Supersymmetry, dark matter and the LHC
GGI Conference: The Dark Matter connection:Theory & Experiment
May 20, 2010[PN]
Outline
Connection of DM to LHC with LSP= !0
Other LHC and dark matter related talks: By Dutta, Kraml, Polesello, Su
Gaugino-Higgsino content of the neutralino and LHCsignatures
Multicomponent dark matter.
SUSY breaking mechanisms
Gravity mediation (1982)
Chamseddine, Arnowitt, PN (1982)Barbieri, Ferrara, Savoy (1982)
Hall, Lykken, Weinberg (1983)
Gauge mediation (1994)Dine, Nelson, Shirman, · · ·
Anomaly mediation (1999)Randall, Sundrum, · · ·
Mixed gravity, anomaly, gauge mediation such as mirage,deflected mirage etc.
Connection of DM to LHC with LSP= !
Typically the satisfaction of the relic density constraints aresatisfied in four broad regions of the SUGRA parameter space.
Bulk regions
Pole regions
Coannihilation regionsWino, stau, stop, gluino · · · coannihilation
Hyperbolic Branch/Focus Point regionChan, Chattopadhyay, PN (1998), Feng, Matchev, Moroi (2000); Baer, Tata
et.al. (2003)
These regions could possibly lead to distinguishable signatures atthe LHC. We explore this possibility specifically for the staucoannihilation region and for for the HB/FP region.
Some Prominent SUSY signatures
In pp collisions at the LHC one will produce gg, gq, qq. The g, qthat are produced will decay producing many signatures
g ! qq, qq!0i , qq!!±
j
q ! qg, q!0i , q!!±
j
!0i , !±
j will decay producing in general multi-leptons and the LSPneutralino will carry large missing energy.
Typical SUSY signals: Jets + leptons+ EmissT .
1 One lepton+jets+EmissT .
2 Opposite sign (OS) dileptons +jets+EmissT .
3 Same sign (SS) dileptons +jets+EmissT .
4 3leptons + jets+EmissT .
5 Tagged b jets and tau jets with and without missing ET .
At the LHC:
Post Trigger Level Cuts
1 In an event, we only select photons, electrons, and muons that have transversemomentum Pp
T > 10 GeV and |!p| < 2.4, p = (", e, µ).
2 Taus which satisfy P!T > 10 GeV and |!! | < 2.0 are selected.
3 For hadronic jets, only those satisfying P jT > 60 GeV and |!j | < 3 are selected.
4 We require a large amount of missing transverse momentum, PmissT > 200 GeV.
5 There are at least two jets that satisfy the PT and ! cuts.
The default post trigger level cuts are standard and are designed to suppress the
Standard Model background, and highlight the SUSY events over a broad class of
models.
Stau Coannihilation and Hyperbolic/Focus point region andDecay Chains
On HB/FP the squarks are generally heavy and thus thegluinos are produced more profusely in this region thansquarks. The gluinos have longer decay chains and thusmissing PT associated with this region is smaller.
g ! qq!0i , qq!!±
j
Also a larger multiplicity of quarks, specfically b quarks,produced in the HB/FP region.
On the Stau co-annihilation branch squarks are light and theyare more profusely produced than gluinos. The squarks haveshorter decay chains, and thus missing PT associated withthis region is larger.
q ! q!0i , q!!±
j
What can we learn from the LHC regarding theorigin of Dark matter?
Feldman, Liu, PN: Phys. Rev. D 78, 083523 (2008), arXiv:0808.1595 [hep-ph]
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Feldman, Liu, PN: Phys. Rev. D 78, 083523 (2008), arXiv:0808.1595 [hep-ph]
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jet is fixed at 2. Here meg ! 1.1 TeV.
Direct detection and NLSPFeldman, Liu, PN, arXiv:0711.4591 [hep-ph]; PLB 662,190(2008)
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The Wall: Chattopadhyay, Corsetti, PN (2003); Baer, Balazs, Belyaev, O,Farril(2003); Roszkowski, Ruiz de Austri, Trotta (2007).
Chargino Wall: Feldman, Liu, PN (2008)
Chargino -NLSP
Higgs -NLSP
Stau -NLSP
Stop -NLSP
Combined LHC and dark matter dataFeldman, Liu, PN: Phys. Rev. D 78, 083523 (2008), arXiv:0808.1595 [hep-ph]
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T cut :
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Feldman, Liu, PN: JHEP 0804:054,2008.40 counting signatures for each parameter point.
