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12/17/07Cosmological Connection at the LHC:Stau Neutralino Coannihilation Case
Dark Matter Dark Matter at the at the LHCLHC
Bhaskar Dutta
Texas A&M University
Dark Matter at the LHC 130th Oct ’ 09
Texas Cosmology Network Meeting, UT, Austin
2
+ ….
Dark Matter and SUSYDark Matter and SUSY
pbM
vann 1~~ 2
2! ><
Dark Matter at the LHC
We need to observe the new layer of matter in order to establish this explanation
The signal : jets + leptons + missing ET
SUSY at the LHC
(or l+l-, τ+τ−)DM
DM
Colored particles get produced and decay into weakly interacting stable particles
High PT jet
High PT jet
[mass difference is large]
The pT of jets and leptons depend on the sparticle masses which are given by models
R-parity conserving
3
(or l+l-, τ+τ−)
Dark Matter at the LHC
mSUGRAmSUGRA: Minimal Scenario: Minimal Scenario
4 parameters+ 1 sign
du
Zdu
HHW
MA
Mm
Mm
MH/H
in of Sign :)sign(
at coupingTrilinear :
at massscalar Common :
at mass gaugino Common :
at :tan
(2)
GUT0
GUT0
GUT1/2
µµµ
!
=
Dark Matter at the LHC 44
Minimal Supersymmetry Standard Model has more than 100 parameters
•We may not have enough observables to establish them
•We start with a simple scenario and go to complicated cases
SUSY ModelsSUSY Models
Dark Matter Allowed RegionsDark Matter Allowed Regionstanβ = 40A0 = 0, µ > 0
ab
c
Excluded by1)Rare B decay b sγ2)No CDM candidate3)Muon magnetic moment
a
bc
m0 (
GeV
)
m1/2 (GeV)
Over-dense DM Region22
Coannihilation Region11
FP/HB Region33
Dark Matter at the LHC 55
Observables at the LHCObservables at the LHC
Mjττ&Mjτ
97%SU
SY
Ma
sse
s
(CDM)
pT τ > 40 GeV
pT τ > 20 GeV
ET jet > 100 G
eV
Mττ& pT(τ)
100%
The observables include:Z, h, W, τ, t, b, jet, l and missing energyThe observables are determined by the underlying physics of the model
Dark Matter at the LHC
CaseCase 1. 1. CoannihilationCoannihilation Region Region
100%
97%
SU
SY
Ma
sse
s
(CDM)2 quarks+2 τ’s
+missingenergy
7
Low energy taus characterize the CA region
However, one needs to measure the model parameters to predict thedark matter content in this scenario
Dark Matter at the LHC
+ ….
Griest, Seckel ’91
Arnowitt, Dutta, Kamon,Toback’08
Determining Determining mSUGRAmSUGRA Parameters ParametersSolved by inverting the following functions:
140tan
160
4350
5210
0
2/1
0
±=
±=
±=
±=
!
A
m
m
),tan,( 02/10
2~01
AmmZh !"
=#
1fb 10
!=L
1fb 50
!
)fb 70( %1.4
)fb 30( %2.6/
1
12~
2~ 0
101
!
!
=
="" hh##
$
),tan,,(
),(
),tan,,(
),(
002/14
peak )(
eff
02/13
peak
eff
002/12
peak
02/11
peak
AmmXM
mmXM
AmmXM
mmXM
b
j
!
!""
""
=
=
=
=
10 fb-1
Dark Matter at the LHC 88Phys.Rev.Lett.100:231802,2008.
Case 2 : Over-dense regionCase 2 : Over-dense region
h
m1/2=440, m0=471, tanβ=40, mtop=175
u
87%
1041 1044
500
393
181
341
114
46213%
Z91
ETmiss > 180 GeV;
N(jet) > 2 with ET > 200 GeV;ET
miss + ETj1 + ET
j2 > 600 GeV
Dark Matter at the LHC 99
N(b) > 2 withPT > 100 GeV; 0.4< ΔRbb < 1
DeterminingDetermining ΩΩhh22
Solved by inverting the following functions:
1839tan
950
15440
50472
0
21
0
±=
±=
±=
±=
!
A
m
m
/
),tan,( 02/10
2~01
AmmZh !"
=#1fb 1000
!=L
%~h/h ~~ 150ÙÙ 2201
01 !!
"
)tan(
)tan(
)(
)(
00214
peak )(
eff
00213
peak )(
eff
0212
peak
eff
0211
point end
A,,m,mXM
A,,m,mXM
m,mXM
m,mXM
/
bb
/
b
/
/jbb
!
!
=
=
=
=
1000 fb1000 fb-1-1
Dark Matter at the LHC 1010
Phys.Rev.D79:055002,2009 Dutta, Kamon,Nanopoulos etal ’09
Case 3 : Focus Point /HBCase 3 : Focus Point /HBProspects at the LHCProspects at the LHC:A few mass measurementsare available: 2nd and 3rd
neutralinos, and gluino
g~
0
i
~!
q~ l~ Z
ZZ
Z
m0, A0, µ, tanβ
m1/2, µ, tanβ
Dark Matter at the LHC 1111
!!!!!
"
#
$$$$$
%
&
''
''
'
'
=
0
0
0
0
2
1
0
µ
µ
((
((
((
((
)
scMssM
ccMcsM
scMccMM
ssMcsMM
WZWZ
WZWZ
WZWZ
WZWZ
~Ì M4x4 (m1/2, µ, tanβ )
0
1
0
221 !! ~~ MMD "= 0
1
0
331 !! ~~ MMD "=g~M
)tan( 21
201
!µ"#
,,mZh/~ =
Case 4 : Non-U SUGRACase 4 : Non-U SUGRANature may not be so kind Nature may not be so kind …… Our studies havebeen done based on a minimal scenario (= mSUGRA).……Let’s consider a non-universal scenario: Higgs non-universality: mHu, mHd m0
Steps:Steps:1) Reduce Higgs coupling parameter, µ, by increasing2) mHu, … More annihilation (less abundance) correct values of Ωh2
3) Find smoking gun signals Technique to calculate Ωh2
SUGRA Models at the LHC 1212
!
Dark Matter at the LHC 13
Extraction of Model ParametersExtraction of Model Parameters
End-points-nonuniversalM(jW) [ ] = 714.6 GeVM(jW) [ ] = 727.3 GeV[use 2 τ’s since ]M(jW)[ ] = 652.4 GeV[use Z since ]M(jW) [ ] = 738.6 GeV
0
1
±
1 ! ""0± !22
""
0± !32
""
±
1! "" 04
1
0
0
2!""! m±#
We can use stop decay chainIn this case we use a b/t
We have 3 (4) parameters in the chargino-neutralino system:m1/2, µ, tanβ (m1,m2, µ, tanβ)
0
1
0
2!! Z"
Theory:738.8
~500 GeV
M(bW)
M(jW)
Similarly, M(tZ) =338 GeV00
3 1! ""
Mtττ, Mjττ etc can also be constructed
Dark Matter at the LHC
ConclusionSignature contains missing energy (R parity conserving) many jets and leptons : Discovering SUSY should not be a problem!
Once SUSY is discovered, attempts will be made to measure the sparticle masses (highly non trivial!), establish the model and make connection between particle physics and cosmologyDifferent cosmologically motivated regions of the minimal model have distinct signatures.It is possible to determine model parameters and the relic density based on the LHC measurements
Dark Matter at the LHC
Work is in progress to determine non-universal modelParameters----looks promising
