Research ArticleMSSM Dark Matter in Light of Higgs and LUX Results

W Abdallah12 and S Khalil1

1Center for Fundamental Physics Zewail City of Science and Technology 6th of October City Giza 12588 Egypt2Department of Mathematics Faculty of Science Cairo University Giza 12613 Egypt

Correspondence should be addressed to W Abdallah wabdallahzewailcityedueg

Received 26 September 2015 Accepted 6 December 2015

Academic Editor Enrico Lunghi

Copyright copy 2016 W Abdallah and S Khalil This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited The publication of this article was funded by SCOAP3

The constraints imposed on theMinimal Supersymmetric StandardModel (MSSM) parameter space by the Large Hadron Collider(LHC) Higgs mass limit and gluino mass lower bound are revisited We also analyze the thermal relic abundance of lightestneutralino which is the Lightest Supersymmetric Particle (LSP) We show that the combined LHC and relic abundance constraintsrule out most of the MSSM parameter space except a very narrow region with very large tan120573 (sim50) Within this region weemphasize that the spin-independent scattering cross section of the LSP with a proton is less than the latest Large UndergroundXenon (LUX) limit by at least two orders of magnitude Finally we argue that nonthermal Dark Matter (DM) scenario mayrelax the constraints imposed on the MSSM parameter space Namely the following regions are obtained 119898

0≃ O(4)TeV and

11989812

≃ 600GeV for low tan120573 (sim10)1198980sim 119898

12≃ O(1) TeV or119898

0≃ O(4)TeV and119898

12≃ 700GeV for large tan120573 (sim50)

1 Introduction

The most recent observations by the Planck satellite con-firmed that 268 of the universe content is in the form ofDM and the usual visible matter only accounts for 5 [1]The LSP remains one of the best candidates for the DM [2 3]It is a Weakly Interacting Massive Particle (WIMP) that cannaturally account for the observed relic density of DM

Despite the absence of direct experimental verificationSupersymmetry (SUSY) is still the most promising candidatefor a unified theory beyond the Standard Model (SM) SUSYis a generalization of the space-time symmetries of the quan-tum field theory that links the matter particles (quarks andleptons) with the force-carrying particles and implies thatthere are additional ldquosuperparticlesrdquo necessary to completethe symmetry In this regard SUSY solves the problem of thequadratic divergence in the Higgs sector of the SM in a veryelegant natural way The most simple supersymmetric exten-sion of the SM which is the most widely studied is known asthe MSSM [4ndash11] In this model certain universality of softSUSY breaking terms is assumed at grand unification scaleTherefore the SUSY spectrum is determined by the followingfour parameters universal scalar mass119898

0 universal gaugino

mass 11989812

universal trilinear coupling 1198600 and the ratio of

the vacuum expectation values of Higgs bosons tan120573 Inaddition due to 119877-parity conservation SUSY particles areproduced or destroyed only in pairs and therefore the LSP isabsolutely stable implying that it might constitute a possiblecandidate for DM as first suggested by Goldberg in 1983 [12]So although the original motivation of SUSY has nothing todo with the DM problem it turns out that it provides a stableneutral particle and hence a candidate for solving the DMproblem

The landmark discovery of the SM-like Higgs boson atthe LHC with mass sim125GeV [13 14] might be an indicationfor the presence of SUSY Indeed the MSSM predicts thatthere is an upper bound of 130GeV on the Higgs massHowever this mass of lightest Higgs boson implies that theSUSY particles are quite heavy This may justify the negativesearches for SUSY at the LHC run-I [15ndash18] However it isclearly generating a new ldquolittle hierarchy problemrdquo

Moreover the relic density data [1] and upper limits onthe DM scattering cross sections on nuclei (LUX [19] andother direct detection experiments [20 21]) impose stringentconstraints on the parameter space of the MSSM [22ndash25]In fact combining the collider astrophysics and rare decay

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2016 Article ID 5687463 10 pageshttpdxdoiorg10115520165687463

2 Advances in High Energy Physics

constraints [26ndash36] almost rules out theMSSM It is temptingtherefore to explore well motivated extensions of the MSSMsuch as NMSSM [37 38] and BLSSM [39 40] which mayalleviate the little hierarchy problem of the MSSM throughadditional contributions to Higgs mass [37 38 41] and alsoprovide newDMcandidates [42ndash45] thatmay account for therelic density with no conflict with other phenomenologicalconstraints

In this paper we analyze the constraints imposed by theHiggs mass limit and the gluino lower bound which are themost stringent collider constraints on the constrainedMSSM(minimal SUGRA model hereafter referred to as MSSM)parameter space In particular these constraints imply thatthe gaugino mass 119898

12 resides within the mass range

620GeV ≲ 11989812

≲ 2000GeV while the other parameters aremuch less constrained We study the effect of the measuredDM relic density on the MSSM allowed parameter spaceWe emphasized that in this case all parameter space is ruledout except for few points around tan120573 sim 50 119898

0sim 1TeV

and 11989812

sim 15TeV We also investigate the direct detectionrate of the LSP at these allowed points in light of the latestLUX result Finally we show that if one assumes nonstandardscenario of cosmologywith low reheating temperature wherethe LSP may reach equilibrium before the reheating timethen the relic abundance constraints on (119898

0 119898

12) can be

significantly relaxedThe paper is organized as follows In Section 2 we briefly

introduce the MSSM and study the constraints on (1198980 119898

12)

plane from Higgs and gluino mass experimental limits InSection 3 we study the thermal relic abundance of the LSPin the allowed region of parameter space We show that thecombined LHCand relic abundance constraints rule outmostof the parameter space except the case of very large tan120573We also provide the expected rate of direct LSP detection atthese points with large tan120573 and TeV masses Section 4 isdevoted to nonthermal scenario of DM and how it can relaxthe constraints imposed on MSSM parameter space Finallywe give our conclusions in Section 5

2 MSSM after the LHC Run-I

The particle content of the MSSM is three generations of(chiral) quark and lepton superfields the (vector) superfieldsare necessary to gauge 119878119880(3)

119862times 119878119880(2)

119871times119880(1)

119884gauge of the

SM and two (chiral) 119878119880(2) doublet Higgs superfields Theintroduction of a second Higgs doublet is necessary in orderto cancel the anomalies produced by the fermionic membersof the first Higgs superfield and also to givemasses to both upand down type quarks The interactions between Higgs andmatter superfields are described by the superpotential

119882 = ℎ119880119876

119871119880119888

119871119867

2+ ℎ

119863119876

119871119863119888

119871119867

1+ ℎ

119871119871119871119864119888

119871119867

1

+ 1205831198671119867

2

(1)

Here119876119871contains 119878119880(2) (s)quark doublets and119880119888

119871119863119888

119871are the

corresponding singlets (s)lepton doublets and singlets residein 119871

119871and 119864119888

119871 respectively 119867

1and 119867

2denote Higgs super-

fields with hypercharge 119884 = ∓12 Further due to the factthat Higgs and lepton doublet superfields have the same

119878119880(3)119862

times 119878119880(2)119871times 119880(1)

119884quantum numbers we have

additional terms that can be written as

1198821015840 = 120582119894119895119896119871119894119871119895119864119888

119896+ 1205821015840

119894119895119896119871119894119876

119895119863119888

119896+ 12058210158401015840

119894119895119896119863119888

119894119863119888

119895119880119888

119896

+ 120583119894119871119894119867

2

(2)

These terms violate baryon and lepton number explicitly andlead to proton decay at unacceptable rates To forbid theseterms a new symmetry called 119877-parity is introduced whichis defined as 119877

119875= (minus1)3119861+119871+2119878 where 119861 and 119871 are baryon and

lepton number and 119878 is the spin There are two remarkablephenomenological implications of the presence of 119877-parity(i) SUSY particles are produced or destroyed only in pair (ii)the LSP is absolutely stable and hence it might constitute apossible candidate for DM

In theMSSM a certain universality of soft SUSY breakingterms at grand unification scale 119872

119883= 3 times 1016 GeV is

assumed These terms are defined as 1198980 the universal scalar

softmass11989812

the universal gauginomass1198600 the universal

trilinear coupling 119861 and the bilinear coupling (the softmixing between the Higgs scalars) In order to discuss thephysical implication of soft SUSY breaking at low energywe need to renormalize these parameters from 119872

119883down to

electroweak scale which has been performed using SARAH[46] and the spectrum has been calculated using SPheno [4748] In addition the MSSM contains another two free SUSYparameters 120583 and tan120573 = ⟨119867

2⟩⟨119867

1⟩ Two of these free

parameters 120583 and 119861 can be determined by the electroweakbreaking conditions

1205832 =1198982

1198671

minus 1198982

1198672

tan2120573tan2120573 minus 1

minus1198722

119885

2 (3)

sin 2120573 =minus21198982

3

1198982

1+ 1198982

2

(4)

Thus the MSSM has only four independent free parameters119898

0 119898

12 119860

0 tan120573 besides the sign of120583 which determine the

whole spectrumIn the MSSM the mass of the lightest Higgs state can be

approximated at the one-loop level as [49ndash52]

1198982

ℎle 1198722

119885+

31198922

1612058721198722

119882

1198984

119905

sin2120573log(

1198982

1

1198982

2

1198984

119905

) (5)

Therefore if one assumes that the stop masses are of orderTeV then the one-loop effect leads to a correction of orderO(100) GeV which implies that

119898MSSMℎ

≲ radic(90GeV)2 + (100GeV)2 ≃ 135GeV (6)

The two-loop corrections reduce this upper bound by fewGeVs [53ndash55] Hence theMSSMpredicts the following upperbound for the Higgs mass119898

ℎ≲ 130GeV which was consist-

ent with themeasured value of Higgsmass (of order 125GeV)at the LHC [13 14]

In Figure 1 we display the contour plot of the SM-like Higgs boson 119898

ℎisin [124 126]GeV in (119898

0 119898

12)

Advances in High Energy Physics 3

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

(a)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

(b)

Figure 1 MSSM parameter space for tan120573 = 10 (a) and 50 (b) with 1198600= 0 and 2 TeV The green region indicates 124 ≲ 119898

ℎ≲ 126GeV The

blue region is excluded because the lightest neutralino is not the LSPThe pink region is excluded due to the absence of radiative electroweaksymmetry breaking (1205832 becomes negative) The gray shadow lines denote the excluded area because of119898

lt 14TeV

plane for different values of 1198600and tan120573 It is remarkable

that the smaller the value of 1198600is the smaller the value

of 11989812

is needed to satisfy this value of Higgs mass Itis also clear that the scalar mass 119898

0remains essentially

unconstrained by Higgs mass limit It can vary from fewhundred GeVs to few TeVs Such large values of 119898

12seem

to imply a quite heavy SUSY spectrum much heavier thanthe lower bound imposed by direct searches at the LHCexperiments in centre of mass energies radic119904 = 7 8TeV andtotal integrated luminosity of order 20 fbminus1 Furthermorethe LHC lower limit on the gluino mass 119898

≳ 14TeV

[56 57] excluded the values of 11989812

lt 620GeV whichwas allowed by Higgs mass constraints for 119898

0gt 4TeV

Furthermore this region is shown with dashed lines inFigure 1

3 Dark Matter Constraints onMSSM Parameter Space

31 The LSP as Dark Matter Candidate The neutralinos 120594119894

(119894 = 1 2 3 4) are the physical (mass) superpositions of twofermionic partners of the two neutral gauge bosons calledgaugino

0 (bino) and 0

3(wino) and of the two neutral

Higgs bosons called Higgsinos 0

1and

0

2 The neutralino

mass matrix is given by [58ndash61]

119872119873= (

(

1198721

0 minus119872119885cos120573 sin 120579

119882119872

119885sin120573 sin 120579

119882

0 1198722

119872119885cos120573 cos 120579

119882minus119872

119885sin120573 cos 120579

119882

minus119872119885cos120573 sin 120579

119882119872

119885cos120573 cos 120579

1198820 minus120583

119872119885sin120573 sin 120579

119882minus119872

119885sin120573 cos 120579

119882minus120583 0

)

)

(7)

4 Advances in High Energy Physics

where 1198721and 119872

2are related due to the universality of

the gaugino masses at the grand unification scale 1198721

=

(31198922

151198922

2)119872

2 where 119892

1 119892

2are the gauge couplings of 119880(1)

119884

and 119878119880(2)119871 respectively This Hermitian matrix is diago-

nalized by a unitary transformation of the neutralino fields119872

diag119873

= 119873dagger119872119873119873 The lightest eigenvalue of this matrix and

the corresponding eigenstate say 120594 has good chance of beingthe LSP The lightest neutralino will be a linear combinationof the original fields

120594 = 119873110

+ 11987312

0

+ 11987313

0

1+ 119873

14

0

2 (8)

The phenomenology and cosmology of the neutralino aregoverned primarily by its mass and composition A usefulparameter for describing the neutralino composition is thegaugino ldquopurityrdquo function119891

119892= |119873

11|2+|119873

12|2 [58ndash61] If119891

119892gt

05 then the neutralino is primarily gaugino and if 119891119892lt 05

then the neutralino is primarily Higgsino Actually if |120583| gt|119872

2| ge 119872

119885 the two lightest neutralino states will be deter-

mined by the gaugino components similarly the light char-gino will be mostly a charged wino while if |120583| lt |119872

2| the

two lighter neutralinos and the lighter chargino are all mostlyHiggsinos with mass close to |120583| Finally if |120583| ≃ |119872

2| the

states will be strongly mixedHere two remarks are in order (i) The abovementioned

constraints in 11989812

from Higgs mass limit and gluino masslower bound imply that 119898

120594≳ 240GeV which is larger

than the limits obtained from direct searches at the LHCMoreover an upper bound of order one TeV is also obtained(from Higgs mass constraint) (ii) In this region of allowedparameter space the LSP is essentially pure bino as shown inFigure 2 This can be easily understood from the fact that 120583-parameter determined by the radiative electroweak breakingcondition (3) is typically of order 119898

0and hence it is much

heavier than the gaugino mass1198721

32 Relic Density As advocated in the previous section theLSP inMSSM the lightest neutralino 120594 is a perfect candidatefor DM Here we assume that 120594 was in thermal equilibriumwith the SM particles in the early universe and decoupledwhen it was nonrelativistic Once 120594 annihilation rate Γ

120594=

⟨120590ann120594

V⟩119899120594dropped below the expansion rate of the universe

Γ120594le 119867 the LSP particles stop to annihilate and fall out of

equilibriumand their relic density remains intact till nowTheabove ⟨120590ann

120594V⟩ refers to thermally averaged total cross section

for annihilation of 120594120594 into lighter particles times the relativevelocity V

The relic density is then determined by the Boltzmannequation for the LSP number density (119899

120594) and the law of

entropy conservation

119889119899120594

119889119905= minus3119867119899

120594minus ⟨120590ann

120594V⟩ [(119899

120594)2

minus (119899eq120594)2

]

119889119904

119889119905= minus3119867119904

(9)

where 119899eq120594

is the LSP equilibrium number density whichas a function of temperature 119879 is given by 119899eq

120594=

300 400 500 600 700 800 900096

097

098

099

100

fg

m120594 (GeV)

Figure 2The mass of lightest neutralino versus the purity functionin the region of parameter space allowed by gluino and Higgs masslimits

119892120594(119898

1205941198792120587)32119890minus119898120594119879 Here119898

120594and 119892

120594are the mass and the

number of degrees of freedomof the LSP respectively Finally119904 is the entropy density In the standard cosmology the Hub-ble parameter 119867 is given by 119867(119879) = 2120587radic120587119892

lowast45(1198792119872

119875119897)

where 119872119875119897= 122 times 1019 GeV and 119892

lowastis the number of rela-

tivistic degrees of freedom for MSSM 119892lowast≃ 22875 Let us

introduce the variable 119909 = 119898120594119879 and define 119884 = 119899

120594119904 with

119884eq = 119899eq120594119904 In this case the Boltzmann equation is given by

119889119884

119889119909=

1

3119867

119889119904

119889119909⟨120590ann

120594V⟩ (1198842 minus 1198842

eq) (10)

In radiation domination era the entropy as a function of thetemperature is given by

119904 (119909) =21205872

45119892lowast119904(119909)119898

3

120594119909minus3 (11)

which is deduced from the fact that 119904 = (120588 + 119901)119879 and 119892lowast119904

is the effective degrees of freedom for the entropy densityTherefore one finds

119889119904

119889119909= minus

3119904

119909 (12)

Thus with assuming 119892lowast≃ 119892

lowast119904

the following expression forthe Boltzmann equation for the LSP number density isobtained

119889119884

119889119909= minusradic

120587119892lowast

45119872

119875119897119898

120594

⟨120590ann120594

V⟩

1199092(1198842 minus 1198842

eq) (13)

If one considers the s-wave and p-wave annihilationprocesses only the thermal average ⟨120590ann

120594V⟩ then shows as

⟨120590ann120594

V⟩ ≃ 119886120594+6119887

120594

119909 (14)

Advances in High Energy Physics 5

f

AZ

f f

120594

120594

120594

120594

120594

120594

f

ff

f

Figure 3 Feynman diagrams contributing to early-universe neutralino 120594 annihilation into fermions through sfermions119885-gauge boson andHiggs

where 119886120594and 119887

120594are the s-wave and p-wave contributions of

annihilation processes respectively The relic density of theDM candidate is given by

Ωℎ2 =119898

1205941199040119884120594(infin)

120588119888ℎ2

(15)

where 1199040= 228215 times 10minus41 GeV3120588

119888= 80992ℎ2times10minus47 GeV4

and by solving the Boltzmann equation one can find 119884120594(infin)

as follows [62]

119884120594 (infin) =

1

120582120594

(119886120594

119909 (119879119891)+

3119887120594

1199092 (119879119891))

minus1

(16)

where 119879119891is the freeze-out temperature 120582

120594= 119904(119898

120594)119867(119898

120594)

and 119909(119879119891) is given by

119909 (119879119891) = ln[[

[

120572120594120582120594119888 (119888 + 2)

radic119909 (119879119891)

(119886120594+

6119887120594

119909 (119879119891))]]

]

(17)

where 120572120594= (4521205874)radic1205878(119892

120594119892

lowast119904

(119879119891)) the value 119888 = 12

results in a typical accuracy of about 5ndash10 more than suf-ficient for our purposes here

