Table Of Content

Supersymmetry after the Higgs Pran Nath∗ Department of Physics, Northeastern University, Boston, MA 02115, USA A brief review is given of the implications of a 126 GeV Higgs boson for the discovery of supersymmetry. Thus a 126 GeV Higgs boson is problematic within the Standard Model because of vacuum instability pointing to new physics beyond the Standard Model. The problem of vacuum stabilityisovercomeintheSUGRAGUTmodelbutthe126GeVHiggsmassimpliesthattheaver- ageSUSYscaleliesintheseveralTeVregion. ThelargenessoftheSUSYscalerelievesthetension onSUGRAmodelssinceithelpssuppressflavorchangingneutralcurrentsandCPviolatingeffects and also helps in extending the proton life time arising from baryon and lepton number violating dimensionfiveoperators. Thegeometryofradiativebreakingoftheelectroweaksymmetryandfine tuninginviewofthelargeSUSYscaleareanalyzed.ConsistencywiththeBrookhaveng −2result µ is discussed. It is also shown that a large SUSY scale implied by the 126 GeV Higgs boson mass allowsforlightgauginos(gluino,charginos,neutralinos)andsleptons. Thesealongwiththelighter 5 thirdgenerationsquarksaretheprimecandidatesfordiscoveryatRUNIIoftheLHC.Implication 1 of the 126 GeV Higgs boson for the direct search for dark matter is discussed. Also discussed are 0 the sparticles mass hierarchies and their relationship with the simplified models under the Higgs 2 boson mass constraint. n a J In 2012 the Large Hadron Collider (LHC) made a the large SUSY scale implied by the Higgs boson mass. 7 landmark discovery of a new boson. Thus the CMS and The sparticle landscape is an important indicator of the ATLAS collaborations discovered a boson with a mass underlyingfundamentaltheoryandinSectionVIwedis- ] h of 126 GeV [1–4]. It is now confirmed that this newly cuss the sparticle landscape after the Higgs boson dis- ∼ p discovered particle is the long sought after Higgs boson covery. The connection of this landscape to the so called - [5–8] which plays a central role in the breaking of the simplified models is also discussed. The implications of p electroweak symmetry. While the observed particle is the Higgs boson mass at 126 on the search for dark mat- e h the last missing piece of the Standard Model there are terindirectdetectionisdiscussedinSectionVII.Future [ strong indications that at the same time its discovery prospects are discussed in Section VIII. portends discovery of a new realm of physics specifically 1 supersymmetry. Below we elaborate on this theme in v 9 further detail. I. HIGGS BOSON AND NEW PHYSICS 7 6 The outline of the rest of the paper is as follows: In Within the Standard Model a Higgs boson mass of 1 Section I we discuss the status of the Higgs boson in 126 GeV is problematic. Thus renormalization group 0 the Standard Model, the issue of vacuum instability and ∼ analyses show that vacuum stability up to the Planck . 1 the need for new physics beyond the Standard Model. scale can be excluded at the 2σ level for the Standard 0 In Section II we consider the implications of a 126 GeV Model for M < 126 GeV [12] as illustrated in Fig. 1. 5 Higgsbosonwithintheframeworkofsupersymmetryand h Here one finds that the quartic Higgs boson coupling 1 specificallyintheframeworkofsupergravityunifiedmod- within the Standard Model turns negative at a scale : v els. As is well known a 126 GeV Higgs boson within su- around 1011 GeV making the vacuum unstable [12]. i persymmetryleadstoahighSUSYscaleM withM ly- X s s However, as exhibited in Fig. 1 the result is rather sen- ingintheTeVregion. OntheotherhandtheBrookhaven sitive to the mass of the top quark (see also [13]). Thus r a gµ 2experiment[9]showsa3σdeviationfromtheStan- lowervaluesofthetopmasstendtostabilizethevacuum − dard Model