40 Signatures Description 40 Signatures Description(1) ! 0L 0 Lepton (22)!0T 0 !(2)!1L 1 Lepton (23)!1T (23)!1 !(3)!2L 2 Lepton (24)!2T (24)!2 !(4)!3L 3 Lepton (25)!3T (25)!3 !(5)!4L 4 Lepton and more (26)!4T 4 ! and more
(6)!0L1b 0 Lepton + 1 b-jet (27)!0T1b 0 ! + 1 b-jet(7)!1L1b 1 Lepton + 1 b-jet (28)!1T1b 1 ! + 1 b-jet(8)!2L1b 2 Lepton + 1 b-jet (29)!2T1b 2 ! + 1 b-jet(9)!0L2b 0 Lepton + 2 b-jet (30)!0T2b 0 ! + 2 b-jet(10)!1L2b 1 Lepton + 2 b-jet (31)!1T2b 1 ! + 2 b-jet(11)!2L2b 2 Lepton + 2 b-jet (32)!2T2b 2 ! + 2 b-jet(12)!ep e+ in 1L (33)!em e− in 1L(13)!mp µ+ in 1L (34)!mm µ− in 1L(14)!tp !+ in 1T (35)!tm !− in 1T(15)!OS Opposite Sign Di-Lepton (36)!0b 0 b-jet(16)!SS Same Sign Di-Lepton (37)!1b 1 b-jet
(17)!OSSF Opp Sign Same Flavor Di-Lepton (38)!2b 2 b-jet(18)!SSSF Same Sign Same Flavor Di-Lepton (39)!3b 3 b-jet(19)!OST Opposite Sign Di-! (40)!4b 4 b-jet and more(20)!SST Same Sign Di-!((21)!TL 1 ! plus 1 Lepton
Feldman, Liu, PN: JHEP 0804:054,2008.
Kinematical signatures1. P miss
T2. PT peak value
3. Effective Mass = P missT +
!j P j
T
4.Invariant Mass of all jets5.. Invariant Mass of e+e! pair6. Invariant Mass of µ+µ! pair7. Invariant Mass of !+!! pair
A list of the kinematical signatures analyzed for each point in the SUGRA modelparameter space. L = e, µ signifies only electrons and muons.
OSSF Di-leptonFeldman, Liu, PN: JHEP 0804:054,2008.
0 50 100 150 2000
20
40
60
80
100
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Feldman, Liu, PN: arXiv:0808.1595 [hep-ph].
Hyperbolic Branch
Stau Coannihilation
Signatures and backgrounds for mSPsFeldman, Liu, PN: JHEP 0804:054,2008.
0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0L/N
1L/N
SOP
SM
mSP1
mSP2
mSP3
mSP4
mSP5
mSP6
mSP7
mSP8
mSP11
mSP12
mSP13
mSP14
mSP16
SM
0.3 0.5 0.7 0.9
0.1
0.2
0.3
0.4
0b/N
1b/N
SOP
SUP
CP
HP
SM
mSP1
mSP2
mSP3
mSP4
mSP5
mSP6
mSP7
mSP8
mSP11
mSP12
mSP13
mSP14
mSP16
SM
0.1 0.2 0.3 0.40
0.1
0.2
1b/N
2b/N
SOP
SUP
HP
CP
SM
mSP1
mSP2
mSP3
mSP4
mSP5
mSP6
mSP7
mSP8
mSP11
mSP12
mSP13
mSP14
mSP16
SM
0.1 0.3 0.5 0.7 0.9200
400
600
800
0b/N
Ave
rage
Mis
sing
PT (G
eV)
SOP
SUP
HP
CP
mSP4
SM
mSP1mSP2mSP3mSP4mSP5mSP6mSP7mSP8mSP11mSP12mSP13mSP14mSP16SM
HB
Stau Co
HB
Stau Co
Stau Co
Stau Co
HB
HB
SUSY: like-sign dileptons
40
Similar sensitivity seen in like-sign dilepton analysis
1 fb-1
0.1 fb-1
Very soon the LHC will surpass
the Tevatron in the search for SUSY
From Conway’s talk at Pheno 2010
(GeV)0
m500 1000 1500 2000 2500
(G
eV)
1/2
m
100
200
300
400
500
600
500 GeV
600 GeV
800 GeV
1 TeV
1.2 TeV
111 GeV
114 GeV
LHC7 - All Channels
LS
P!"