The lightest neutralino may annihilate into fermion-antifermion (119891119891) 119882+119882minus 119885119885 119882+119867minus 119885119860 119885119867 119885ℎ and119867+119867minus and all other contributions of neutral Higgs For abino-like LSP that is 119873

11≃ 1 and 119873

1119894≃ 0 119894 = 2 3 4 one

finds that the relevant annihilation channels are the fermion-antifermion ones as shown in Figure 3 and all other chan-nels are instead suppressed Also the annihilation processmediated by 119885-gauge boson is suppressed due to the small119885120594120594 coupling prop 1198732

13minus 1198732

14 except at the resonance when

119898120594sim 119872

1198852 which is no longer possible due to the above-

mentioned constraints Furthermore one finds that the t-channel annihilation (first Feynman diagram in Figure 3) ispredominantly into leptons through the exchanges of thethree slepton families (119897

119871 119877) with 119897 = 119890 120583 120591 The squarks

exchanges are suppressed due to their large massesIn Figure 4 we display the constraint from the observed

limits of Ωℎ2 on the plane (1198980-119898

12) for 119860

0= 0 2000GeV

tan120573 = 10 50 and 120583 gt 0 Here we used micrOMEGAs [63]to compute the complete relic abundance of the lightest

neutralino taking into account the possibility of having coan-nihilation with the next-to-lightest supersymmetric particlewhich is typically the lightest stau Note that this type of coan-nihilation is not included in the approximated expressions in(14)ndash(17) In this figure the red regions correspond to a relicabundance within the measured limits [1]

009 lt Ωℎ2 lt 014 (18)

It is noticeable that with low tan120573 (sim10) this region corre-sponds to light 119898

12(lt500GeV) where significant coanni-

hilation between the LSP and stau took place However thispossibility is now excluded by the Higgs and gluino massconstraints [64] At large tan120573 another region is alloweddue to possible resonance due to 119904-channel annihilation ofthe DM pair into fermion-antifermion via the pseudoscalarHiggs boson 119860 at 119872

119860≃ 2119898

120594[65] For 119860

0= 0 a very small

part of this region is allowed by the Higgs mass constraintwhile for large 119860

0(sim2 TeV) slight enhancement of this part

can be achieved In Figure 5 we zoom in on this region toshow the explicit dependence of the relic abundance on theLSP mass and large values of tan120573 As can be seen from thisfigure there is no point that can satisfy the relic abundancestringent constraints with tan120573 lt 30

33 Direct Detection Perhaps themost natural way of search-ing for the neutralino DM is provided by direct experi-ments where the effects induced in appropriate detectors byneutralino-nucleus elastic scattering may be measured Theelastic-scattering cross section of the LSPwith a given nucleushas two contributions spin-dependent contribution arisingfrom 119885 and exchange diagrams and spin-independent(scalar) contribution due to the Higgs and squark exchangediagrams which is typically suppressed The effective scalarinteraction of neutralino with a quark is given by

Lscalar = 119891119902120594120594119902119902 (19)

where 119891119902is the neutralino-quark effective coupling The

scalar cross section of the neutralino scattering with targetnucleus at zero momentum transfer is given by [2]

120590SI0=41198982

119903

120587(119885119891

119901+ (119860 minus 119885)119891

119899)2

(20)

where 119885 and 119860 minus 119885 are the number of protons and neu-trons respectively 119898

119903= 119898

119873119898

120594(119898

119873+ 119898

120594) where 119898

119873is

6 Advances in High Energy Physics

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 10 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

Figure 4 LSP relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The LUX result is satisfied by the

yellow region The other color codes are as in Figure 1

500 550 600 650 700 750 800009

010

011

012

013

014

Ωh2

m120594 (GeV)

Figure 5 The relic abundance versus the mass of the LSP fordifferent values of tan120573 Red points indicate 40 le tan120573 le 50 andblue points 30 le tan120573 lt 40 All points satisfy the abovementionedconstraints

the nucleus mass and 119891119901 119891

119899are the neutralino coupling

to protons and neutrons respectively The differential scalarcross section for nonzero momentum transfer 119902 can now bewritten

119889120590SI1198891199022

=120590SI0

41198982

119903V21198652 (1199022) 0 lt 1199022 lt 41198982

119903V2 (21)

10 20 50 100 200 500 1000 2000m120594 (GeV)

120590p SI(cm

2)

10minus45

10minus47

10minus49

10minus51

LUX

Figure 6 Spin-independent scattering cross section of the LSP witha proton versus the mass of the LSP within the region allowed by allconstraints (from the LHC and relic abundance)

where V is the neutrino velocity and 119865(1199022) is the form factor[2] In Figure 6 we display the MSSM prediction for spin-independent scattering cross section of the LSP with a proton(120590119901SI = int

41198982

119903V2

0(119889120590SI119889119902

2)|119891119899=119891119901

1198891199022) after imposing the LHC

Advances in High Energy Physics 7

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)

Figure 7 LSP nonthermal relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The color codes are

as in Figure 1

and relic abundance constraints It is clear that our results for120590119901

SI are less than the recent LUX bound (blue curve) by at leasttwo orders of magnitude This would explain the negativeresults of direct searches so far

4 Nonthermal Dark Matter andMSSM Parameter Space

In the previous section we assumed standard cosmologyscenario where the reheating temperature 119879RH is very largenamely119879RH ≫ 119879

119891≃ 10GeVHowever the only constraint on

the reheating temperature which could be associated withdecay of any scalar field 120601 not only the inflaton field is119879RH ≳ 1MeV in order not to spoil the successful predictionsof big bang nucleosynthesis

A detailed analysis of the relic density with a low reheat-ing temperature has been carried out in [66] It was empha-sized that for a large annihilation cross section ⟨120590annV⟩ ≳

10minus14 GeVminus2 so that the neutralino reaches equilibriumbefore reheating and if there are a large number of neutrali-nos produced by the scalar field 120601 decay then the relic densityis estimated as [67]

Ωℎ2 =3119898

120594Γ120601

2 (2120587245) 119892lowast(119879RH) 119879

3

RH ⟨120590ann120594

V⟩ℎ2

120588119888119904

0

(22)

Here the reheating temperature is defined as [62]

119879RH = (90

1205872119892lowast(119879RH)

)

14

(Γ120601119872

119875119897)12

(23)

where the decay width Γ120601is given by

Γ120601=

1

2120587

1198983

120601

Λ2 (24)

The scaleΛ is the effective suppression scale which is of orderthe grand unification scale119872

119883Therefore for scalar fieldwith

mass 119898120601≃ 107 GeV one finds Γ

120601≃ 10minus11 GeV and in our

calculations we have used 119892lowast

= 1075 due to the consid-eration of a low reheating temperature scenario

In Figure 7 we show the constraints imposed on theMSSM (119898

0-119898

12) plane in case of nonthermal relic abun-

dance of the LSP for tan120573 = 10 50 and 1198600= 0 2TeV In this

plot we also imposed the LHC constraints namely the Higgsmass limit and the gluino mass lower bound similar to thecase of thermal scenario It is clear from this figure that thestringent constraints imposed on theMSSM parameter spaceby thermal relic abundance are now relaxed and now lowtan120573 (sim10) is allowed but with very heavy 119898

0(simO(4)TeV)

and 11989812

≃ 600GeV In addition the following two regionsare now allowed with large tan120573 (sim50) (i) 119898

0sim 119898

12≃

8 Advances in High Energy Physics

O(1)TeV (ii)1198980≃ O(4)TeV and119898

12≃ 700GeV The SUSY

spectrum associated with these regions of parameters spacecould be striking signature for nonthermal scenario at theLHC

5 Conclusion

We have studied the constraints imposed on the MSSMparameter space by the Higgsmass limit and the gluino lowerbound which are the most stringent collider constraintsobtained from the LHC run-I at energy 8 TeV We showedthat 119898

12resides within the mass range 620GeV ≲ 119898

12≲

2000GeV while the other parameters (1198980 119860

0 tan120573) are

much less constrained We also studied the effect of themeasured DM relic density on the MSSM allowed parameterspace It turns out that most of the MSSM parameter spaceis ruled out except for few points around tan120573 sim 50119898

0sim 1TeV and 119898

12sim 15TeV We calculated the spin-

independent scattering cross section of the LSP with a protonin this allowed region We showed that our prediction for120590119901

SI is less than the recent LUX bound by at least two ordersof magnitude We have also analyzed the nonthermal DMscenario for the LSPWe showed that the constraints imposedon the MSSM parameter space are relaxed and low tan120573 isnow allowed with 119898

0≃ O(4)TeV and 119898

12≃ 600GeV Also

two allowed regions are now associated with large tan120573 (sim50) namely 119898

0sim 119898

12≃ O(1)TeV or 119898

0≃ O(4)TeV and

11989812

≃ 700GeV

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by the STDF Project 13858the ICTP Grant AC-80 and the European Union FP7 ITNINVISIBLES (Marie Curie Actions PITN-GA-2011-289442)

References

[1] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquo Astronomy ampAstrophysics vol 571 article A16 2014

[2] G Jungman M Kamionkowski and K Griest ldquoSupersymmet-ric dark matterrdquo Physics Report vol 267 no 5-6 pp 195ndash3731996

[3] G Bertone D Hooper and J Silk ldquoParticle dark matter evi-dence candidates and constraintsrdquo Physics Reports vol 405 no5-6 pp 279ndash390 2005

[4] H PNilles ldquoSupersymmetry supergravity andparticle physicsrdquoPhysics Reports vol 110 no 1-2 pp 1ndash162 1984

[5] J D Lykken ldquoIntroduction tosupersymmetryrdquo In press httparxivorgabshep-th9612114

[6] J Wess and J Bagger Supersymmetry and Supergravity Prince-ton University Press Princeton NJ USA 2nd edition 1991

[7] H E Haber and G Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[8] S P Martin ldquoA Supersymmetry Primerrdquo Advanced Series onDirections in High Energy Physics vol 21 pp 1ndash153 2010Advanced Series on Directions in High Energy Physics vol 18pp 1ndash98 1998

[9] D J H Chung L L Everett G L Kane S F King J D Lykkenand L TWang ldquoThe soft supersymmetry-breaking Lagrangiantheory and applicationsrdquo Physics Reports vol 407 no 1ndash3 pp 1ndash203 2005

[10] M Drees P Roy and R M GodboleTheory and Phenomenol-ogy of Sparticles World Scientific Singapore 2005

[11] H Baer and X Tata Weak Scale Supersymmetry From Super-fields to Scattering Events Cambridge University Press Cam-bridge UK 2006

[12] H Goldberg ldquoConstraint on the photino mass from cosmol-ogyrdquo Physical Review Letters vol 50 no 19 pp 1419ndash14221983 Erratum-ibid Physical Review Letters vol 103 Article ID099905 2009

[13] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[14] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoObser-vation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHCrdquo Physics Letters B vol 716 no 1 pp30ndash61 2012

[15] G Aad B Abbott J Abdallah et al ldquoSummary of the ATLASexperimentrsquos sensitivity to supersymmetry after LHC Run 1mdashinterpreted in the phenomenological MSSMrdquo Journal of HighEnergy Physics vol 2015 article 134 2015

[16] A Gaz ldquoSUSY searches at CMSrdquo In press httparxivorgabs14111886

[17] I Melzer-Pellmann and P Pralavorio ldquoLessons for SUSY fromthe LHC after the first runrdquo The European Physical Journal Cvol 74 article 2801 2014

[18] N Craig ldquoThe state ofsupersymmetry after Run I of the LHCrdquohttparxivorgabs13090528

[19] D S Akerib H M Araujo X Bai et al ldquoFirst results from theLUX dark matter experiment at the Sanford UndergroundResearch Facilityrdquo Physical Review Letters vol 112 Article ID091303 2014

[20] E Aprile ldquoThe Xenon1T dark matter search experimentrdquo inSources and Detection of Dark Matter and Dark Energy in theUniverse vol 148 of Springer Proceedings in Physics pp 93ndash96Springer 2013

[21] E AprileMAlfonsi K Arisaka et al ldquoDarkmatter results from225 live days of XENON100 datardquo Physical Review Letters vol109 no 18 Article ID 181301 6 pages 2012

[22] H Baer V Barger and A Mustafayev ldquoImplications of a125GeV Higgs scalar for the LHC supersymmetry and neu-tralino dark matter searchesrdquo Physical Review D vol 85 ArticleID 075010 2012

[23] J Ellis and K A Olive ldquoRevisiting the higgs mass and darkmatter in the CMSSMrdquo The European Physical Journal C vol72 article 2005 2012

[24] O Buchmueller R Cavanaugh M Citron et al ldquoThe CMSSMand NUHM1 in light of 7 TeV LHC 119861

119904rarr 120583+120583minus and

XENON100 datardquoThe European Physical Journal C vol 72 no11 article 2243 2012

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

2 Advances in High Energy Physics

constraints [26ndash36] almost rules out theMSSM It is temptingtherefore to explore well motivated extensions of the MSSMsuch as NMSSM [37 38] and BLSSM [39 40] which mayalleviate the little hierarchy problem of the MSSM throughadditional contributions to Higgs mass [37 38 41] and alsoprovide newDMcandidates [42ndash45] thatmay account for therelic density with no conflict with other phenomenologicalconstraints

In this paper we analyze the constraints imposed by theHiggs mass limit and the gluino lower bound which are themost stringent collider constraints on the constrainedMSSM(minimal SUGRA model hereafter referred to as MSSM)parameter space In particular these constraints imply thatthe gaugino mass 119898

12 resides within the mass range

620GeV ≲ 11989812

≲ 2000GeV while the other parameters aremuch less constrained We study the effect of the measuredDM relic density on the MSSM allowed parameter spaceWe emphasized that in this case all parameter space is ruledout except for few points around tan120573 sim 50 119898

0sim 1TeV

and 11989812

sim 15TeV We also investigate the direct detectionrate of the LSP at these allowed points in light of the latestLUX result Finally we show that if one assumes nonstandardscenario of cosmologywith low reheating temperature wherethe LSP may reach equilibrium before the reheating timethen the relic abundance constraints on (119898

0 119898

12) can be

significantly relaxedThe paper is organized as follows In Section 2 we briefly

introduce the MSSM and study the constraints on (1198980 119898

12)

plane from Higgs and gluino mass experimental limits InSection 3 we study the thermal relic abundance of the LSPin the allowed region of parameter space We show that thecombined LHCand relic abundance constraints rule outmostof the parameter space except the case of very large tan120573We also provide the expected rate of direct LSP detection atthese points with large tan120573 and TeV masses Section 4 isdevoted to nonthermal scenario of DM and how it can relaxthe constraints imposed on MSSM parameter space Finallywe give our conclusions in Section 5

2 MSSM after the LHC Run-I

The particle content of the MSSM is three generations of(chiral) quark and lepton superfields the (vector) superfieldsare necessary to gauge 119878119880(3)

119862times 119878119880(2)

119871times119880(1)

119884gauge of the

SM and two (chiral) 119878119880(2) doublet Higgs superfields Theintroduction of a second Higgs doublet is necessary in orderto cancel the anomalies produced by the fermionic membersof the first Higgs superfield and also to givemasses to both upand down type quarks The interactions between Higgs andmatter superfields are described by the superpotential

119882 = ℎ119880119876

119871119880119888

119871119867

2+ ℎ

119863119876

119871119863119888

119871119867

1+ ℎ

119871119871119871119864119888

119871119867

1

+ 1205831198671119867

2

(1)

Here119876119871contains 119878119880(2) (s)quark doublets and119880119888

119871119863119888

119871are the

corresponding singlets (s)lepton doublets and singlets residein 119871

119871and 119864119888

119871 respectively 119867

1and 119867

2denote Higgs super-

fields with hypercharge 119884 = ∓12 Further due to the factthat Higgs and lepton doublet superfields have the same

119878119880(3)119862

times 119878119880(2)119871times 119880(1)

119884quantum numbers we have

additional terms that can be written as

1198821015840 = 120582119894119895119896119871119894119871119895119864119888

119896+ 1205821015840

119894119895119896119871119894119876

119895119863119888

119896+ 12058210158401015840

119894119895119896119863119888

119894119863119888

119895119880119888

119896

+ 120583119894119871119894119867

2

(2)

These terms violate baryon and lepton number explicitly andlead to proton decay at unacceptable rates To forbid theseterms a new symmetry called 119877-parity is introduced whichis defined as 119877

119875= (minus1)3119861+119871+2119878 where 119861 and 119871 are baryon and

lepton number and 119878 is the spin There are two remarkablephenomenological implications of the presence of 119877-parity(i) SUSY particles are produced or destroyed only in pair (ii)the LSP is absolutely stable and hence it might constitute apossible candidate for DM

In theMSSM a certain universality of soft SUSY breakingterms at grand unification scale 119872

119883= 3 times 1016 GeV is

assumed These terms are defined as 1198980 the universal scalar

softmass11989812

the universal gauginomass1198600 the universal

trilinear coupling 119861 and the bilinear coupling (the softmixing between the Higgs scalars) In order to discuss thephysical implication of soft SUSY breaking at low energywe need to renormalize these parameters from 119872

119883down to

electroweak scale which has been performed using SARAH[46] and the spectrum has been calculated using SPheno [4748] In addition the MSSM contains another two free SUSYparameters 120583 and tan120573 = ⟨119867

2⟩⟨119867

1⟩ Two of these free

parameters 120583 and 119861 can be determined by the electroweakbreaking conditions

1205832 =1198982

1198671

minus 1198982

1198672

tan2120573tan2120573 minus 1

minus1198722

119885

2 (3)

sin 2120573 =minus21198982

3

1198982

1+ 1198982

2

(4)

Thus the MSSM has only four independent free parameters119898

0 119898

12 119860

0 tan120573 besides the sign of120583 which determine the

whole spectrumIn the MSSM the mass of the lightest Higgs state can be

approximated at the one-loop level as [49ndash52]

1198982

ℎle 1198722

119885+

31198922

1612058721198722

119882

1198984

119905

sin2120573log(

1198982

1

1198982

2

1198984

119905

) (5)

Therefore if one assumes that the stop masses are of orderTeV then the one-loop effect leads to a correction of orderO(100) GeV which implies that

