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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
2
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
3
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
4
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
5
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
7
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
8
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
23
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)