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/
)19.3( 2.01.3/
0.26.10
;19141;15260
;21831 ;25748
01
02
01
02
~~
~~
~~
~~
theoryMM
theoryMM
M
MM
MM
g
g
gqL
10 fb-1
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
4350
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
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