119898MSSMℎ

≲ radic(90GeV)2 + (100GeV)2 ≃ 135GeV (6)

The two-loop corrections reduce this upper bound by fewGeVs [53ndash55] Hence theMSSMpredicts the following upperbound for the Higgs mass119898

ℎ≲ 130GeV which was consist-

ent with themeasured value of Higgsmass (of order 125GeV)at the LHC [13 14]

In Figure 1 we display the contour plot of the SM-like Higgs boson 119898

ℎisin [124 126]GeV in (119898

0 119898

12)

Advances in High Energy Physics 3

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

(a)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

(b)

Figure 1 MSSM parameter space for tan120573 = 10 (a) and 50 (b) with 1198600= 0 and 2 TeV The green region indicates 124 ≲ 119898

ℎ≲ 126GeV The

blue region is excluded because the lightest neutralino is not the LSPThe pink region is excluded due to the absence of radiative electroweaksymmetry breaking (1205832 becomes negative) The gray shadow lines denote the excluded area because of119898

lt 14TeV

plane for different values of 1198600and tan120573 It is remarkable

that the smaller the value of 1198600is the smaller the value

of 11989812

is needed to satisfy this value of Higgs mass Itis also clear that the scalar mass 119898

0remains essentially

unconstrained by Higgs mass limit It can vary from fewhundred GeVs to few TeVs Such large values of 119898

12seem

to imply a quite heavy SUSY spectrum much heavier thanthe lower bound imposed by direct searches at the LHCexperiments in centre of mass energies radic119904 = 7 8TeV andtotal integrated luminosity of order 20 fbminus1 Furthermorethe LHC lower limit on the gluino mass 119898

≳ 14TeV

[56 57] excluded the values of 11989812

lt 620GeV whichwas allowed by Higgs mass constraints for 119898

0gt 4TeV

Furthermore this region is shown with dashed lines inFigure 1

3 Dark Matter Constraints onMSSM Parameter Space

31 The LSP as Dark Matter Candidate The neutralinos 120594119894

(119894 = 1 2 3 4) are the physical (mass) superpositions of twofermionic partners of the two neutral gauge bosons calledgaugino

0 (bino) and 0

3(wino) and of the two neutral

Higgs bosons called Higgsinos 0

1and

0

2 The neutralino

mass matrix is given by [58ndash61]

119872119873= (

(

1198721

0 minus119872119885cos120573 sin 120579

119882119872

119885sin120573 sin 120579

119882

0 1198722

119872119885cos120573 cos 120579

119882minus119872

119885sin120573 cos 120579

119882

minus119872119885cos120573 sin 120579

119882119872

119885cos120573 cos 120579

1198820 minus120583

119872119885sin120573 sin 120579

119882minus119872

119885sin120573 cos 120579

119882minus120583 0

)

)

(7)

4 Advances in High Energy Physics

where 1198721and 119872

2are related due to the universality of

the gaugino masses at the grand unification scale 1198721

=

(31198922

151198922

2)119872

2 where 119892

1 119892

2are the gauge couplings of 119880(1)

119884

and 119878119880(2)119871 respectively This Hermitian matrix is diago-

nalized by a unitary transformation of the neutralino fields119872

diag119873

= 119873dagger119872119873119873 The lightest eigenvalue of this matrix and

the corresponding eigenstate say 120594 has good chance of beingthe LSP The lightest neutralino will be a linear combinationof the original fields

120594 = 119873110

+ 11987312

0

+ 11987313

0

1+ 119873

14

0

2 (8)

The phenomenology and cosmology of the neutralino aregoverned primarily by its mass and composition A usefulparameter for describing the neutralino composition is thegaugino ldquopurityrdquo function119891

119892= |119873

11|2+|119873

12|2 [58ndash61] If119891

119892gt

05 then the neutralino is primarily gaugino and if 119891119892lt 05

then the neutralino is primarily Higgsino Actually if |120583| gt|119872

2| ge 119872

119885 the two lightest neutralino states will be deter-

mined by the gaugino components similarly the light char-gino will be mostly a charged wino while if |120583| lt |119872

2| the

two lighter neutralinos and the lighter chargino are all mostlyHiggsinos with mass close to |120583| Finally if |120583| ≃ |119872

2| the

states will be strongly mixedHere two remarks are in order (i) The abovementioned

constraints in 11989812

from Higgs mass limit and gluino masslower bound imply that 119898

120594≳ 240GeV which is larger

than the limits obtained from direct searches at the LHCMoreover an upper bound of order one TeV is also obtained(from Higgs mass constraint) (ii) In this region of allowedparameter space the LSP is essentially pure bino as shown inFigure 2 This can be easily understood from the fact that 120583-parameter determined by the radiative electroweak breakingcondition (3) is typically of order 119898

0and hence it is much

heavier than the gaugino mass1198721

32 Relic Density As advocated in the previous section theLSP inMSSM the lightest neutralino 120594 is a perfect candidatefor DM Here we assume that 120594 was in thermal equilibriumwith the SM particles in the early universe and decoupledwhen it was nonrelativistic Once 120594 annihilation rate Γ

120594=

⟨120590ann120594

V⟩119899120594dropped below the expansion rate of the universe

Γ120594le 119867 the LSP particles stop to annihilate and fall out of

equilibriumand their relic density remains intact till nowTheabove ⟨120590ann

120594V⟩ refers to thermally averaged total cross section

for annihilation of 120594120594 into lighter particles times the relativevelocity V

The relic density is then determined by the Boltzmannequation for the LSP number density (119899

120594) and the law of

entropy conservation

119889119899120594

119889119905= minus3119867119899

120594minus ⟨120590ann

120594V⟩ [(119899

120594)2

minus (119899eq120594)2

]

119889119904

119889119905= minus3119867119904

(9)

where 119899eq120594

is the LSP equilibrium number density whichas a function of temperature 119879 is given by 119899eq

120594=

300 400 500 600 700 800 900096

097

098

099

100

fg

m120594 (GeV)

Figure 2The mass of lightest neutralino versus the purity functionin the region of parameter space allowed by gluino and Higgs masslimits

119892120594(119898

1205941198792120587)32119890minus119898120594119879 Here119898

120594and 119892

120594are the mass and the

number of degrees of freedomof the LSP respectively Finally119904 is the entropy density In the standard cosmology the Hub-ble parameter 119867 is given by 119867(119879) = 2120587radic120587119892

lowast45(1198792119872

119875119897)

where 119872119875119897= 122 times 1019 GeV and 119892

lowastis the number of rela-

tivistic degrees of freedom for MSSM 119892lowast≃ 22875 Let us

introduce the variable 119909 = 119898120594119879 and define 119884 = 119899

120594119904 with

119884eq = 119899eq120594119904 In this case the Boltzmann equation is given by

119889119884

119889119909=

1

3119867

119889119904

119889119909⟨120590ann

120594V⟩ (1198842 minus 1198842

eq) (10)

In radiation domination era the entropy as a function of thetemperature is given by

119904 (119909) =21205872

45119892lowast119904(119909)119898

3

120594119909minus3 (11)

which is deduced from the fact that 119904 = (120588 + 119901)119879 and 119892lowast119904

is the effective degrees of freedom for the entropy densityTherefore one finds

119889119904

119889119909= minus

3119904

119909 (12)

Thus with assuming 119892lowast≃ 119892

lowast119904

the following expression forthe Boltzmann equation for the LSP number density isobtained

119889119884

119889119909= minusradic

120587119892lowast

45119872

119875119897119898

120594

⟨120590ann120594

V⟩

1199092(1198842 minus 1198842

eq) (13)

If one considers the s-wave and p-wave annihilationprocesses only the thermal average ⟨120590ann

120594V⟩ then shows as

⟨120590ann120594

V⟩ ≃ 119886120594+6119887

120594

119909 (14)

Advances in High Energy Physics 5

f

AZ

f f

120594

120594

120594

120594

120594

120594

f

ff

f

Figure 3 Feynman diagrams contributing to early-universe neutralino 120594 annihilation into fermions through sfermions119885-gauge boson andHiggs

where 119886120594and 119887

120594are the s-wave and p-wave contributions of

annihilation processes respectively The relic density of theDM candidate is given by

Ωℎ2 =119898

1205941199040119884120594(infin)

120588119888ℎ2

(15)

where 1199040= 228215 times 10minus41 GeV3120588

119888= 80992ℎ2times10minus47 GeV4

and by solving the Boltzmann equation one can find 119884120594(infin)

as follows [62]

119884120594 (infin) =

1

120582120594

(119886120594

119909 (119879119891)+

3119887120594

1199092 (119879119891))

minus1

(16)

where 119879119891is the freeze-out temperature 120582

120594= 119904(119898

120594)119867(119898

120594)

and 119909(119879119891) is given by

119909 (119879119891) = ln[[

[

120572120594120582120594119888 (119888 + 2)

radic119909 (119879119891)

(119886120594+

6119887120594

119909 (119879119891))]]

]

(17)

where 120572120594= (4521205874)radic1205878(119892

120594119892

lowast119904

(119879119891)) the value 119888 = 12

results in a typical accuracy of about 5ndash10 more than suf-ficient for our purposes here

The lightest neutralino may annihilate into fermion-antifermion (119891119891) 119882+119882minus 119885119885 119882+119867minus 119885119860 119885119867 119885ℎ and119867+119867minus and all other contributions of neutral Higgs For abino-like LSP that is 119873

11≃ 1 and 119873

1119894≃ 0 119894 = 2 3 4 one

finds that the relevant annihilation channels are the fermion-antifermion ones as shown in Figure 3 and all other chan-nels are instead suppressed Also the annihilation processmediated by 119885-gauge boson is suppressed due to the small119885120594120594 coupling prop 1198732

13minus 1198732

14 except at the resonance when

119898120594sim 119872

1198852 which is no longer possible due to the above-

mentioned constraints Furthermore one finds that the t-channel annihilation (first Feynman diagram in Figure 3) ispredominantly into leptons through the exchanges of thethree slepton families (119897

119871 119877) with 119897 = 119890 120583 120591 The squarks

exchanges are suppressed due to their large massesIn Figure 4 we display the constraint from the observed

limits of Ωℎ2 on the plane (1198980-119898

12) for 119860

0= 0 2000GeV

tan120573 = 10 50 and 120583 gt 0 Here we used micrOMEGAs [63]to compute the complete relic abundance of the lightest

neutralino taking into account the possibility of having coan-nihilation with the next-to-lightest supersymmetric particlewhich is typically the lightest stau Note that this type of coan-nihilation is not included in the approximated expressions in(14)ndash(17) In this figure the red regions correspond to a relicabundance within the measured limits [1]

009 lt Ωℎ2 lt 014 (18)

It is noticeable that with low tan120573 (sim10) this region corre-sponds to light 119898

12(lt500GeV) where significant coanni-

hilation between the LSP and stau took place However thispossibility is now excluded by the Higgs and gluino massconstraints [64] At large tan120573 another region is alloweddue to possible resonance due to 119904-channel annihilation ofthe DM pair into fermion-antifermion via the pseudoscalarHiggs boson 119860 at 119872

119860≃ 2119898

120594[65] For 119860

0= 0 a very small

part of this region is allowed by the Higgs mass constraintwhile for large 119860

0(sim2 TeV) slight enhancement of this part

can be achieved In Figure 5 we zoom in on this region toshow the explicit dependence of the relic abundance on theLSP mass and large values of tan120573 As can be seen from thisfigure there is no point that can satisfy the relic abundancestringent constraints with tan120573 lt 30

33 Direct Detection Perhaps themost natural way of search-ing for the neutralino DM is provided by direct experi-ments where the effects induced in appropriate detectors byneutralino-nucleus elastic scattering may be measured Theelastic-scattering cross section of the LSPwith a given nucleushas two contributions spin-dependent contribution arisingfrom 119885 and exchange diagrams and spin-independent(scalar) contribution due to the Higgs and squark exchangediagrams which is typically suppressed The effective scalarinteraction of neutralino with a quark is given by

Lscalar = 119891119902120594120594119902119902 (19)

where 119891119902is the neutralino-quark effective coupling The

scalar cross section of the neutralino scattering with targetnucleus at zero momentum transfer is given by [2]

120590SI0=41198982

119903

120587(119885119891

119901+ (119860 minus 119885)119891

119899)2

(20)

where 119885 and 119860 minus 119885 are the number of protons and neu-trons respectively 119898

119903= 119898

119873119898

120594(119898

119873+ 119898

120594) where 119898

119873is

6 Advances in High Energy Physics

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 10 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

Figure 4 LSP relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The LUX result is satisfied by the

yellow region The other color codes are as in Figure 1

500 550 600 650 700 750 800009

010

011

012

013

014

Ωh2

m120594 (GeV)

Figure 5 The relic abundance versus the mass of the LSP fordifferent values of tan120573 Red points indicate 40 le tan120573 le 50 andblue points 30 le tan120573 lt 40 All points satisfy the abovementionedconstraints

the nucleus mass and 119891119901 119891

119899are the neutralino coupling

to protons and neutrons respectively The differential scalarcross section for nonzero momentum transfer 119902 can now bewritten

119889120590SI1198891199022

=120590SI0

41198982

119903V21198652 (1199022) 0 lt 1199022 lt 41198982

119903V2 (21)

10 20 50 100 200 500 1000 2000m120594 (GeV)

120590p SI(cm

2)

10minus45

10minus47

10minus49

10minus51

LUX

Figure 6 Spin-independent scattering cross section of the LSP witha proton versus the mass of the LSP within the region allowed by allconstraints (from the LHC and relic abundance)

where V is the neutrino velocity and 119865(1199022) is the form factor[2] In Figure 6 we display the MSSM prediction for spin-independent scattering cross section of the LSP with a proton(120590119901SI = int

41198982

119903V2

0(119889120590SI119889119902

2)|119891119899=119891119901

1198891199022) after imposing the LHC

Advances in High Energy Physics 7

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)

Figure 7 LSP nonthermal relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The color codes are

as in Figure 1

and relic abundance constraints It is clear that our results for120590119901

SI are less than the recent LUX bound (blue curve) by at leasttwo orders of magnitude This would explain the negativeresults of direct searches so far

4 Nonthermal Dark Matter andMSSM Parameter Space

In the previous section we assumed standard cosmologyscenario where the reheating temperature 119879RH is very largenamely119879RH ≫ 119879

119891≃ 10GeVHowever the only constraint on

the reheating temperature which could be associated withdecay of any scalar field 120601 not only the inflaton field is119879RH ≳ 1MeV in order not to spoil the successful predictionsof big bang nucleosynthesis

A detailed analysis of the relic density with a low reheat-ing temperature has been carried out in [66] It was empha-sized that for a large annihilation cross section ⟨120590annV⟩ ≳

10minus14 GeVminus2 so that the neutralino reaches equilibriumbefore reheating and if there are a large number of neutrali-nos produced by the scalar field 120601 decay then the relic densityis estimated as [67]

Ωℎ2 =3119898

120594Γ120601

2 (2120587245) 119892lowast(119879RH) 119879

3

RH ⟨120590ann120594

V⟩ℎ2

120588119888119904

0

(22)

Here the reheating temperature is defined as [62]

119879RH = (90

1205872119892lowast(119879RH)

)

14

(Γ120601119872

119875119897)12

(23)

where the decay width Γ120601is given by

Γ120601=

1

2120587

1198983

120601

Λ2 (24)

The scaleΛ is the effective suppression scale which is of orderthe grand unification scale119872

119883Therefore for scalar fieldwith

mass 119898120601≃ 107 GeV one finds Γ

120601≃ 10minus11 GeV and in our

calculations we have used 119892lowast

= 1075 due to the consid-eration of a low reheating temperature scenario

In Figure 7 we show the constraints imposed on theMSSM (119898

0-119898

12) plane in case of nonthermal relic abun-

dance of the LSP for tan120573 = 10 50 and 1198600= 0 2TeV In this

plot we also imposed the LHC constraints namely the Higgsmass limit and the gluino mass lower bound similar to thecase of thermal scenario It is clear from this figure that thestringent constraints imposed on theMSSM parameter spaceby thermal relic abundance are now relaxed and now lowtan120573 (sim10) is allowed but with very heavy 119898

0(simO(4)TeV)

and 11989812

≃ 600GeV In addition the following two regionsare now allowed with large tan120573 (sim50) (i) 119898

0sim 119898

12≃

8 Advances in High Energy Physics

O(1)TeV (ii)1198980≃ O(4)TeV and119898

12≃ 700GeV The SUSY

spectrum associated with these regions of parameters spacecould be striking signature for nonthermal scenario at theLHC

5 Conclusion

We have studied the constraints imposed on the MSSMparameter space by the Higgsmass limit and the gluino lowerbound which are the most stringent collider constraintsobtained from the LHC run-I at energy 8 TeV We showedthat 119898

12resides within the mass range 620GeV ≲ 119898

12≲

2000GeV while the other parameters (1198980 119860

0 tan120573) are

much less constrained We also studied the effect of themeasured DM relic density on the MSSM allowed parameterspace It turns out that most of the MSSM parameter spaceis ruled out except for few points around tan120573 sim 50119898

0sim 1TeV and 119898

12sim 15TeV We calculated the spin-

independent scattering cross section of the LSP with a protonin this allowed region We showed that our prediction for120590119901

SI is less than the recent LUX bound by at least two ordersof magnitude We have also analyzed the nonthermal DMscenario for the LSPWe showed that the constraints imposedon the MSSM parameter space are relaxed and low tan120573 isnow allowed with 119898

0≃ O(4)TeV and 119898

12≃ 600GeV Also

two allowed regions are now associated with large tan120573 (sim50) namely 119898

0sim 119898

12≃ O(1)TeV or 119898

0≃ O(4)TeV and

11989812

≃ 700GeV

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by the STDF Project 13858the ICTP Grant AC-80 and the European Union FP7 ITNINVISIBLES (Marie Curie Actions PITN-GA-2011-289442)

References

[1] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquo Astronomy ampAstrophysics vol 571 article A16 2014

[2] G Jungman M Kamionkowski and K Griest ldquoSupersymmet-ric dark matterrdquo Physics Report vol 267 no 5-6 pp 195ndash3731996

[3] G Bertone D Hooper and J Silk ldquoParticle dark matter evi-dence candidates and constraintsrdquo Physics Reports vol 405 no5-6 pp 279ndash390 2005

