density at the LHC 16

MMjj Distribution Distribution

Mpeak depends on m0, m1/2j

Measurement of Relic Density at the LHC 17

MMeffeff 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]

Measurement of Relic Density at the LHC 18

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

Meffpeak …. insensitive to A0 and tan.

m1/2 (GeV) m0 (GeV)

Measurement of Relic Density at the LHC 19

MMeffeff((bb)) Distribution Distribution

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

Measurement of Relic Density at the LHC 20

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

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

A0 tan

m1/2 m0

Measurement of Relic Density at the LHC 21

Determining Model Determining Model ParametersParameters

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

02/13 AmmfMmmfM beffeff

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

The Model parameters are solved by inverting the following functions:

m0=205 4; m1/2=350 4.2; A0=0 16; tan= 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)

j, etc

Gaugino Universality can be checked (at 15% level)!

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

q~M g~M

~M 2

~M

M

Measurement of Relic Density at the LHC 22

Relic Density and LuminosityRelic Density and Luminosity How does the uncertainty in the Dark

Matter relic density change with Luminosity?

h2/h2 ~ 6% (30 fb-1)

L= 50 fb-1

L= 10 fb-1

Measurement of Relic Density at the LHC

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h2/h2 ~ 6% (30 fb-1)

Analysis with visible ET > 20 GeV establishes stau-

neutralino coannihilation region

Meff will establish the existence of SUSY

Different observables are needed to establish

the dark matter allowed regions in a SUSY model at the LHC

Squark, Gluino, stau, neutralino(1,2) can be determined without using mSUGRA assumptions

Gaugino universality can be checked at 15% level

Conclusion

The mSUGRA parameters are determined using :1) Meff

peak 2)Mjpeak 3)M

peak 4) Meffpeak(b)

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