LEP excluded
(G
eV)
g~m
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
(GeV)0
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m
100
200
300
400
500
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-10.33 fb-10.1 fb
g~m
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= 172.6 GeVt
> 0, m! = 45, # = 0, tan0A
Baer, Barger, Lessa, Tata arXiv:1004.3594 [hep-ph] mSUGRA
Gaugino -Higgsino Content of the Neutralino and LHCSignatures
The signatures at the LHC will be dependent on the gaugino vshiggsino content of the neutralino. Thus the neutralino wavefunction can be expanded as
χ = αλB + βλW + γh1 + δh2
For illustration we consider two models.
Model 1: A pure Wino model (PWM) where the neutralino isalmost 100% wino. Models of this type arise in anomalymediated breaking. One characteristic of such models is thatthe lighter chargino and the neutralino are essentiallydegenerate.Model 2: As second example we consider a mixedHiggino-Wino model (HWM) which has a substantial higgsinocomponent.
These models lead to distinguishable signatures at the LHC.
Pure Wino and Higgsino-Wino model examples
Pure Wino Model (PWM)
(m0, m1/2, A0, tan !) = (1000, 850, 0, 10),
("1,2,3, signµ) = (0, !.7, 0, +).
#0 = .009$B!0.996$W + .081h1 ! .023h2
Higgsino-wino model (HWM)
(m0, m1/2, A0, tan !) = (800, 558, 0, 5),
("1,2,3, signµ) = (!0.09, !.5, !.51, +).
#0 = .726$B!0.616$W + .26h1 ! .16h2
Sparticle masses in mixed Higgsino-Wino and Pure Winomodels
Feldman, Liu, PN, Nelson, PRD D 80, 075001 (2009)
Mass HWM PWM Mass HWM PWMme!0
1198.9 195.2 mt1
648.5 1516
me!02
217.0 357.0 mt2866.8 1749
me!03
429.9 1025 mb1841.4 1729
me!04
451.3 1029 mb2970.2 1902
me!±1
208.8 195.5 m"1 817.7 1011
me!±2
448.6 1036 m"2 822.8 1041
mg 707.1 1929
Relevant sparticle mass spectra for the HWM and PWM as calculated from the
high-scale boundary conditions. All masses are in GeV.
E!ective mass distribution
Feldman, Liu, PN, Nelson, PRD D 80, 075001 (2009)
Effective Mass (GeV)0 500 1000 1500 2000 2500 3000
-1
Even
ts/3
0 G
eV
/5 f
b
0
50
100
150
200
250
300 Data Set
-1Background: 5 fb
-1Model HWM: 5 fb
-1Model PWM: 100 fb
DistributioneffM
Meff is defined as the scalar sum of the transverse momenta of four hardest jets
PT ! (200,150,50,50) GeV in the event plus missing energy (EmissT ! 200
GeV).The plot is of events for the Higgsino-Wino model (for 5fb!1 yellow) and for
Pure Wino model (100 fb!1 blue).
The invariant mass distribution of two b-jets events inHiggsino-Wino model.
Feldman, Liu, PN, Nelson, PRD D 80, 075001 (2009)
0 200 400 600 800 10000
10
20
30
40
50
60
!"#$%$&'()$*+,-./-+($0-))$0%%$12'34
5,'+()678$2'3698$:%!9
LHC @ 14 TeV
0 200 400 600 800 10000
50
100
150
200
250
300
350SUSY
SM
In HWM gluino is light and will be produced in significant amounts at the LHC. Now
g ! bb + !0, and so mg " (Mbbinv)kink + m!0 . Embedded window shows mass
distributions for SUSY and SM with a 200 GeV EmissT cut. To suppress SM
background take (i) a 400 GeV EmissT cut, (ii) two more jets besides 2 b-tagged jets.
Monojet SignaturesFeldman, Liu, PN, Nelson, PRD 80, 075001 (2009)
HWM PWM
Object Cuts (GeV) Events S/√
B Events S/√
B
pjetT ≥ 150, #ET ≥ 150 1994 2.13 3442 3.68
pjetT ≥ 200, #ET ≥ 150 1302 2.52 1983 3.84
pjetT ≥ 150, #ET ≥ 200 1334 2.53 2147 4.08
pjetT ≥ 200, #ET ≥ 200 1241 2.58 1904 3.95
pjetT ≥ 150, #ET ≥ 300 659 3.57 771 4.17
Table: Monojet signature for the HWM and the PWM: Event counts are after100 fb!1 of integrated luminosity for various choices of cuts on total !ET and jet pT .All signatures involve a lepton veto and require no other jets in the event with
pjetT " 20 GeV. No transverse sphericity cut was applied in any of these signatures.