[4] H PNilles ldquoSupersymmetry supergravity andparticle physicsrdquoPhysics Reports vol 110 no 1-2 pp 1ndash162 1984

[5] J D Lykken ldquoIntroduction tosupersymmetryrdquo In press httparxivorgabshep-th9612114

[6] J Wess and J Bagger Supersymmetry and Supergravity Prince-ton University Press Princeton NJ USA 2nd edition 1991

[7] H E Haber and G Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[8] S P Martin ldquoA Supersymmetry Primerrdquo Advanced Series onDirections in High Energy Physics vol 21 pp 1ndash153 2010Advanced Series on Directions in High Energy Physics vol 18pp 1ndash98 1998

[9] D J H Chung L L Everett G L Kane S F King J D Lykkenand L TWang ldquoThe soft supersymmetry-breaking Lagrangiantheory and applicationsrdquo Physics Reports vol 407 no 1ndash3 pp 1ndash203 2005

[10] M Drees P Roy and R M GodboleTheory and Phenomenol-ogy of Sparticles World Scientific Singapore 2005

[11] H Baer and X Tata Weak Scale Supersymmetry From Super-fields to Scattering Events Cambridge University Press Cam-bridge UK 2006

[12] H Goldberg ldquoConstraint on the photino mass from cosmol-ogyrdquo Physical Review Letters vol 50 no 19 pp 1419ndash14221983 Erratum-ibid Physical Review Letters vol 103 Article ID099905 2009

[13] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[14] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoObser-vation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHCrdquo Physics Letters B vol 716 no 1 pp30ndash61 2012

[15] G Aad B Abbott J Abdallah et al ldquoSummary of the ATLASexperimentrsquos sensitivity to supersymmetry after LHC Run 1mdashinterpreted in the phenomenological MSSMrdquo Journal of HighEnergy Physics vol 2015 article 134 2015

[16] A Gaz ldquoSUSY searches at CMSrdquo In press httparxivorgabs14111886

[17] I Melzer-Pellmann and P Pralavorio ldquoLessons for SUSY fromthe LHC after the first runrdquo The European Physical Journal Cvol 74 article 2801 2014

[18] N Craig ldquoThe state ofsupersymmetry after Run I of the LHCrdquohttparxivorgabs13090528

[19] D S Akerib H M Araujo X Bai et al ldquoFirst results from theLUX dark matter experiment at the Sanford UndergroundResearch Facilityrdquo Physical Review Letters vol 112 Article ID091303 2014

[20] E Aprile ldquoThe Xenon1T dark matter search experimentrdquo inSources and Detection of Dark Matter and Dark Energy in theUniverse vol 148 of Springer Proceedings in Physics pp 93ndash96Springer 2013

[21] E AprileMAlfonsi K Arisaka et al ldquoDarkmatter results from225 live days of XENON100 datardquo Physical Review Letters vol109 no 18 Article ID 181301 6 pages 2012

[22] H Baer V Barger and A Mustafayev ldquoImplications of a125GeV Higgs scalar for the LHC supersymmetry and neu-tralino dark matter searchesrdquo Physical Review D vol 85 ArticleID 075010 2012

[23] J Ellis and K A Olive ldquoRevisiting the higgs mass and darkmatter in the CMSSMrdquo The European Physical Journal C vol72 article 2005 2012

[24] O Buchmueller R Cavanaugh M Citron et al ldquoThe CMSSMand NUHM1 in light of 7 TeV LHC 119861

119904rarr 120583+120583minus and

XENON100 datardquoThe European Physical Journal C vol 72 no11 article 2243 2012

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

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FluidsJournal of

Atomic and Molecular Physics

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances in Condensed Matter Physics

OpticsInternational Journal of

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AstronomyAdvances in

International Journal of

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Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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GravityJournal of

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AstrophysicsJournal of

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Physics Research International

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Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

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Soft MatterJournal of

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AerodynamicsJournal of

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PhotonicsJournal of

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Journal of

Biophysics

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ThermodynamicsJournal of

Advances in High Energy Physics 3

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

(a)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

(b)

Figure 1 MSSM parameter space for tan120573 = 10 (a) and 50 (b) with 1198600= 0 and 2 TeV The green region indicates 124 ≲ 119898

ℎ≲ 126GeV The

blue region is excluded because the lightest neutralino is not the LSPThe pink region is excluded due to the absence of radiative electroweaksymmetry breaking (1205832 becomes negative) The gray shadow lines denote the excluded area because of119898

lt 14TeV

plane for different values of 1198600and tan120573 It is remarkable

that the smaller the value of 1198600is the smaller the value

of 11989812

is needed to satisfy this value of Higgs mass Itis also clear that the scalar mass 119898

0remains essentially

unconstrained by Higgs mass limit It can vary from fewhundred GeVs to few TeVs Such large values of 119898

12seem

to imply a quite heavy SUSY spectrum much heavier thanthe lower bound imposed by direct searches at the LHCexperiments in centre of mass energies radic119904 = 7 8TeV andtotal integrated luminosity of order 20 fbminus1 Furthermorethe LHC lower limit on the gluino mass 119898

≳ 14TeV

[56 57] excluded the values of 11989812

lt 620GeV whichwas allowed by Higgs mass constraints for 119898

0gt 4TeV

Furthermore this region is shown with dashed lines inFigure 1

3 Dark Matter Constraints onMSSM Parameter Space

31 The LSP as Dark Matter Candidate The neutralinos 120594119894

(119894 = 1 2 3 4) are the physical (mass) superpositions of twofermionic partners of the two neutral gauge bosons calledgaugino

0 (bino) and 0

3(wino) and of the two neutral

Higgs bosons called Higgsinos 0

1and

0

2 The neutralino

mass matrix is given by [58ndash61]

119872119873= (

(

1198721

0 minus119872119885cos120573 sin 120579

119882119872

119885sin120573 sin 120579

119882

0 1198722

119872119885cos120573 cos 120579

119882minus119872

119885sin120573 cos 120579

119882

minus119872119885cos120573 sin 120579

119882119872

119885cos120573 cos 120579

1198820 minus120583

119872119885sin120573 sin 120579

119882minus119872

119885sin120573 cos 120579

119882minus120583 0

)

)

(7)

4 Advances in High Energy Physics

where 1198721and 119872

2are related due to the universality of

the gaugino masses at the grand unification scale 1198721

=

(31198922

151198922

2)119872

2 where 119892

1 119892

2are the gauge couplings of 119880(1)

119884

and 119878119880(2)119871 respectively This Hermitian matrix is diago-

nalized by a unitary transformation of the neutralino fields119872

diag119873

= 119873dagger119872119873119873 The lightest eigenvalue of this matrix and

the corresponding eigenstate say 120594 has good chance of beingthe LSP The lightest neutralino will be a linear combinationof the original fields

120594 = 119873110

+ 11987312

0

+ 11987313

0

1+ 119873

14

0

2 (8)

The phenomenology and cosmology of the neutralino aregoverned primarily by its mass and composition A usefulparameter for describing the neutralino composition is thegaugino ldquopurityrdquo function119891

119892= |119873

11|2+|119873

12|2 [58ndash61] If119891

119892gt

05 then the neutralino is primarily gaugino and if 119891119892lt 05

then the neutralino is primarily Higgsino Actually if |120583| gt|119872

2| ge 119872

119885 the two lightest neutralino states will be deter-

mined by the gaugino components similarly the light char-gino will be mostly a charged wino while if |120583| lt |119872

2| the

two lighter neutralinos and the lighter chargino are all mostlyHiggsinos with mass close to |120583| Finally if |120583| ≃ |119872

2| the

states will be strongly mixedHere two remarks are in order (i) The abovementioned

constraints in 11989812

from Higgs mass limit and gluino masslower bound imply that 119898

120594≳ 240GeV which is larger

than the limits obtained from direct searches at the LHCMoreover an upper bound of order one TeV is also obtained(from Higgs mass constraint) (ii) In this region of allowedparameter space the LSP is essentially pure bino as shown inFigure 2 This can be easily understood from the fact that 120583-parameter determined by the radiative electroweak breakingcondition (3) is typically of order 119898

0and hence it is much

heavier than the gaugino mass1198721

32 Relic Density As advocated in the previous section theLSP inMSSM the lightest neutralino 120594 is a perfect candidatefor DM Here we assume that 120594 was in thermal equilibriumwith the SM particles in the early universe and decoupledwhen it was nonrelativistic Once 120594 annihilation rate Γ

120594=

⟨120590ann120594

V⟩119899120594dropped below the expansion rate of the universe

Γ120594le 119867 the LSP particles stop to annihilate and fall out of

equilibriumand their relic density remains intact till nowTheabove ⟨120590ann

120594V⟩ refers to thermally averaged total cross section

for annihilation of 120594120594 into lighter particles times the relativevelocity V

The relic density is then determined by the Boltzmannequation for the LSP number density (119899

120594) and the law of

entropy conservation

119889119899120594

119889119905= minus3119867119899

120594minus ⟨120590ann

120594V⟩ [(119899

120594)2

minus (119899eq120594)2

]

119889119904

119889119905= minus3119867119904

(9)

where 119899eq120594

is the LSP equilibrium number density whichas a function of temperature 119879 is given by 119899eq

120594=

300 400 500 600 700 800 900096

097

098

099

100

fg

m120594 (GeV)

Figure 2The mass of lightest neutralino versus the purity functionin the region of parameter space allowed by gluino and Higgs masslimits

119892120594(119898

1205941198792120587)32119890minus119898120594119879 Here119898

120594and 119892

120594are the mass and the

number of degrees of freedomof the LSP respectively Finally119904 is the entropy density In the standard cosmology the Hub-ble parameter 119867 is given by 119867(119879) = 2120587radic120587119892

lowast45(1198792119872

119875119897)

where 119872119875119897= 122 times 1019 GeV and 119892

lowastis the number of rela-

tivistic degrees of freedom for MSSM 119892lowast≃ 22875 Let us

introduce the variable 119909 = 119898120594119879 and define 119884 = 119899

120594119904 with

119884eq = 119899eq120594119904 In this case the Boltzmann equation is given by

119889119884

119889119909=

1

3119867

119889119904

119889119909⟨120590ann

120594V⟩ (1198842 minus 1198842

eq) (10)

In radiation domination era the entropy as a function of thetemperature is given by

119904 (119909) =21205872

45119892lowast119904(119909)119898

3

120594119909minus3 (11)

which is deduced from the fact that 119904 = (120588 + 119901)119879 and 119892lowast119904

is the effective degrees of freedom for the entropy densityTherefore one finds

119889119904

119889119909= minus

3119904

119909 (12)

Thus with assuming 119892lowast≃ 119892

lowast119904

the following expression forthe Boltzmann equation for the LSP number density isobtained

119889119884

119889119909= minusradic

120587119892lowast

45119872

119875119897119898

120594

⟨120590ann120594

V⟩

1199092(1198842 minus 1198842

eq) (13)

If one considers the s-wave and p-wave annihilationprocesses only the thermal average ⟨120590ann

120594V⟩ then shows as

⟨120590ann120594

V⟩ ≃ 119886120594+6119887

120594

119909 (14)

Advances in High Energy Physics 5

f

AZ

f f

120594

120594

120594

120594

120594

120594

f

ff

f

Figure 3 Feynman diagrams contributing to early-universe neutralino 120594 annihilation into fermions through sfermions119885-gauge boson andHiggs

where 119886120594and 119887

120594are the s-wave and p-wave contributions of

annihilation processes respectively The relic density of theDM candidate is given by

Ωℎ2 =119898

1205941199040119884120594(infin)

120588119888ℎ2

(15)

where 1199040= 228215 times 10minus41 GeV3120588

119888= 80992ℎ2times10minus47 GeV4

and by solving the Boltzmann equation one can find 119884120594(infin)

as follows [62]

119884120594 (infin) =

1

120582120594

(119886120594

119909 (119879119891)+

3119887120594

1199092 (119879119891))

minus1

(16)

where 119879119891is the freeze-out temperature 120582

120594= 119904(119898

120594)119867(119898

120594)

and 119909(119879119891) is given by

119909 (119879119891) = ln[[

[

120572120594120582120594119888 (119888 + 2)

radic119909 (119879119891)

(119886120594+

6119887120594

119909 (119879119891))]]

]

(17)

where 120572120594= (4521205874)radic1205878(119892

120594119892

lowast119904

(119879119891)) the value 119888 = 12

results in a typical accuracy of about 5ndash10 more than suf-ficient for our purposes here

The lightest neutralino may annihilate into fermion-antifermion (119891119891) 119882+119882minus 119885119885 119882+119867minus 119885119860 119885119867 119885ℎ and119867+119867minus and all other contributions of neutral Higgs For abino-like LSP that is 119873

11≃ 1 and 119873

1119894≃ 0 119894 = 2 3 4 one

finds that the relevant annihilation channels are the fermion-antifermion ones as shown in Figure 3 and all other chan-nels are instead suppressed Also the annihilation processmediated by 119885-gauge boson is suppressed due to the small119885120594120594 coupling prop 1198732

13minus 1198732

14 except at the resonance when

119898120594sim 119872

1198852 which is no longer possible due to the above-

mentioned constraints Furthermore one finds that the t-channel annihilation (first Feynman diagram in Figure 3) ispredominantly into leptons through the exchanges of thethree slepton families (119897

119871 119877) with 119897 = 119890 120583 120591 The squarks

exchanges are suppressed due to their large massesIn Figure 4 we display the constraint from the observed

limits of Ωℎ2 on the plane (1198980-119898

12) for 119860

0= 0 2000GeV

tan120573 = 10 50 and 120583 gt 0 Here we used micrOMEGAs [63]to compute the complete relic abundance of the lightest

neutralino taking into account the possibility of having coan-nihilation with the next-to-lightest supersymmetric particlewhich is typically the lightest stau Note that this type of coan-nihilation is not included in the approximated expressions in(14)ndash(17) In this figure the red regions correspond to a relicabundance within the measured limits [1]

009 lt Ωℎ2 lt 014 (18)

It is noticeable that with low tan120573 (sim10) this region corre-sponds to light 119898

12(lt500GeV) where significant coanni-

hilation between the LSP and stau took place However thispossibility is now excluded by the Higgs and gluino massconstraints [64] At large tan120573 another region is alloweddue to possible resonance due to 119904-channel annihilation ofthe DM pair into fermion-antifermion via the pseudoscalarHiggs boson 119860 at 119872

119860≃ 2119898

120594[65] For 119860

0= 0 a very small

part of this region is allowed by the Higgs mass constraintwhile for large 119860

0(sim2 TeV) slight enhancement of this part

can be achieved In Figure 5 we zoom in on this region toshow the explicit dependence of the relic abundance on theLSP mass and large values of tan120573 As can be seen from thisfigure there is no point that can satisfy the relic abundancestringent constraints with tan120573 lt 30

33 Direct Detection Perhaps themost natural way of search-ing for the neutralino DM is provided by direct experi-ments where the effects induced in appropriate detectors byneutralino-nucleus elastic scattering may be measured Theelastic-scattering cross section of the LSPwith a given nucleushas two contributions spin-dependent contribution arisingfrom 119885 and exchange diagrams and spin-independent(scalar) contribution due to the Higgs and squark exchangediagrams which is typically suppressed The effective scalarinteraction of neutralino with a quark is given by

Lscalar = 119891119902120594120594119902119902 (19)

where 119891119902is the neutralino-quark effective coupling The

scalar cross section of the neutralino scattering with targetnucleus at zero momentum transfer is given by [2]

120590SI0=41198982

119903

120587(119885119891

119901+ (119860 minus 119885)119891

119899)2

(20)

where 119885 and 119860 minus 119885 are the number of protons and neu-trons respectively 119898

119903= 119898

119873119898

120594(119898

119873+ 119898

120594) where 119898

119873is

6 Advances in High Energy Physics

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 10 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

Figure 4 LSP relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The LUX result is satisfied by the

yellow region The other color codes are as in Figure 1

500 550 600 650 700 750 800009

010

011

012

013

014

Ωh2

m120594 (GeV)

Figure 5 The relic abundance versus the mass of the LSP fordifferent values of tan120573 Red points indicate 40 le tan120573 le 50 andblue points 30 le tan120573 lt 40 All points satisfy the abovementionedconstraints

the nucleus mass and 119891119901 119891

119899are the neutralino coupling

to protons and neutrons respectively The differential scalarcross section for nonzero momentum transfer 119902 can now bewritten

119889120590SI1198891199022

=120590SI0

41198982

119903V21198652 (1199022) 0 lt 1199022 lt 41198982

119903V2 (21)

10 20 50 100 200 500 1000 2000m120594 (GeV)

120590p SI(cm

2)

10minus45

10minus47

10minus49

10minus51

LUX

Figure 6 Spin-independent scattering cross section of the LSP witha proton versus the mass of the LSP within the region allowed by allconstraints (from the LHC and relic abundance)

where V is the neutrino velocity and 119865(1199022) is the form factor[2] In Figure 6 we display the MSSM prediction for spin-independent scattering cross section of the LSP with a proton(120590119901SI = int

41198982

119903V2

0(119889120590SI119889119902

2)|119891119899=119891119901

1198891199022) after imposing the LHC

Advances in High Energy Physics 7

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)

Figure 7 LSP nonthermal relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The color codes are

as in Figure 1

and relic abundance constraints It is clear that our results for120590119901

SI are less than the recent LUX bound (blue curve) by at leasttwo orders of magnitude This would explain the negativeresults of direct searches so far

4 Nonthermal Dark Matter andMSSM Parameter Space

In the previous section we assumed standard cosmologyscenario where the reheating temperature 119879RH is very largenamely119879RH ≫ 119879

119891≃ 10GeVHowever the only constraint on

the reheating temperature which could be associated withdecay of any scalar field 120601 not only the inflaton field is119879RH ≳ 1MeV in order not to spoil the successful predictionsof big bang nucleosynthesis

A detailed analysis of the relic density with a low reheat-ing temperature has been carried out in [66] It was empha-sized that for a large annihilation cross section ⟨120590annV⟩ ≳

10minus14 GeVminus2 so that the neutralino reaches equilibriumbefore reheating and if there are a large number of neutrali-nos produced by the scalar field 120601 decay then the relic densityis estimated as [67]

