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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
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