Multicomponent dark matterFeldman, Liu, PN, Peim, arXiv:1004.0649
PRD to appear
Dark matter may be constituted of more than one component.
!CDM h2 =X
i
!CDM ih2.
U(1)X × U(1)C extension where U(1)X is hidden sector and U(1)C is theanomaly free combination Le − Lµ .
L = LMSSM + LU (1)2 + "L,
where LU (1)2 is the kinetic energy for the X and C multiplets and for LSt weassume the following form
"L =
Zd2!d2! [(M1C + M!
2X + S + S)2 + (M!1C + M2X + S! + S!)2].
A Dirac fermion is placed in the hidden sector. The new particles in this model consistof
spin 0 : ", "!, #, #!
spin1
2: $, %0
5, %06, %0
7, %08
spin 1 : Z!, Z!!.
Various other works on multicomponent DMJE Kim
Cirelli, Cline---
!! (Q
Y,Q
X)
U(1)X SU(3)
C X SU(2)
L X U(1)
Y
Connector
Sector
Visible
Sector
MSSM (B","
B, D
B) (C
","
C, D
C)
Stueckelberg
FI D Terms Hidden
Sector
U(1)n
Axions
Mixing between U_X(hidden) and U_Y (hypercharge) as a probe of the hidden sector was introduced in Kors, PN, Phys.Lett.B586:366-372,2004.
Hidden Sector and Leptophilic Couplings
The basic interaction of Xµ and of Cµ with matter is given by
Lint = gXQX!"µ!Xµ +∑
f
gCQfCf"µfCµ
where f runs over e and µ families and where QeC = !Qµ
C. Inthe mass diagonal basis the interaction assumes the form
Lint = (gXQX!"µ! cos #X !∑
f
gCQfCf"µf sin #X)Z!
µ
+(gXQX!"µ! sin #X +∑
f
gCQfCf"µf cos #X)Z!!
µ.
These interactions lead to the annihilation of !! into e+e" andµ+µ" via the Z!, Z!! poles for which we assume Breit-Wignerforms.
Z′ and Z′′ resonances
The partial Z′, Z′′ decay widths
Γ(Z′ → ff) = (gC QfC sin !X )2
MZ !
12",
Γ(Z′′ → ff) = (gC QfC cos !X )2
MZ !!
12",
Γ(Z′ → ##) = (gC QfC cos !X )2
MZ !
12"(1 +
2M2ψ
M2Z !
)(1 −4M2
ψ
M2Z !
)1/2Θ(MZ ! − 2Mψ ) (1)
and similarly for the partial decay width of the Z′′ into ## with MZ ! → MZ !! andcos !X → sin !X .
For small mixing angle !X Z′ decay width into ff is much smaller than theZ′′ decay width into ff.
If Mψ $ MZ !/2, the Z′ decay width into ## will be small due tokinematical suppression while the Z′′ decay width into ## will be small due tomixing angle.
The above results in Z′ to be a narrow resonance.
Constraints from gµ ! 2
Their exchange gives
∆(gµ ! 2) =g2
Cm2µ
24π2
[sin2 θX
M2Z!
+cos2 θX
M2Z!!
].
The current error is
∆(gµ ! 2) = 1.2 " 10!9
in the determination of gµ ! 2.Assuming θX is small, one finds the following constraint on αC,
αC ! 0.001(
MZ!!
300 GeV
)2
,
where αC = g2C/4π. Precision electroweak fits are una!ected.
Dark matter possibilities in the U(1)X ! U(1)C extension.
Two component dark matter: Dirac (!), Majorana (").
Three component dark matter: Dirac (!), scalars (#, #!).
Four component dark matter:Dirac (!), Majorana (")and scalars (#, #!, ).
Two component dark matter: ! and "
! + ! " Z, Z!, $ " SM + SM!,
" + " " (s : Z!, Z, h, H, A, %), (t/u : fa, "i, "±k )
" SM + SM! + plus coannihilations
Boltzmann equations for the two component model
dn!
dt= !3Hn! !
1
2"σv#!! (n2
! ! n2!,eq), (3)
dn"
dt= !3Hn" ! "σv#""(n2
" ! n2",eq) +
1
2"σv#!!!""(n2
! ! n2!,eq).
Here "σv#!! refers to ψψ $ ff, χχ, and "σv#"" stands for "σv#""!SM SM! .
Total relic density
(!h2)WMAP = (!!h2)0 + (!"h2)0 %C!