Ωℎ2 =3119898

120594Γ120601

2 (2120587245) 119892lowast(119879RH) 119879

3

RH ⟨120590ann120594

V⟩ℎ2

120588119888119904

0

(22)

Here the reheating temperature is defined as [62]

119879RH = (90

1205872119892lowast(119879RH)

)

14

(Γ120601119872

119875119897)12

(23)

where the decay width Γ120601is given by

Γ120601=

1

2120587

1198983

120601

Λ2 (24)

The scaleΛ is the effective suppression scale which is of orderthe grand unification scale119872

119883Therefore for scalar fieldwith

mass 119898120601≃ 107 GeV one finds Γ

120601≃ 10minus11 GeV and in our

calculations we have used 119892lowast

= 1075 due to the consid-eration of a low reheating temperature scenario

In Figure 7 we show the constraints imposed on theMSSM (119898

0-119898

12) plane in case of nonthermal relic abun-

dance of the LSP for tan120573 = 10 50 and 1198600= 0 2TeV In this

plot we also imposed the LHC constraints namely the Higgsmass limit and the gluino mass lower bound similar to thecase of thermal scenario It is clear from this figure that thestringent constraints imposed on theMSSM parameter spaceby thermal relic abundance are now relaxed and now lowtan120573 (sim10) is allowed but with very heavy 119898

0(simO(4)TeV)

and 11989812

≃ 600GeV In addition the following two regionsare now allowed with large tan120573 (sim50) (i) 119898

0sim 119898

12≃

8 Advances in High Energy Physics

O(1)TeV (ii)1198980≃ O(4)TeV and119898

12≃ 700GeV The SUSY

spectrum associated with these regions of parameters spacecould be striking signature for nonthermal scenario at theLHC

5 Conclusion

We have studied the constraints imposed on the MSSMparameter space by the Higgsmass limit and the gluino lowerbound which are the most stringent collider constraintsobtained from the LHC run-I at energy 8 TeV We showedthat 119898

12resides within the mass range 620GeV ≲ 119898

12≲

2000GeV while the other parameters (1198980 119860

0 tan120573) are

much less constrained We also studied the effect of themeasured DM relic density on the MSSM allowed parameterspace It turns out that most of the MSSM parameter spaceis ruled out except for few points around tan120573 sim 50119898

0sim 1TeV and 119898

12sim 15TeV We calculated the spin-

independent scattering cross section of the LSP with a protonin this allowed region We showed that our prediction for120590119901

SI is less than the recent LUX bound by at least two ordersof magnitude We have also analyzed the nonthermal DMscenario for the LSPWe showed that the constraints imposedon the MSSM parameter space are relaxed and low tan120573 isnow allowed with 119898

0≃ O(4)TeV and 119898

12≃ 600GeV Also

two allowed regions are now associated with large tan120573 (sim50) namely 119898

0sim 119898

12≃ O(1)TeV or 119898

0≃ O(4)TeV and

11989812

≃ 700GeV

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by the STDF Project 13858the ICTP Grant AC-80 and the European Union FP7 ITNINVISIBLES (Marie Curie Actions PITN-GA-2011-289442)

References

[1] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquo Astronomy ampAstrophysics vol 571 article A16 2014

[2] G Jungman M Kamionkowski and K Griest ldquoSupersymmet-ric dark matterrdquo Physics Report vol 267 no 5-6 pp 195ndash3731996

[3] G Bertone D Hooper and J Silk ldquoParticle dark matter evi-dence candidates and constraintsrdquo Physics Reports vol 405 no5-6 pp 279ndash390 2005

[4] H PNilles ldquoSupersymmetry supergravity andparticle physicsrdquoPhysics Reports vol 110 no 1-2 pp 1ndash162 1984

[5] J D Lykken ldquoIntroduction tosupersymmetryrdquo In press httparxivorgabshep-th9612114

[6] J Wess and J Bagger Supersymmetry and Supergravity Prince-ton University Press Princeton NJ USA 2nd edition 1991

[7] H E Haber and G Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[8] S P Martin ldquoA Supersymmetry Primerrdquo Advanced Series onDirections in High Energy Physics vol 21 pp 1ndash153 2010Advanced Series on Directions in High Energy Physics vol 18pp 1ndash98 1998

[9] D J H Chung L L Everett G L Kane S F King J D Lykkenand L TWang ldquoThe soft supersymmetry-breaking Lagrangiantheory and applicationsrdquo Physics Reports vol 407 no 1ndash3 pp 1ndash203 2005

[10] M Drees P Roy and R M GodboleTheory and Phenomenol-ogy of Sparticles World Scientific Singapore 2005

[11] H Baer and X Tata Weak Scale Supersymmetry From Super-fields to Scattering Events Cambridge University Press Cam-bridge UK 2006

[12] H Goldberg ldquoConstraint on the photino mass from cosmol-ogyrdquo Physical Review Letters vol 50 no 19 pp 1419ndash14221983 Erratum-ibid Physical Review Letters vol 103 Article ID099905 2009

[13] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[14] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoObser-vation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHCrdquo Physics Letters B vol 716 no 1 pp30ndash61 2012

[15] G Aad B Abbott J Abdallah et al ldquoSummary of the ATLASexperimentrsquos sensitivity to supersymmetry after LHC Run 1mdashinterpreted in the phenomenological MSSMrdquo Journal of HighEnergy Physics vol 2015 article 134 2015

[16] A Gaz ldquoSUSY searches at CMSrdquo In press httparxivorgabs14111886

[17] I Melzer-Pellmann and P Pralavorio ldquoLessons for SUSY fromthe LHC after the first runrdquo The European Physical Journal Cvol 74 article 2801 2014

[18] N Craig ldquoThe state ofsupersymmetry after Run I of the LHCrdquohttparxivorgabs13090528

[19] D S Akerib H M Araujo X Bai et al ldquoFirst results from theLUX dark matter experiment at the Sanford UndergroundResearch Facilityrdquo Physical Review Letters vol 112 Article ID091303 2014

[20] E Aprile ldquoThe Xenon1T dark matter search experimentrdquo inSources and Detection of Dark Matter and Dark Energy in theUniverse vol 148 of Springer Proceedings in Physics pp 93ndash96Springer 2013

[21] E AprileMAlfonsi K Arisaka et al ldquoDarkmatter results from225 live days of XENON100 datardquo Physical Review Letters vol109 no 18 Article ID 181301 6 pages 2012

[22] H Baer V Barger and A Mustafayev ldquoImplications of a125GeV Higgs scalar for the LHC supersymmetry and neu-tralino dark matter searchesrdquo Physical Review D vol 85 ArticleID 075010 2012

[23] J Ellis and K A Olive ldquoRevisiting the higgs mass and darkmatter in the CMSSMrdquo The European Physical Journal C vol72 article 2005 2012

[24] O Buchmueller R Cavanaugh M Citron et al ldquoThe CMSSMand NUHM1 in light of 7 TeV LHC 119861

119904rarr 120583+120583minus and

XENON100 datardquoThe European Physical Journal C vol 72 no11 article 2243 2012

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

4 Advances in High Energy Physics

where 1198721and 119872

2are related due to the universality of

the gaugino masses at the grand unification scale 1198721

=

(31198922

151198922

2)119872

2 where 119892

1 119892

2are the gauge couplings of 119880(1)

119884

and 119878119880(2)119871 respectively This Hermitian matrix is diago-

nalized by a unitary transformation of the neutralino fields119872

diag119873

= 119873dagger119872119873119873 The lightest eigenvalue of this matrix and

the corresponding eigenstate say 120594 has good chance of beingthe LSP The lightest neutralino will be a linear combinationof the original fields

120594 = 119873110

+ 11987312

0

+ 11987313

0

1+ 119873

14

0

2 (8)

The phenomenology and cosmology of the neutralino aregoverned primarily by its mass and composition A usefulparameter for describing the neutralino composition is thegaugino ldquopurityrdquo function119891

119892= |119873

11|2+|119873

12|2 [58ndash61] If119891

119892gt

05 then the neutralino is primarily gaugino and if 119891119892lt 05

then the neutralino is primarily Higgsino Actually if |120583| gt|119872

2| ge 119872

119885 the two lightest neutralino states will be deter-

mined by the gaugino components similarly the light char-gino will be mostly a charged wino while if |120583| lt |119872

2| the

two lighter neutralinos and the lighter chargino are all mostlyHiggsinos with mass close to |120583| Finally if |120583| ≃ |119872

2| the

states will be strongly mixedHere two remarks are in order (i) The abovementioned

constraints in 11989812

from Higgs mass limit and gluino masslower bound imply that 119898

120594≳ 240GeV which is larger

than the limits obtained from direct searches at the LHCMoreover an upper bound of order one TeV is also obtained(from Higgs mass constraint) (ii) In this region of allowedparameter space the LSP is essentially pure bino as shown inFigure 2 This can be easily understood from the fact that 120583-parameter determined by the radiative electroweak breakingcondition (3) is typically of order 119898

0and hence it is much

heavier than the gaugino mass1198721

32 Relic Density As advocated in the previous section theLSP inMSSM the lightest neutralino 120594 is a perfect candidatefor DM Here we assume that 120594 was in thermal equilibriumwith the SM particles in the early universe and decoupledwhen it was nonrelativistic Once 120594 annihilation rate Γ

120594=

⟨120590ann120594

V⟩119899120594dropped below the expansion rate of the universe

Γ120594le 119867 the LSP particles stop to annihilate and fall out of

equilibriumand their relic density remains intact till nowTheabove ⟨120590ann

120594V⟩ refers to thermally averaged total cross section

for annihilation of 120594120594 into lighter particles times the relativevelocity V

The relic density is then determined by the Boltzmannequation for the LSP number density (119899

120594) and the law of

entropy conservation

119889119899120594

119889119905= minus3119867119899

120594minus ⟨120590ann

120594V⟩ [(119899

120594)2

minus (119899eq120594)2

]

119889119904

119889119905= minus3119867119904

(9)

where 119899eq120594

is the LSP equilibrium number density whichas a function of temperature 119879 is given by 119899eq

120594=

300 400 500 600 700 800 900096

097

098

099

100

fg

m120594 (GeV)

Figure 2The mass of lightest neutralino versus the purity functionin the region of parameter space allowed by gluino and Higgs masslimits

119892120594(119898

1205941198792120587)32119890minus119898120594119879 Here119898

120594and 119892

120594are the mass and the

number of degrees of freedomof the LSP respectively Finally119904 is the entropy density In the standard cosmology the Hub-ble parameter 119867 is given by 119867(119879) = 2120587radic120587119892

lowast45(1198792119872

119875119897)

where 119872119875119897= 122 times 1019 GeV and 119892

lowastis the number of rela-

tivistic degrees of freedom for MSSM 119892lowast≃ 22875 Let us

introduce the variable 119909 = 119898120594119879 and define 119884 = 119899

120594119904 with

119884eq = 119899eq120594119904 In this case the Boltzmann equation is given by

119889119884

119889119909=

1

3119867

119889119904

119889119909⟨120590ann

120594V⟩ (1198842 minus 1198842

eq) (10)

In radiation domination era the entropy as a function of thetemperature is given by

119904 (119909) =21205872

45119892lowast119904(119909)119898

3

120594119909minus3 (11)

which is deduced from the fact that 119904 = (120588 + 119901)119879 and 119892lowast119904

is the effective degrees of freedom for the entropy densityTherefore one finds

119889119904

119889119909= minus

3119904

119909 (12)

Thus with assuming 119892lowast≃ 119892

lowast119904

the following expression forthe Boltzmann equation for the LSP number density isobtained

119889119884

119889119909= minusradic

120587119892lowast

45119872

119875119897119898

120594

⟨120590ann120594

V⟩

1199092(1198842 minus 1198842

eq) (13)

If one considers the s-wave and p-wave annihilationprocesses only the thermal average ⟨120590ann

120594V⟩ then shows as

⟨120590ann120594

V⟩ ≃ 119886120594+6119887

120594

119909 (14)

Advances in High Energy Physics 5

f

AZ

f f

120594

120594

120594

120594

120594

120594

f

ff

f

Figure 3 Feynman diagrams contributing to early-universe neutralino 120594 annihilation into fermions through sfermions119885-gauge boson andHiggs

where 119886120594and 119887

120594are the s-wave and p-wave contributions of

annihilation processes respectively The relic density of theDM candidate is given by

Ωℎ2 =119898

1205941199040119884120594(infin)

120588119888ℎ2

(15)

where 1199040= 228215 times 10minus41 GeV3120588

119888= 80992ℎ2times10minus47 GeV4

and by solving the Boltzmann equation one can find 119884120594(infin)

as follows [62]

119884120594 (infin) =

1

120582120594

(119886120594

119909 (119879119891)+

3119887120594

1199092 (119879119891))

minus1

(16)

where 119879119891is the freeze-out temperature 120582

120594= 119904(119898

120594)119867(119898

120594)

and 119909(119879119891) is given by

119909 (119879119891) = ln[[

[

120572120594120582120594119888 (119888 + 2)

radic119909 (119879119891)

(119886120594+

6119887120594

119909 (119879119891))]]

]

(17)

where 120572120594= (4521205874)radic1205878(119892

120594119892

lowast119904

(119879119891)) the value 119888 = 12

results in a typical accuracy of about 5ndash10 more than suf-ficient for our purposes here

The lightest neutralino may annihilate into fermion-antifermion (119891119891) 119882+119882minus 119885119885 119882+119867minus 119885119860 119885119867 119885ℎ and119867+119867minus and all other contributions of neutral Higgs For abino-like LSP that is 119873

11≃ 1 and 119873

1119894≃ 0 119894 = 2 3 4 one

finds that the relevant annihilation channels are the fermion-antifermion ones as shown in Figure 3 and all other chan-nels are instead suppressed Also the annihilation processmediated by 119885-gauge boson is suppressed due to the small119885120594120594 coupling prop 1198732

13minus 1198732

14 except at the resonance when

119898120594sim 119872

1198852 which is no longer possible due to the above-

mentioned constraints Furthermore one finds that the t-channel annihilation (first Feynman diagram in Figure 3) ispredominantly into leptons through the exchanges of thethree slepton families (119897

119871 119877) with 119897 = 119890 120583 120591 The squarks

exchanges are suppressed due to their large massesIn Figure 4 we display the constraint from the observed

limits of Ωℎ2 on the plane (1198980-119898

12) for 119860

0= 0 2000GeV

tan120573 = 10 50 and 120583 gt 0 Here we used micrOMEGAs [63]to compute the complete relic abundance of the lightest

neutralino taking into account the possibility of having coan-nihilation with the next-to-lightest supersymmetric particlewhich is typically the lightest stau Note that this type of coan-nihilation is not included in the approximated expressions in(14)ndash(17) In this figure the red regions correspond to a relicabundance within the measured limits [1]

009 lt Ωℎ2 lt 014 (18)

It is noticeable that with low tan120573 (sim10) this region corre-sponds to light 119898

12(lt500GeV) where significant coanni-

hilation between the LSP and stau took place However thispossibility is now excluded by the Higgs and gluino massconstraints [64] At large tan120573 another region is alloweddue to possible resonance due to 119904-channel annihilation ofthe DM pair into fermion-antifermion via the pseudoscalarHiggs boson 119860 at 119872

119860≃ 2119898

120594[65] For 119860

0= 0 a very small

part of this region is allowed by the Higgs mass constraintwhile for large 119860

0(sim2 TeV) slight enhancement of this part

can be achieved In Figure 5 we zoom in on this region toshow the explicit dependence of the relic abundance on theLSP mass and large values of tan120573 As can be seen from thisfigure there is no point that can satisfy the relic abundancestringent constraints with tan120573 lt 30

33 Direct Detection Perhaps themost natural way of search-ing for the neutralino DM is provided by direct experi-ments where the effects induced in appropriate detectors byneutralino-nucleus elastic scattering may be measured Theelastic-scattering cross section of the LSPwith a given nucleushas two contributions spin-dependent contribution arisingfrom 119885 and exchange diagrams and spin-independent(scalar) contribution due to the Higgs and squark exchangediagrams which is typically suppressed The effective scalarinteraction of neutralino with a quark is given by

Lscalar = 119891119902120594120594119902119902 (19)

where 119891119902is the neutralino-quark effective coupling The

scalar cross section of the neutralino scattering with targetnucleus at zero momentum transfer is given by [2]

120590SI0=41198982

119903

120587(119885119891

119901+ (119860 minus 119885)119891

119899)2

(20)

where 119885 and 119860 minus 119885 are the number of protons and neu-trons respectively 119898

119903= 119898

119873119898

120594(119898

119873+ 119898

120594) where 119898

119873is

6 Advances in High Energy Physics

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 10 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

Figure 4 LSP relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The LUX result is satisfied by the

yellow region The other color codes are as in Figure 1

500 550 600 650 700 750 800009

010

011

012

013

014

Ωh2

m120594 (GeV)

Figure 5 The relic abundance versus the mass of the LSP fordifferent values of tan120573 Red points indicate 40 le tan120573 le 50 andblue points 30 le tan120573 lt 40 All points satisfy the abovementionedconstraints

the nucleus mass and 119891119901 119891

119899are the neutralino coupling

to protons and neutrons respectively The differential scalarcross section for nonzero momentum transfer 119902 can now bewritten

119889120590SI1198891199022

=120590SI0

41198982

119903V21198652 (1199022) 0 lt 1199022 lt 41198982

119903V2 (21)

10 20 50 100 200 500 1000 2000m120594 (GeV)

120590p SI(cm

2)

10minus45

10minus47

10minus49

10minus51

LUX

Figure 6 Spin-independent scattering cross section of the LSP witha proton versus the mass of the LSP within the region allowed by allconstraints (from the LHC and relic abundance)

where V is the neutrino velocity and 119865(1199022) is the form factor[2] In Figure 6 we display the MSSM prediction for spin-independent scattering cross section of the LSP with a proton(120590119901SI = int

41198982

119903V2

0(119889120590SI119889119902

2)|119891119899=119891119901

1198891199022) after imposing the LHC

Advances in High Energy Physics 7

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)

Figure 7 LSP nonthermal relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The color codes are

as in Figure 1

and relic abundance constraints It is clear that our results for120590119901

SI are less than the recent LUX bound (blue curve) by at leasttwo orders of magnitude This would explain the negativeresults of direct searches so far

4 Nonthermal Dark Matter andMSSM Parameter Space

In the previous section we assumed standard cosmologyscenario where the reheating temperature 119879RH is very largenamely119879RH ≫ 119879

119891≃ 10GeVHowever the only constraint on

the reheating temperature which could be associated withdecay of any scalar field 120601 not only the inflaton field is119879RH ≳ 1MeV in order not to spoil the successful predictionsof big bang nucleosynthesis

A detailed analysis of the relic density with a low reheat-ing temperature has been carried out in [66] It was empha-sized that for a large annihilation cross section ⟨120590annV⟩ ≳

10minus14 GeVminus2 so that the neutralino reaches equilibriumbefore reheating and if there are a large number of neutrali-nos produced by the scalar field 120601 decay then the relic densityis estimated as [67]

Ωℎ2 =3119898

120594Γ120601

2 (2120587245) 119892lowast(119879RH) 119879

3

RH ⟨120590ann120594

V⟩ℎ2

120588119888119904

0

(22)

Here the reheating temperature is defined as [62]

119879RH = (90

1205872119892lowast(119879RH)

)

14

(Γ120601119872

119875119897)12

(23)

where the decay width Γ120601is given by

Γ120601=

1

2120587

1198983

120601

Λ2 (24)

The scaleΛ is the effective suppression scale which is of orderthe grand unification scale119872

119883Therefore for scalar fieldwith

mass 119898120601≃ 107 GeV one finds Γ

120601≃ 10minus11 GeV and in our

calculations we have used 119892lowast

= 1075 due to the consid-eration of a low reheating temperature scenario

In Figure 7 we show the constraints imposed on theMSSM (119898

0-119898

12) plane in case of nonthermal relic abun-

dance of the LSP for tan120573 = 10 50 and 1198600= 0 2TeV In this

plot we also imposed the LHC constraints namely the Higgsmass limit and the gluino mass lower bound similar to thecase of thermal scenario It is clear from this figure that thestringent constraints imposed on theMSSM parameter spaceby thermal relic abundance are now relaxed and now lowtan120573 (sim10) is allowed but with very heavy 119898

0(simO(4)TeV)

and 11989812

≃ 600GeV In addition the following two regionsare now allowed with large tan120573 (sim50) (i) 119898

0sim 119898

12≃

8 Advances in High Energy Physics

O(1)TeV (ii)1198980≃ O(4)TeV and119898

12≃ 700GeV The SUSY

spectrum associated with these regions of parameters spacecould be striking signature for nonthermal scenario at theLHC

5 Conclusion

We have studied the constraints imposed on the MSSMparameter space by the Higgsmass limit and the gluino lowerbound which are the most stringent collider constraintsobtained from the LHC run-I at energy 8 TeV We showedthat 119898

12resides within the mass range 620GeV ≲ 119898

12≲

2000GeV while the other parameters (1198980 119860

0 tan120573) are

much less constrained We also studied the effect of themeasured DM relic density on the MSSM allowed parameterspace It turns out that most of the MSSM parameter spaceis ruled out except for few points around tan120573 sim 50119898

0sim 1TeV and 119898

12sim 15TeV We calculated the spin-

independent scattering cross section of the LSP with a protonin this allowed region We showed that our prediction for120590119901

SI is less than the recent LUX bound by at least two ordersof magnitude We have also analyzed the nonthermal DMscenario for the LSPWe showed that the constraints imposedon the MSSM parameter space are relaxed and low tan120573 isnow allowed with 119898

0≃ O(4)TeV and 119898

12≃ 600GeV Also

two allowed regions are now associated with large tan120573 (sim50) namely 119898

0sim 119898

12≃ O(1)TeV or 119898

0≃ O(4)TeV and

11989812

≃ 700GeV

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by the STDF Project 13858the ICTP Grant AC-80 and the European Union FP7 ITNINVISIBLES (Marie Curie Actions PITN-GA-2011-289442)

References

[1] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquo Astronomy ampAstrophysics vol 571 article A16 2014

[2] G Jungman M Kamionkowski and K Griest ldquoSupersymmet-ric dark matterrdquo Physics Report vol 267 no 5-6 pp 195ndash3731996

[3] G Bertone D Hooper and J Silk ldquoParticle dark matter evi-dence candidates and constraintsrdquo Physics Reports vol 405 no5-6 pp 279ndash390 2005

[4] H PNilles ldquoSupersymmetry supergravity andparticle physicsrdquoPhysics Reports vol 110 no 1-2 pp 1ndash162 1984

[5] J D Lykken ldquoIntroduction tosupersymmetryrdquo In press httparxivorgabshep-th9612114

[6] J Wess and J Bagger Supersymmetry and Supergravity Prince-ton University Press Princeton NJ USA 2nd edition 1991

[7] H E Haber and G Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[8] S P Martin ldquoA Supersymmetry Primerrdquo Advanced Series onDirections in High Energy Physics vol 21 pp 1ndash153 2010Advanced Series on Directions in High Energy Physics vol 18pp 1ndash98 1998

[9] D J H Chung L L Everett G L Kane S F King J D Lykkenand L TWang ldquoThe soft supersymmetry-breaking Lagrangiantheory and applicationsrdquo Physics Reports vol 407 no 1ndash3 pp 1ndash203 2005

[10] M Drees P Roy and R M GodboleTheory and Phenomenol-ogy of Sparticles World Scientific Singapore 2005

[11] H Baer and X Tata Weak Scale Supersymmetry From Super-fields to Scattering Events Cambridge University Press Cam-bridge UK 2006

[12] H Goldberg ldquoConstraint on the photino mass from cosmol-ogyrdquo Physical Review Letters vol 50 no 19 pp 1419ndash14221983 Erratum-ibid Physical Review Letters vol 103 Article ID099905 2009

[13] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[14] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoObser-vation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHCrdquo Physics Letters B vol 716 no 1 pp30ndash61 2012

[15] G Aad B Abbott J Abdallah et al ldquoSummary of the ATLASexperimentrsquos sensitivity to supersymmetry after LHC Run 1mdashinterpreted in the phenomenological MSSMrdquo Journal of HighEnergy Physics vol 2015 article 134 2015

[16] A Gaz ldquoSUSY searches at CMSrdquo In press httparxivorgabs14111886

[17] I Melzer-Pellmann and P Pralavorio ldquoLessons for SUSY fromthe LHC after the first runrdquo The European Physical Journal Cvol 74 article 2801 2014

[18] N Craig ldquoThe state ofsupersymmetry after Run I of the LHCrdquohttparxivorgabs13090528

[19] D S Akerib H M Araujo X Bai et al ldquoFirst results from theLUX dark matter experiment at the Sanford UndergroundResearch Facilityrdquo Physical Review Letters vol 112 Article ID091303 2014

[20] E Aprile ldquoThe Xenon1T dark matter search experimentrdquo inSources and Detection of Dark Matter and Dark Energy in theUniverse vol 148 of Springer Proceedings in Physics pp 93ndash96Springer 2013

[21] E AprileMAlfonsi K Arisaka et al ldquoDarkmatter results from225 live days of XENON100 datardquo Physical Review Letters vol109 no 18 Article ID 181301 6 pages 2012

[22] H Baer V Barger and A Mustafayev ldquoImplications of a125GeV Higgs scalar for the LHC supersymmetry and neu-tralino dark matter searchesrdquo Physical Review D vol 85 ArticleID 075010 2012

[23] J Ellis and K A Olive ldquoRevisiting the higgs mass and darkmatter in the CMSSMrdquo The European Physical Journal C vol72 article 2005 2012

[24] O Buchmueller R Cavanaugh M Citron et al ldquoThe CMSSMand NUHM1 in light of 7 TeV LHC 119861

119904rarr 120583+120583minus and

XENON100 datardquoThe European Physical Journal C vol 72 no11 article 2243 2012

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in High Energy Physics 5

f

AZ

f f

120594

120594

120594

120594

120594

120594

f

ff

f

Figure 3 Feynman diagrams contributing to early-universe neutralino 120594 annihilation into fermions through sfermions119885-gauge boson andHiggs

where 119886120594and 119887

120594are the s-wave and p-wave contributions of

annihilation processes respectively The relic density of theDM candidate is given by

Ωℎ2 =119898

1205941199040119884120594(infin)

120588119888ℎ2

(15)

where 1199040= 228215 times 10minus41 GeV3120588

119888= 80992ℎ2times10minus47 GeV4

and by solving the Boltzmann equation one can find 119884120594(infin)

as follows [62]

119884120594 (infin) =

1

120582120594

(119886120594

119909 (119879119891)+

3119887120594

1199092 (119879119891))

minus1

(16)

where 119879119891is the freeze-out temperature 120582

120594= 119904(119898

120594)119867(119898

120594)

and 119909(119879119891) is given by

119909 (119879119891) = ln[[

[

120572120594120582120594119888 (119888 + 2)

radic119909 (119879119891)

(119886120594+

6119887120594

119909 (119879119891))]]

]

(17)

where 120572120594= (4521205874)radic1205878(119892

120594119892

lowast119904

(119879119891)) the value 119888 = 12

results in a typical accuracy of about 5ndash10 more than suf-ficient for our purposes here

The lightest neutralino may annihilate into fermion-antifermion (119891119891) 119882+119882minus 119885119885 119882+119867minus 119885119860 119885119867 119885ℎ and119867+119867minus and all other contributions of neutral Higgs For abino-like LSP that is 119873

11≃ 1 and 119873

1119894≃ 0 119894 = 2 3 4 one

finds that the relevant annihilation channels are the fermion-antifermion ones as shown in Figure 3 and all other chan-nels are instead suppressed Also the annihilation processmediated by 119885-gauge boson is suppressed due to the small119885120594120594 coupling prop 1198732

13minus 1198732

14 except at the resonance when

119898120594sim 119872

1198852 which is no longer possible due to the above-

mentioned constraints Furthermore one finds that the t-channel annihilation (first Feynman diagram in Figure 3) ispredominantly into leptons through the exchanges of thethree slepton families (119897

119871 119877) with 119897 = 119890 120583 120591 The squarks

exchanges are suppressed due to their large massesIn Figure 4 we display the constraint from the observed

limits of Ωℎ2 on the plane (1198980-119898

12) for 119860

0= 0 2000GeV

tan120573 = 10 50 and 120583 gt 0 Here we used micrOMEGAs [63]to compute the complete relic abundance of the lightest

neutralino taking into account the possibility of having coan-nihilation with the next-to-lightest supersymmetric particlewhich is typically the lightest stau Note that this type of coan-nihilation is not included in the approximated expressions in(14)ndash(17) In this figure the red regions correspond to a relicabundance within the measured limits [1]

009 lt Ωℎ2 lt 014 (18)

It is noticeable that with low tan120573 (sim10) this region corre-sponds to light 119898

12(lt500GeV) where significant coanni-

hilation between the LSP and stau took place However thispossibility is now excluded by the Higgs and gluino massconstraints [64] At large tan120573 another region is alloweddue to possible resonance due to 119904-channel annihilation ofthe DM pair into fermion-antifermion via the pseudoscalarHiggs boson 119860 at 119872

119860≃ 2119898

120594[65] For 119860

0= 0 a very small

part of this region is allowed by the Higgs mass constraintwhile for large 119860

0(sim2 TeV) slight enhancement of this part

can be achieved In Figure 5 we zoom in on this region toshow the explicit dependence of the relic abundance on theLSP mass and large values of tan120573 As can be seen from thisfigure there is no point that can satisfy the relic abundancestringent constraints with tan120573 lt 30

33 Direct Detection Perhaps themost natural way of search-ing for the neutralino DM is provided by direct experi-ments where the effects induced in appropriate detectors byneutralino-nucleus elastic scattering may be measured Theelastic-scattering cross section of the LSPwith a given nucleushas two contributions spin-dependent contribution arisingfrom 119885 and exchange diagrams and spin-independent(scalar) contribution due to the Higgs and squark exchangediagrams which is typically suppressed The effective scalarinteraction of neutralino with a quark is given by

Lscalar = 119891119902120594120594119902119902 (19)

where 119891119902is the neutralino-quark effective coupling The

scalar cross section of the neutralino scattering with targetnucleus at zero momentum transfer is given by [2]

120590SI0=41198982

119903

120587(119885119891

119901+ (119860 minus 119885)119891

119899)2

(20)

where 119885 and 119860 minus 119885 are the number of protons and neu-trons respectively 119898

119903= 119898

119873119898

120594(119898

119873+ 119898

120594) where 119898

119873is

6 Advances in High Energy Physics

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 10 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

Figure 4 LSP relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The LUX result is satisfied by the

yellow region The other color codes are as in Figure 1

500 550 600 650 700 750 800009

010

011

012

013

014

Ωh2

m120594 (GeV)

Figure 5 The relic abundance versus the mass of the LSP fordifferent values of tan120573 Red points indicate 40 le tan120573 le 50 andblue points 30 le tan120573 lt 40 All points satisfy the abovementionedconstraints

the nucleus mass and 119891119901 119891

119899are the neutralino coupling

to protons and neutrons respectively The differential scalarcross section for nonzero momentum transfer 119902 can now bewritten

119889120590SI1198891199022

=120590SI0

41198982

119903V21198652 (1199022) 0 lt 1199022 lt 41198982

119903V2 (21)

10 20 50 100 200 500 1000 2000m120594 (GeV)

120590p SI(cm

2)

10minus45

10minus47

10minus49

10minus51

LUX

Figure 6 Spin-independent scattering cross section of the LSP witha proton versus the mass of the LSP within the region allowed by allconstraints (from the LHC and relic abundance)

where V is the neutrino velocity and 119865(1199022) is the form factor[2] In Figure 6 we display the MSSM prediction for spin-independent scattering cross section of the LSP with a proton(120590119901SI = int

41198982

119903V2

0(119889120590SI119889119902

2)|119891119899=119891119901

1198891199022) after imposing the LHC

Advances in High Energy Physics 7

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)

Figure 7 LSP nonthermal relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The color codes are

as in Figure 1

and relic abundance constraints It is clear that our results for120590119901

SI are less than the recent LUX bound (blue curve) by at leasttwo orders of magnitude This would explain the negativeresults of direct searches so far

4 Nonthermal Dark Matter andMSSM Parameter Space

In the previous section we assumed standard cosmologyscenario where the reheating temperature 119879RH is very largenamely119879RH ≫ 119879

119891≃ 10GeVHowever the only constraint on

the reheating temperature which could be associated withdecay of any scalar field 120601 not only the inflaton field is119879RH ≳ 1MeV in order not to spoil the successful predictionsof big bang nucleosynthesis

A detailed analysis of the relic density with a low reheat-ing temperature has been carried out in [66] It was empha-sized that for a large annihilation cross section ⟨120590annV⟩ ≳

10minus14 GeVminus2 so that the neutralino reaches equilibriumbefore reheating and if there are a large number of neutrali-nos produced by the scalar field 120601 decay then the relic densityis estimated as [67]

Ωℎ2 =3119898

120594Γ120601

2 (2120587245) 119892lowast(119879RH) 119879

3

RH ⟨120590ann120594

V⟩ℎ2

120588119888119904

0

(22)

Here the reheating temperature is defined as [62]

119879RH = (90

1205872119892lowast(119879RH)

)

14

(Γ120601119872

119875119897)12

(23)

where the decay width Γ120601is given by

Γ120601=

1

2120587

1198983

120601

Λ2 (24)

The scaleΛ is the effective suppression scale which is of orderthe grand unification scale119872

119883Therefore for scalar fieldwith

mass 119898120601≃ 107 GeV one finds Γ

120601≃ 10minus11 GeV and in our

calculations we have used 119892lowast

= 1075 due to the consid-eration of a low reheating temperature scenario

In Figure 7 we show the constraints imposed on theMSSM (119898

0-119898

12) plane in case of nonthermal relic abun-

dance of the LSP for tan120573 = 10 50 and 1198600= 0 2TeV In this

plot we also imposed the LHC constraints namely the Higgsmass limit and the gluino mass lower bound similar to thecase of thermal scenario It is clear from this figure that thestringent constraints imposed on theMSSM parameter spaceby thermal relic abundance are now relaxed and now lowtan120573 (sim10) is allowed but with very heavy 119898

0(simO(4)TeV)

and 11989812

≃ 600GeV In addition the following two regionsare now allowed with large tan120573 (sim50) (i) 119898

0sim 119898

12≃

8 Advances in High Energy Physics

O(1)TeV (ii)1198980≃ O(4)TeV and119898

12≃ 700GeV The SUSY

spectrum associated with these regions of parameters spacecould be striking signature for nonthermal scenario at theLHC

5 Conclusion

We have studied the constraints imposed on the MSSMparameter space by the Higgsmass limit and the gluino lowerbound which are the most stringent collider constraintsobtained from the LHC run-I at energy 8 TeV We showedthat 119898

12resides within the mass range 620GeV ≲ 119898

12≲

2000GeV while the other parameters (1198980 119860

0 tan120573) are

much less constrained We also studied the effect of themeasured DM relic density on the MSSM allowed parameterspace It turns out that most of the MSSM parameter spaceis ruled out except for few points around tan120573 sim 50119898

0sim 1TeV and 119898

12sim 15TeV We calculated the spin-

independent scattering cross section of the LSP with a protonin this allowed region We showed that our prediction for120590119901

SI is less than the recent LUX bound by at least two ordersof magnitude We have also analyzed the nonthermal DMscenario for the LSPWe showed that the constraints imposedon the MSSM parameter space are relaxed and low tan120573 isnow allowed with 119898

0≃ O(4)TeV and 119898

12≃ 600GeV Also

two allowed regions are now associated with large tan120573 (sim50) namely 119898

0sim 119898

12≃ O(1)TeV or 119898

0≃ O(4)TeV and

11989812

≃ 700GeV

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by the STDF Project 13858the ICTP Grant AC-80 and the European Union FP7 ITNINVISIBLES (Marie Curie Actions PITN-GA-2011-289442)

References

[1] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquo Astronomy ampAstrophysics vol 571 article A16 2014

[2] G Jungman M Kamionkowski and K Griest ldquoSupersymmet-ric dark matterrdquo Physics Report vol 267 no 5-6 pp 195ndash3731996