J!0
+C"
J"0
,
C" %1.07 & 109 GeV"1
pg#(χ)Mpl
, C! % 2 &1.07 & 109 GeV"1
pg#(ψ)Mpl
,
J"0 =
Z xχf
0"σv#"" dx , J!
0 =
Z xψf
0"σv#!! dx .
The local density of dark matter
ρ$,!/ρ$," ' (!!h2)0/(!"h2)0.
Multi-component Dark Matter
Feldman, Liu, PN, Peim arXiv:1004.0649000
Positron flux p flux
!"#$%&$'&&'()*$+(,*-./(01$"23*%2
&$'&&'()*$+(,*-./(01$"23*%2
!!(U(1)X : Bhaloe = 5, Ωh2
! = (50%)(Ωh2)!+"
456('0,
!!((U(1)X !U(1)C : Bhaloe = 2, Ωh2
! = (60%)(Ωh2)!+"
E GeV
e/(e
+e)
788
787
789
78!9
78!7
!!"#$%!&'()*!!+,&!-.!/!/%!012*
!3451647!851%9:!'!!!012!
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?8@@
A);BCA8
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+F!+
+FF
+F+
+F.
+F!G
+F!H
+F!I
+F!J
+F!K
+F!.
+F!+
Two-component Dark Matter Model
Feldman, Liu, PN, Peim arXiv:1004.0649000
Photon flux !SI
!"!!!#$%!
!"&!'!"!(!'"!!!)$%(*+&(,(,-
0
o < l < 360
o
10o < |b| < 20
o
!!"#."/
0".)1!23
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722
727
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72!;
72!&
<=*>!?#@"#A
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Neutralino Component Mass (GeV)
!S
I (
cm
2)
!
!
"# $# %# &## &'# &"# &$#&#
!"(
&#!"$
&#!")
&#!""
&#!"*
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&#!"&
+,-./0!///!'##%
1,020&#!'##(
3456!6789:;!'##%
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!3456!6789:;!?@AAB
1,020&##!'#&#
0.6-!3C:DEF;7
0.6-!3&"!0
'
0.6-!6G7H
0.6-!6G:8
0.6-!=A8F;7
How large a spin independent cross section in neutralinoproton scattering?
Explore the cross sections under the following set of constraints
Radiative electroweak symmetry breaking constraint (REWSB)
Relic density constraint
Experimental constraints on sparticle masses, FCNCconstraints etc.
One finds that REWSB constraints by themselves allow !SI aslarge as 10−40 cm−2 or even larger. However, the cross sectionsare cut down under the relic density and other experimentalconstraints. Specifically it is di!cult to get !SI ! 10−40 cm−2
at m! = 10 GeV with all the experimental constraints imposed.
COGENT Feldman, Liu, PN arXiv: 1003.0437,
PRD to appear
LSP Neutralino Mass (GeV)
!S
I c
m2
!
!
" #$ #" %$ %" &$ &" '$ '" "$#$
!''
#$!'&
#$!'%
#$!'#
#$!'$
CoGeNT 2010DAMA/LIBRA Interp.
Compatible
REWSB ONLY:
NO MASS LIMITS, NO WMAP,
NO FLAVOR CONSTRAINTS
LSP Neutralino Mass (GeV) !
SI c
m2
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CoGeNT 2010DAMA/LIBRA Interp.
Compatible
REWSB AND SPARTICLE
MASS LIMITS IMPOSED.
SQUARE IN WMAP RANGE.
Difficult to get 10−40 cm2 at m! = 10 GeV with REWSB andexperimental constraints.
Also: Kuflick, Pierce, Zurek
Conclusions
The LHC data will be very helpful in establishing the earlyhistory of the universe, e.g., whether dark matter originatedvia stau co-annihilation or on the hyperbolic branch, or bysome other mechanism.
Dark matter experiments along with LHC data will helpdecipher the nature of dark matter including if it isconstituted of one or more than one components.
Extra Transparencies
Positron excess vs WMAP
The basic issue: one needs < σv >∼ 10!24cm3/s for positronexcess and < σv >∼ 10!26cm3/s for relic density. Di!erentpossibilities
Breit-Wigner pole enhancement of < σv > in the galaxyFeldman, Liu, PN; Ibe, Murayama, Yanagida
The Boost from Coannihilation (BCo) mechanism to enhancerelic densityFeldman, Liu, PN, Nelson
Sommerfeld enhancement
Non-thermal processes to enhance relic density.
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Enhancement of annihilation cross section in the galaxy
Feldman, Liu, PN, PRD 79, 063509 (2009)
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