[3] G Bertone D Hooper and J Silk ldquoParticle dark matter evi-dence candidates and constraintsrdquo Physics Reports vol 405 no5-6 pp 279ndash390 2005

[4] H PNilles ldquoSupersymmetry supergravity andparticle physicsrdquoPhysics Reports vol 110 no 1-2 pp 1ndash162 1984

[5] J D Lykken ldquoIntroduction tosupersymmetryrdquo In press httparxivorgabshep-th9612114

[6] J Wess and J Bagger Supersymmetry and Supergravity Prince-ton University Press Princeton NJ USA 2nd edition 1991

[7] H E Haber and G Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[8] S P Martin ldquoA Supersymmetry Primerrdquo Advanced Series onDirections in High Energy Physics vol 21 pp 1ndash153 2010Advanced Series on Directions in High Energy Physics vol 18pp 1ndash98 1998

[9] D J H Chung L L Everett G L Kane S F King J D Lykkenand L TWang ldquoThe soft supersymmetry-breaking Lagrangiantheory and applicationsrdquo Physics Reports vol 407 no 1ndash3 pp 1ndash203 2005

[10] M Drees P Roy and R M GodboleTheory and Phenomenol-ogy of Sparticles World Scientific Singapore 2005

[11] H Baer and X Tata Weak Scale Supersymmetry From Super-fields to Scattering Events Cambridge University Press Cam-bridge UK 2006

[12] H Goldberg ldquoConstraint on the photino mass from cosmol-ogyrdquo Physical Review Letters vol 50 no 19 pp 1419ndash14221983 Erratum-ibid Physical Review Letters vol 103 Article ID099905 2009

[13] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[14] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoObser-vation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHCrdquo Physics Letters B vol 716 no 1 pp30ndash61 2012

[15] G Aad B Abbott J Abdallah et al ldquoSummary of the ATLASexperimentrsquos sensitivity to supersymmetry after LHC Run 1mdashinterpreted in the phenomenological MSSMrdquo Journal of HighEnergy Physics vol 2015 article 134 2015

[16] A Gaz ldquoSUSY searches at CMSrdquo In press httparxivorgabs14111886

[17] I Melzer-Pellmann and P Pralavorio ldquoLessons for SUSY fromthe LHC after the first runrdquo The European Physical Journal Cvol 74 article 2801 2014

[18] N Craig ldquoThe state ofsupersymmetry after Run I of the LHCrdquohttparxivorgabs13090528

[19] D S Akerib H M Araujo X Bai et al ldquoFirst results from theLUX dark matter experiment at the Sanford UndergroundResearch Facilityrdquo Physical Review Letters vol 112 Article ID091303 2014

[20] E Aprile ldquoThe Xenon1T dark matter search experimentrdquo inSources and Detection of Dark Matter and Dark Energy in theUniverse vol 148 of Springer Proceedings in Physics pp 93ndash96Springer 2013

[21] E AprileMAlfonsi K Arisaka et al ldquoDarkmatter results from225 live days of XENON100 datardquo Physical Review Letters vol109 no 18 Article ID 181301 6 pages 2012

[22] H Baer V Barger and A Mustafayev ldquoImplications of a125GeV Higgs scalar for the LHC supersymmetry and neu-tralino dark matter searchesrdquo Physical Review D vol 85 ArticleID 075010 2012

[23] J Ellis and K A Olive ldquoRevisiting the higgs mass and darkmatter in the CMSSMrdquo The European Physical Journal C vol72 article 2005 2012

[24] O Buchmueller R Cavanaugh M Citron et al ldquoThe CMSSMand NUHM1 in light of 7 TeV LHC 119861

119904rarr 120583+120583minus and

XENON100 datardquoThe European Physical Journal C vol 72 no11 article 2243 2012

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

6 Advances in High Energy Physics

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 10 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)

Figure 4 LSP relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The LUX result is satisfied by the

yellow region The other color codes are as in Figure 1

500 550 600 650 700 750 800009

010

011

012

013

014

Ωh2

m120594 (GeV)

Figure 5 The relic abundance versus the mass of the LSP fordifferent values of tan120573 Red points indicate 40 le tan120573 le 50 andblue points 30 le tan120573 lt 40 All points satisfy the abovementionedconstraints

the nucleus mass and 119891119901 119891

119899are the neutralino coupling

to protons and neutrons respectively The differential scalarcross section for nonzero momentum transfer 119902 can now bewritten

119889120590SI1198891199022

=120590SI0

41198982

119903V21198652 (1199022) 0 lt 1199022 lt 41198982

119903V2 (21)

10 20 50 100 200 500 1000 2000m120594 (GeV)

120590p SI(cm

2)

10minus45

10minus47

10minus49

10minus51

LUX

Figure 6 Spin-independent scattering cross section of the LSP witha proton versus the mass of the LSP within the region allowed by allconstraints (from the LHC and relic abundance)

where V is the neutrino velocity and 119865(1199022) is the form factor[2] In Figure 6 we display the MSSM prediction for spin-independent scattering cross section of the LSP with a proton(120590119901SI = int

41198982

119903V2

0(119889120590SI119889119902

2)|119891119899=119891119901

1198891199022) after imposing the LHC

Advances in High Energy Physics 7

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)

Figure 7 LSP nonthermal relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The color codes are

as in Figure 1

and relic abundance constraints It is clear that our results for120590119901

SI are less than the recent LUX bound (blue curve) by at leasttwo orders of magnitude This would explain the negativeresults of direct searches so far

4 Nonthermal Dark Matter andMSSM Parameter Space

In the previous section we assumed standard cosmologyscenario where the reheating temperature 119879RH is very largenamely119879RH ≫ 119879

119891≃ 10GeVHowever the only constraint on

the reheating temperature which could be associated withdecay of any scalar field 120601 not only the inflaton field is119879RH ≳ 1MeV in order not to spoil the successful predictionsof big bang nucleosynthesis

A detailed analysis of the relic density with a low reheat-ing temperature has been carried out in [66] It was empha-sized that for a large annihilation cross section ⟨120590annV⟩ ≳

10minus14 GeVminus2 so that the neutralino reaches equilibriumbefore reheating and if there are a large number of neutrali-nos produced by the scalar field 120601 decay then the relic densityis estimated as [67]

Ωℎ2 =3119898

120594Γ120601

2 (2120587245) 119892lowast(119879RH) 119879

3

RH ⟨120590ann120594

V⟩ℎ2

120588119888119904

0

(22)

Here the reheating temperature is defined as [62]

119879RH = (90

1205872119892lowast(119879RH)

)

14

(Γ120601119872

119875119897)12

(23)

where the decay width Γ120601is given by

Γ120601=

1

2120587

1198983

120601

Λ2 (24)

The scaleΛ is the effective suppression scale which is of orderthe grand unification scale119872

119883Therefore for scalar fieldwith

mass 119898120601≃ 107 GeV one finds Γ

120601≃ 10minus11 GeV and in our

calculations we have used 119892lowast

= 1075 due to the consid-eration of a low reheating temperature scenario

In Figure 7 we show the constraints imposed on theMSSM (119898

0-119898

12) plane in case of nonthermal relic abun-

dance of the LSP for tan120573 = 10 50 and 1198600= 0 2TeV In this

plot we also imposed the LHC constraints namely the Higgsmass limit and the gluino mass lower bound similar to thecase of thermal scenario It is clear from this figure that thestringent constraints imposed on theMSSM parameter spaceby thermal relic abundance are now relaxed and now lowtan120573 (sim10) is allowed but with very heavy 119898

0(simO(4)TeV)

and 11989812

≃ 600GeV In addition the following two regionsare now allowed with large tan120573 (sim50) (i) 119898

0sim 119898

12≃

8 Advances in High Energy Physics

O(1)TeV (ii)1198980≃ O(4)TeV and119898

12≃ 700GeV The SUSY

spectrum associated with these regions of parameters spacecould be striking signature for nonthermal scenario at theLHC

5 Conclusion

We have studied the constraints imposed on the MSSMparameter space by the Higgsmass limit and the gluino lowerbound which are the most stringent collider constraintsobtained from the LHC run-I at energy 8 TeV We showedthat 119898

12resides within the mass range 620GeV ≲ 119898

12≲

2000GeV while the other parameters (1198980 119860

0 tan120573) are

much less constrained We also studied the effect of themeasured DM relic density on the MSSM allowed parameterspace It turns out that most of the MSSM parameter spaceis ruled out except for few points around tan120573 sim 50119898

0sim 1TeV and 119898

12sim 15TeV We calculated the spin-

independent scattering cross section of the LSP with a protonin this allowed region We showed that our prediction for120590119901

SI is less than the recent LUX bound by at least two ordersof magnitude We have also analyzed the nonthermal DMscenario for the LSPWe showed that the constraints imposedon the MSSM parameter space are relaxed and low tan120573 isnow allowed with 119898

0≃ O(4)TeV and 119898

12≃ 600GeV Also

two allowed regions are now associated with large tan120573 (sim50) namely 119898

0sim 119898

12≃ O(1)TeV or 119898

0≃ O(4)TeV and

11989812

≃ 700GeV

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by the STDF Project 13858the ICTP Grant AC-80 and the European Union FP7 ITNINVISIBLES (Marie Curie Actions PITN-GA-2011-289442)

References

[1] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquo Astronomy ampAstrophysics vol 571 article A16 2014

[2] G Jungman M Kamionkowski and K Griest ldquoSupersymmet-ric dark matterrdquo Physics Report vol 267 no 5-6 pp 195ndash3731996

[3] G Bertone D Hooper and J Silk ldquoParticle dark matter evi-dence candidates and constraintsrdquo Physics Reports vol 405 no5-6 pp 279ndash390 2005

[4] H PNilles ldquoSupersymmetry supergravity andparticle physicsrdquoPhysics Reports vol 110 no 1-2 pp 1ndash162 1984

[5] J D Lykken ldquoIntroduction tosupersymmetryrdquo In press httparxivorgabshep-th9612114

[6] J Wess and J Bagger Supersymmetry and Supergravity Prince-ton University Press Princeton NJ USA 2nd edition 1991

[7] H E Haber and G Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[8] S P Martin ldquoA Supersymmetry Primerrdquo Advanced Series onDirections in High Energy Physics vol 21 pp 1ndash153 2010Advanced Series on Directions in High Energy Physics vol 18pp 1ndash98 1998

[9] D J H Chung L L Everett G L Kane S F King J D Lykkenand L TWang ldquoThe soft supersymmetry-breaking Lagrangiantheory and applicationsrdquo Physics Reports vol 407 no 1ndash3 pp 1ndash203 2005

[10] M Drees P Roy and R M GodboleTheory and Phenomenol-ogy of Sparticles World Scientific Singapore 2005

[11] H Baer and X Tata Weak Scale Supersymmetry From Super-fields to Scattering Events Cambridge University Press Cam-bridge UK 2006

[12] H Goldberg ldquoConstraint on the photino mass from cosmol-ogyrdquo Physical Review Letters vol 50 no 19 pp 1419ndash14221983 Erratum-ibid Physical Review Letters vol 103 Article ID099905 2009

[13] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[14] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoObser-vation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHCrdquo Physics Letters B vol 716 no 1 pp30ndash61 2012

[15] G Aad B Abbott J Abdallah et al ldquoSummary of the ATLASexperimentrsquos sensitivity to supersymmetry after LHC Run 1mdashinterpreted in the phenomenological MSSMrdquo Journal of HighEnergy Physics vol 2015 article 134 2015

[16] A Gaz ldquoSUSY searches at CMSrdquo In press httparxivorgabs14111886

[17] I Melzer-Pellmann and P Pralavorio ldquoLessons for SUSY fromthe LHC after the first runrdquo The European Physical Journal Cvol 74 article 2801 2014

[18] N Craig ldquoThe state ofsupersymmetry after Run I of the LHCrdquohttparxivorgabs13090528

[19] D S Akerib H M Araujo X Bai et al ldquoFirst results from theLUX dark matter experiment at the Sanford UndergroundResearch Facilityrdquo Physical Review Letters vol 112 Article ID091303 2014

[20] E Aprile ldquoThe Xenon1T dark matter search experimentrdquo inSources and Detection of Dark Matter and Dark Energy in theUniverse vol 148 of Springer Proceedings in Physics pp 93ndash96Springer 2013

[21] E AprileMAlfonsi K Arisaka et al ldquoDarkmatter results from225 live days of XENON100 datardquo Physical Review Letters vol109 no 18 Article ID 181301 6 pages 2012

[22] H Baer V Barger and A Mustafayev ldquoImplications of a125GeV Higgs scalar for the LHC supersymmetry and neu-tralino dark matter searchesrdquo Physical Review D vol 85 ArticleID 075010 2012

[23] J Ellis and K A Olive ldquoRevisiting the higgs mass and darkmatter in the CMSSMrdquo The European Physical Journal C vol72 article 2005 2012

[24] O Buchmueller R Cavanaugh M Citron et al ldquoThe CMSSMand NUHM1 in light of 7 TeV LHC 119861

119904rarr 120583+120583minus and

XENON100 datardquoThe European Physical Journal C vol 72 no11 article 2243 2012

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in High Energy Physics 7

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 50 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000

m0(G

eV)

m12 (GeV)

tan120573 = 50 120583 gt 0 A0 = 0GeV

0 500 1000 1500 20000

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 2000GeV

m0(G

eV)

m12 (GeV)0 500 1000 1500 2000

0

1000

2000

3000

4000

5000

6000tan120573 = 10 120583 gt 0 A0 = 0GeV

m0(G

eV)

m12 (GeV)

Figure 7 LSP nonthermal relic abundance constraints (red regions) on (1198980-119898

12) plane for tan120573 and 119860

0as in Figure 1 The color codes are

as in Figure 1

and relic abundance constraints It is clear that our results for120590119901

SI are less than the recent LUX bound (blue curve) by at leasttwo orders of magnitude This would explain the negativeresults of direct searches so far

4 Nonthermal Dark Matter andMSSM Parameter Space

In the previous section we assumed standard cosmologyscenario where the reheating temperature 119879RH is very largenamely119879RH ≫ 119879

119891≃ 10GeVHowever the only constraint on

the reheating temperature which could be associated withdecay of any scalar field 120601 not only the inflaton field is119879RH ≳ 1MeV in order not to spoil the successful predictionsof big bang nucleosynthesis

A detailed analysis of the relic density with a low reheat-ing temperature has been carried out in [66] It was empha-sized that for a large annihilation cross section ⟨120590annV⟩ ≳

10minus14 GeVminus2 so that the neutralino reaches equilibriumbefore reheating and if there are a large number of neutrali-nos produced by the scalar field 120601 decay then the relic densityis estimated as [67]

Ωℎ2 =3119898

120594Γ120601

2 (2120587245) 119892lowast(119879RH) 119879

3

RH ⟨120590ann120594

V⟩ℎ2

120588119888119904

0

(22)

Here the reheating temperature is defined as [62]

119879RH = (90

1205872119892lowast(119879RH)

)

14

(Γ120601119872

119875119897)12

(23)

where the decay width Γ120601is given by

Γ120601=

1

2120587

1198983

120601

Λ2 (24)

The scaleΛ is the effective suppression scale which is of orderthe grand unification scale119872

119883Therefore for scalar fieldwith

mass 119898120601≃ 107 GeV one finds Γ

120601≃ 10minus11 GeV and in our

calculations we have used 119892lowast

= 1075 due to the consid-eration of a low reheating temperature scenario

In Figure 7 we show the constraints imposed on theMSSM (119898

0-119898

12) plane in case of nonthermal relic abun-

dance of the LSP for tan120573 = 10 50 and 1198600= 0 2TeV In this

plot we also imposed the LHC constraints namely the Higgsmass limit and the gluino mass lower bound similar to thecase of thermal scenario It is clear from this figure that thestringent constraints imposed on theMSSM parameter spaceby thermal relic abundance are now relaxed and now lowtan120573 (sim10) is allowed but with very heavy 119898

0(simO(4)TeV)

and 11989812

≃ 600GeV In addition the following two regionsare now allowed with large tan120573 (sim50) (i) 119898

0sim 119898

12≃

8 Advances in High Energy Physics

O(1)TeV (ii)1198980≃ O(4)TeV and119898

12≃ 700GeV The SUSY

spectrum associated with these regions of parameters spacecould be striking signature for nonthermal scenario at theLHC

5 Conclusion

We have studied the constraints imposed on the MSSMparameter space by the Higgsmass limit and the gluino lowerbound which are the most stringent collider constraintsobtained from the LHC run-I at energy 8 TeV We showedthat 119898

12resides within the mass range 620GeV ≲ 119898

12≲

2000GeV while the other parameters (1198980 119860

0 tan120573) are

much less constrained We also studied the effect of themeasured DM relic density on the MSSM allowed parameterspace It turns out that most of the MSSM parameter spaceis ruled out except for few points around tan120573 sim 50119898

0sim 1TeV and 119898

12sim 15TeV We calculated the spin-

independent scattering cross section of the LSP with a protonin this allowed region We showed that our prediction for120590119901

SI is less than the recent LUX bound by at least two ordersof magnitude We have also analyzed the nonthermal DMscenario for the LSPWe showed that the constraints imposedon the MSSM parameter space are relaxed and low tan120573 isnow allowed with 119898

0≃ O(4)TeV and 119898

12≃ 600GeV Also

two allowed regions are now associated with large tan120573 (sim50) namely 119898

0sim 119898

12≃ O(1)TeV or 119898

0≃ O(4)TeV and

11989812

≃ 700GeV

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by the STDF Project 13858the ICTP Grant AC-80 and the European Union FP7 ITNINVISIBLES (Marie Curie Actions PITN-GA-2011-289442)

References

[1] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquo Astronomy ampAstrophysics vol 571 article A16 2014

[2] G Jungman M Kamionkowski and K Griest ldquoSupersymmet-ric dark matterrdquo Physics Report vol 267 no 5-6 pp 195ndash3731996

[3] G Bertone D Hooper and J Silk ldquoParticle dark matter evi-dence candidates and constraintsrdquo Physics Reports vol 405 no5-6 pp 279ndash390 2005

[4] H PNilles ldquoSupersymmetry supergravity andparticle physicsrdquoPhysics Reports vol 110 no 1-2 pp 1ndash162 1984

[5] J D Lykken ldquoIntroduction tosupersymmetryrdquo In press httparxivorgabshep-th9612114

[6] J Wess and J Bagger Supersymmetry and Supergravity Prince-ton University Press Princeton NJ USA 2nd edition 1991

[7] H E Haber and G Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[8] S P Martin ldquoA Supersymmetry Primerrdquo Advanced Series onDirections in High Energy Physics vol 21 pp 1ndash153 2010Advanced Series on Directions in High Energy Physics vol 18pp 1ndash98 1998

[9] D J H Chung L L Everett G L Kane S F King J D Lykkenand L TWang ldquoThe soft supersymmetry-breaking Lagrangiantheory and applicationsrdquo Physics Reports vol 407 no 1ndash3 pp 1ndash203 2005

[10] M Drees P Roy and R M GodboleTheory and Phenomenol-ogy of Sparticles World Scientific Singapore 2005

[11] H Baer and X Tata Weak Scale Supersymmetry From Super-fields to Scattering Events Cambridge University Press Cam-bridge UK 2006

[12] H Goldberg ldquoConstraint on the photino mass from cosmol-ogyrdquo Physical Review Letters vol 50 no 19 pp 1419ndash14221983 Erratum-ibid Physical Review Letters vol 103 Article ID099905 2009

[13] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[14] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoObser-vation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHCrdquo Physics Letters B vol 716 no 1 pp30ndash61 2012

[15] G Aad B Abbott J Abdallah et al ldquoSummary of the ATLASexperimentrsquos sensitivity to supersymmetry after LHC Run 1mdashinterpreted in the phenomenological MSSMrdquo Journal of HighEnergy Physics vol 2015 article 134 2015

[16] A Gaz ldquoSUSY searches at CMSrdquo In press httparxivorgabs14111886

[17] I Melzer-Pellmann and P Pralavorio ldquoLessons for SUSY fromthe LHC after the first runrdquo The European Physical Journal Cvol 74 article 2801 2014

[18] N Craig ldquoThe state ofsupersymmetry after Run I of the LHCrdquohttparxivorgabs13090528

[19] D S Akerib H M Araujo X Bai et al ldquoFirst results from theLUX dark matter experiment at the Sanford UndergroundResearch Facilityrdquo Physical Review Letters vol 112 Article ID091303 2014

[20] E Aprile ldquoThe Xenon1T dark matter search experimentrdquo inSources and Detection of Dark Matter and Dark Energy in theUniverse vol 148 of Springer Proceedings in Physics pp 93ndash96Springer 2013

[21] E AprileMAlfonsi K Arisaka et al ldquoDarkmatter results from225 live days of XENON100 datardquo Physical Review Letters vol109 no 18 Article ID 181301 6 pages 2012

[22] H Baer V Barger and A Mustafayev ldquoImplications of a125GeV Higgs scalar for the LHC supersymmetry and neu-tralino dark matter searchesrdquo Physical Review D vol 85 ArticleID 075010 2012

[23] J Ellis and K A Olive ldquoRevisiting the higgs mass and darkmatter in the CMSSMrdquo The European Physical Journal C vol72 article 2005 2012

[24] O Buchmueller R Cavanaugh M Citron et al ldquoThe CMSSMand NUHM1 in light of 7 TeV LHC 119861

119904rarr 120583+120583minus and

XENON100 datardquoThe European Physical Journal C vol 72 no11 article 2243 2012

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

8 Advances in High Energy Physics

O(1)TeV (ii)1198980≃ O(4)TeV and119898

12≃ 700GeV The SUSY

spectrum associated with these regions of parameters spacecould be striking signature for nonthermal scenario at theLHC

5 Conclusion

We have studied the constraints imposed on the MSSMparameter space by the Higgsmass limit and the gluino lowerbound which are the most stringent collider constraintsobtained from the LHC run-I at energy 8 TeV We showedthat 119898

12resides within the mass range 620GeV ≲ 119898

12≲

2000GeV while the other parameters (1198980 119860

0 tan120573) are

much less constrained We also studied the effect of themeasured DM relic density on the MSSM allowed parameterspace It turns out that most of the MSSM parameter spaceis ruled out except for few points around tan120573 sim 50119898

0sim 1TeV and 119898

12sim 15TeV We calculated the spin-

independent scattering cross section of the LSP with a protonin this allowed region We showed that our prediction for120590119901

SI is less than the recent LUX bound by at least two ordersof magnitude We have also analyzed the nonthermal DMscenario for the LSPWe showed that the constraints imposedon the MSSM parameter space are relaxed and low tan120573 isnow allowed with 119898

0≃ O(4)TeV and 119898

12≃ 600GeV Also

two allowed regions are now associated with large tan120573 (sim50) namely 119898

0sim 119898

12≃ O(1)TeV or 119898

0≃ O(4)TeV and

11989812

≃ 700GeV

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by the STDF Project 13858the ICTP Grant AC-80 and the European Union FP7 ITNINVISIBLES (Marie Curie Actions PITN-GA-2011-289442)

References

[1] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquo Astronomy ampAstrophysics vol 571 article A16 2014

[2] G Jungman M Kamionkowski and K Griest ldquoSupersymmet-ric dark matterrdquo Physics Report vol 267 no 5-6 pp 195ndash3731996

[3] G Bertone D Hooper and J Silk ldquoParticle dark matter evi-dence candidates and constraintsrdquo Physics Reports vol 405 no5-6 pp 279ndash390 2005

[4] H PNilles ldquoSupersymmetry supergravity andparticle physicsrdquoPhysics Reports vol 110 no 1-2 pp 1ndash162 1984

[5] J D Lykken ldquoIntroduction tosupersymmetryrdquo In press httparxivorgabshep-th9612114

[6] J Wess and J Bagger Supersymmetry and Supergravity Prince-ton University Press Princeton NJ USA 2nd edition 1991

[7] H E Haber and G Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[8] S P Martin ldquoA Supersymmetry Primerrdquo Advanced Series onDirections in High Energy Physics vol 21 pp 1ndash153 2010Advanced Series on Directions in High Energy Physics vol 18pp 1ndash98 1998

[9] D J H Chung L L Everett G L Kane S F King J D Lykkenand L TWang ldquoThe soft supersymmetry-breaking Lagrangiantheory and applicationsrdquo Physics Reports vol 407 no 1ndash3 pp 1ndash203 2005

[10] M Drees P Roy and R M GodboleTheory and Phenomenol-ogy of Sparticles World Scientific Singapore 2005

[11] H Baer and X Tata Weak Scale Supersymmetry From Super-fields to Scattering Events Cambridge University Press Cam-bridge UK 2006

[12] H Goldberg ldquoConstraint on the photino mass from cosmol-ogyrdquo Physical Review Letters vol 50 no 19 pp 1419ndash14221983 Erratum-ibid Physical Review Letters vol 103 Article ID099905 2009

[13] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[14] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoObser-vation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHCrdquo Physics Letters B vol 716 no 1 pp30ndash61 2012

[15] G Aad B Abbott J Abdallah et al ldquoSummary of the ATLASexperimentrsquos sensitivity to supersymmetry after LHC Run 1mdashinterpreted in the phenomenological MSSMrdquo Journal of HighEnergy Physics vol 2015 article 134 2015

[16] A Gaz ldquoSUSY searches at CMSrdquo In press httparxivorgabs14111886

[17] I Melzer-Pellmann and P Pralavorio ldquoLessons for SUSY fromthe LHC after the first runrdquo The European Physical Journal Cvol 74 article 2801 2014

[18] N Craig ldquoThe state ofsupersymmetry after Run I of the LHCrdquohttparxivorgabs13090528

[19] D S Akerib H M Araujo X Bai et al ldquoFirst results from theLUX dark matter experiment at the Sanford UndergroundResearch Facilityrdquo Physical Review Letters vol 112 Article ID091303 2014

[20] E Aprile ldquoThe Xenon1T dark matter search experimentrdquo inSources and Detection of Dark Matter and Dark Energy in theUniverse vol 148 of Springer Proceedings in Physics pp 93ndash96Springer 2013

[21] E AprileMAlfonsi K Arisaka et al ldquoDarkmatter results from225 live days of XENON100 datardquo Physical Review Letters vol109 no 18 Article ID 181301 6 pages 2012

[22] H Baer V Barger and A Mustafayev ldquoImplications of a125GeV Higgs scalar for the LHC supersymmetry and neu-tralino dark matter searchesrdquo Physical Review D vol 85 ArticleID 075010 2012

[23] J Ellis and K A Olive ldquoRevisiting the higgs mass and darkmatter in the CMSSMrdquo The European Physical Journal C vol72 article 2005 2012

[24] O Buchmueller R Cavanaugh M Citron et al ldquoThe CMSSMand NUHM1 in light of 7 TeV LHC 119861

119904rarr 120583+120583minus and

XENON100 datardquoThe European Physical Journal C vol 72 no11 article 2243 2012

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in High Energy Physics 9

[25] O Buchmueller R Cavanaugh A De Roeck et al et al ldquoTheCMSSM and NUHM1 after LHC run 1rdquo The European PhysicalJournal C vol 74 article 2922 2014

[26] R Aaij B Adeva M Adinolfi et al ldquoMeasurement of the 1198610

119904rarr

120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus decays atthe LHCb experimentrdquo Physical Review Letters vol 111 no 10Article ID 101805 2013

[27] S Chatrchyan B Betev L Caminada et al ldquoMeasurement ofthe 1198610

119904rarr 120583+120583minus branching fraction and search for 1198610 rarr 120583+120583minus

with the CMS experimentrdquo Physical Review Letters vol 111 no10 Article ID 101804 2013

[28] CMS and LHCbCollaborations ldquoCombination of results on therare decays 1198610

(119904)rarr 120583+120583minus from the CMS and LHCb exper-

imentsrdquo Tech Rep CMS-PAS-BPH-13-007 CERN 2013[29] D Feldman Z Liu and P Nath ldquoLow mass neutralino dark

matter in the minimal supersymmetric standard model withconstraints from 119861

119904rarr 120583+120583minus and Higgs boson search limitsrdquo

Physical ReviewD vol 81 no 11 Article ID 117701 4 pages 2010[30] S Akula D Feldman P Nath and G Peim ldquoExcess observed

in CDF 1198610

119904rarr 120583+120583minus and supersymmetry at the LHCrdquo Physical

Review D vol 84 no 11 Article ID 115011 10 pages 2011[31] Y Amhis Sw Banerjee R Bernhard et al ldquoAverages of b-

hadron c-hadronand tau-lepton properties as of early 2012rdquohttparxivorgabs12071158

[32] B Bhattacherjee M Chakraborti A Chakraborty U Chat-topadhyay D Das and D K Ghosh ldquoImplications of the 98GeV and 125 GeV higgs scenarios in nondecoupling supersym-metry with updatedATLAS CMS and PLANCKdatardquo PhysicalReview D vol 88 no 3 Article ID 035011 2013

[33] U Haisch and F Mahmoudi ldquoMSSM cornered and correlatedrdquoJournal of High Energy Physics vol 2013 no 1 article 61 2013

[34] N Chen D Feldman Z Liu and P Nath ldquoSUSY and higgssignatures implied by cancellations in 119887 rarr 119904120574rdquo Physics LettersB vol 685 no 2-3 pp 174ndash181 2010

[35] M E Gomez T Ibrahim P Nath and S Skadhauge ldquoAnimproved analysis of 119887 rarr 119904120574 in supersymmetryrdquo PhysicalReview D vol 74 no 1 Article ID 015015 19 pages 2006

[36] U Chattopadhyay and P Nath ldquo119887 minus 120591 unification 119892120583minus 2 the

119904+120574 constraint and nonuniversalitiesrdquo Physical Review D vol65 no 7 Article ID 075009 2002

[37] A Djouadi U Ellwanger and A M Teixeira ldquoConstrainednext-to-minimal supersymmetric standard modelrdquo PhysicalReview Letters vol 101 no 10 Article ID 101802 4 pages 2008

[38] A Djouadi U Ellwanger and A M Teixeira ldquoPhenomenologyof the constrainedNMSSMrdquo Journal of High Energy Physics vol2009 no 4 article 31 2009

[39] S Khalil and A Masiero ldquoRadiative BndashL symmetry breaking insupersymmetric modelsrdquo Physics Letters B vol 665 no 5 pp374ndash377 2008

[40] P Fileviez Perez and S Spinner ldquoFate of R parityrdquo PhysicalReview D vol 83 no 3 Article ID 035004 7 pages 2011

[41] A Elsayed S Khalil and S Moretti ldquoHiggs mass corrections inthe SUSY B minus L model with inverse seesawrdquo Physics Letters Bvol 715 no 1ndash3 pp 208ndash213 2012

[42] D Cerdeno C Hugonie D Lopez-Fogliani C Munoz and ATeixeira ldquoTheoretical predictions for the direct detection ofneutralino dark matter in the NMSSMrdquo Journal of High EnergyPhysics vol 2004 no 12 article 048 2004

[43] A Menon D E Morrissey and C E M Wagner ldquoElectroweakbaryogenesis and dark matter in a minimal extension of theMSSMrdquo Physical Review D vol 70 Article ID 035005 2004

[44] S Khalil HOkada andT Toma ldquoRight-handed sneutrino darkmatter in supersymmetric 119861 minus 119871modelrdquo Journal of High EnergyPhysics vol 2011 article 26 2011

[45] S Khalil and H Okada ldquoDark matter in B minus L extended MSSMmodelsrdquo Physical Review D vol 79 no 8 Article ID 083510 9pages 2009

[46] F Staub ldquoSARAH 32 dirac gauginos UFO output and morerdquoComputer Physics Communications vol 184 no 7 pp 1792ndash1809 2013

[47] W Porod ldquoSPheno a program for calculating supersymmetricspectra SUSY particle decays and SUSY particle production at119890+119890minus collidersrdquo Computer Physics Communications vol 153 no2 pp 275ndash315 2003

[48] W Porod and F Staub ldquoSPheno 31 extensions includingflavour CP-phases and models beyond the MSSMrdquo ComputerPhysics Communications vol 183 no 11 pp 2458ndash2469 2012

[49] J R Ellis G Ridolfi and F Zwirner ldquoRadiative corrections tothe masses of supersymmetric Higgs bosonsrdquo Physics Letters Bvol 257 no 1-2 pp 83ndash91 1991

[50] J R Ellis G Ridolfi and F Zwirner ldquoOn radiative correctionsto supersymmetric Higgs boson masses and their implicationsfor LEP searchesrdquo Physics Letters B vol 262 no 4 pp 477ndash4841991

[51] H E Haber and R Hemping ldquoCan the mass of the lightestHiggs boson of the minimal supersymmetric model be largerthanm

119885rdquo Physical Review Letters vol 66 no 14 pp 1815ndash1818

1991[52] Y Okada M Yamaguchi and T Yanagida ldquoRenormalization-

group analysis on the Higgs mass in the softly-broken super-symmetric standardmodelrdquo Physics Letters B vol 262 no 1 pp54ndash58 1991

[53] S Heinemeyer W Hollik and G Weiglein ldquoThe mass of thelightest MSSMHiggs boson a compact analytical expression atthe two-loop levelrdquo Physics Letters B vol 455 no 1ndash4 pp 179ndash191 1999

[54] M Carena H E Haber S Heinemeyer W Hollik C E MWagner and G Weiglein ldquoReconciling the two-loop diagram-matic and effective field theory computations of the mass of thelightest CP-even Higgs boson in the MSSMrdquo Nuclear PhysicsB vol 580 no 1-2 pp 29ndash57 2000

[55] J R Espinosa and R J Zhang ldquoComplete two-loop dominantcorrections to themass of the lightestCP-evenHiggs boson inthe minimal supersymmetric standard modelrdquo Nuclear PhysicsB vol 586 no 1-2 pp 3ndash38 2000

[56] G Aad B Abbott J Abdallah et al ldquoSearch for squarks andgluinos in events with isolated leptons jets and missing trans-verse momentum at radic119904 = 8TeV with the ATLAS detectorrdquoJournal of High Energy Physics vol 2015 no 4 article 116 2015

[57] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch forgluinomediated bottom- and top-squark production inmultijetfinal states in pp collisions at 8 TeVrdquo Physics Letters B vol 725no 4-5 pp 243ndash270 2013

[58] H E Haber and G L Kane ldquoThe search for supersymmetryprobing physics beyond the standard modelrdquo Physics Reportsvol 117 no 2ndash4 pp 75ndash263 1985

[59] J F Gunion and H E Haber ldquoHiggs bosons in supersymmetricmodelsrdquo Nuclear Physics B vol 272 no 1 pp 1ndash76 1986Erratum Nuclear Physics B vol 402 pp 567ndash569 1993

[60] M M El Kheishen A A Shafik and A A Aboshousha ldquoAna-lytic formulas for the neutralino masses and the neutralinomixing matrixrdquo Physical Review D vol 45 article 4345 1992

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

10 Advances in High Energy Physics

[61] M Guchait ldquoExact solution of the neutralino mass matrixrdquoZeitschrift fur Physik C vol 57 no 1 pp 157ndash163 1993 Erratumin Zeitschrift fur Physik C vol 61 p 178 1994

[62] E W Kolb and M S Turner The Early Universe vol 70 ofFrontier in Physics Addison-Wesley Redwood City Calif USA1988

[63] G Belanger F Boudjema A Pukhov and A Semenov ldquomicrO-MEGAs 3 a program for calculating dark matter observablesrdquoComputer Physics Communications vol 185 no 3 pp 960ndash9852014

[64] M Chakraborti U Chattopadhyay S Rao and D P RoyldquoHiggsino dark matter in nonuniversal gaugino mass modelsrdquoPhysical Review D vol 91 no 3 Article ID 035022 2015

[65] K Kowalska L Roszkowski and E M Sessolo ldquoTwo ultimatetests of constrained supersymmetryrdquo Journal of High EnergyPhysics vol 2013 article 78 2013

[66] G F Giudice E W Kolb and A Riotto ldquoLargest temperatureof the radiation era and its cosmological implicationsrdquo PhysicalReview D vol 64 no 2 Article ID 023508 2001

[67] T Moroi and L Randall ldquoWino cold dark matter from anomalymediated SUSY breakingrdquo Nuclear Physics B vol 570 no 1-2pp 455ndash472 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of