prediction [10, 11]. An effect of this size re- while the higher values tend to destabilize it. The cur- quires that the average scale of sparticle masses entering rentvalueofthetop. i.e.,M =173.21 0.51 0.71GeV t the loops in the supersymmetric electroweak correction ± ± suggestsvacuuminstability. Thusthediscoveryof 126 tog 2below,i..e,O(100)GeV.Assumingthe3σeffect ∼ µ GeV Higgs boson suggests the need for new physics be- − is robust we discuss in Section III how to reconcile the yond the Standard Model. Such new physics could be high SUSY scale that is indicated by the 126 GeV Higgs supersymmetry and from here on we focus on this possi- boson mass with the low SUSY scale indicated by the bility. Brookhaven experiment. In Section IV we discuss the implications of the Higgs boson mass and the geometry of radiative electroweak symmetry breaking (REWSB). II. 126 GEV HIGGS BOSON WITHIN SUSY InSectionVwediscusstheissueoffinetuninginviewof In contrast to the case of the Standard Model, in supergravity unified models (SUGRA GUT) with the min- ∗ Email: [email protected] imal supersymmetric standard model (MSSM) particle 2 spectrum vacuum stability can be achieved up to high scales with color and charge conservation (for a recent 0.10 analysisofvacuumstabilityaftertheHiggsbosondiscov- 0.08 3Σbandsin ery see [14]). However, in MSSM the lightest CP even Mt(cid:61)173.1(cid:177) 0.6GeV(cid:72)gray(cid:76) Α3(cid:72)MZ(cid:76)(cid:61)0.1184(cid:177)0.0007(cid:72)red(cid:76) Higgs boson has a mass which lies below MZ [15–18] Λ 0.06 Mh(cid:61)125.7(cid:177) 0.3GeV(cid:72)blue(cid:76) cmaMonarZdsrseaso[p1floo9∼no–dp21i3n2c]g.o6lryGrNeaecoVtwhioirgntehhqieusSieUrnxeeSpseYedareisldmacraetglnoeetapllyolulioylnlpgoictbisonsremrrtevhaceestdsiosenaHvbieaogrnvgadesl Higgsquarticcoupling 000...000024 Mt(cid:61)171.3GeV TeV region [24–30]. In fact the observed Higgs mass is Αs(cid:72)MZ(cid:76)(cid:61)0.1205 close to the upper limit predicted in grand unified su- (cid:45)0.02 Αs(cid:72)MZ(cid:76)(cid:61)0.1163 pergravity models [31–34] which predict an upper limit Mt(cid:61)174.9GeV (cid:45)0.04 of around 130GeV [28, 29, 35–39] (For recent reviews of 102 104 106 108 1010 1012 1014 1016 1018 1020 Higgs and supersymmetry see [40, 41]). It is possible to RGEscaleΜinGeV reducetheSUSYscalebyincludingextramatterorfrom DtermcontributionsfromanextraU(1)sector(see,e.g., FIG. 1. RG evolution of the quartic coupling λ in the Stan- [42] and the references therein). However, we will focus dard Model varying M , M and α by ±3σ. From [12]. t h s on the implications of the 126 GeV Higgs boson mass within the MSSM framework. Here it is instructive to ask if the Higgs boson mass measurement can shed some light on merits of the various supersymmetry breaking mechanisms. A relative comparison is given in Fig. 2 and Fig. 3. Specifically, the mSUGRA analysis of Fig. 2 and Fig. 3 uses universal boundary conditions of supergravity models which are parametrized by the following set: m ,m ,A ,tanβ,sign(µ). (1) 0 1/2 0 Here m0 is the universal scalar mass, m1/2 is the univer- FIG. 2. The maximal Higgs mass in the constrained MSSM salgauginomass,A0istheuniversaltrilinearcouplingall modelsmSUGRA,mGMSBandmAMSB(wheremGMSMis at the grand unification scale, tanβ =<H >/<H > the minimal gauge mediated symmetry breaking model and 2 1 where H gives mass to the up quarks and H gives mAMSB is the minimal anomaly mediated symmetry break- 2 1 mass to the down quarks and the leptons and µ ingmodel)asafunctionoftheSUSYscaleMs whenthetop is the Higgs mixing parameter that appears in the quark mass is varied in the range Mt = 170–176 GeV.From [36]. superpotential in the form µH H . The analysis of 1 2 Fig. 2 and Fig. 3 shows that a loop correction of the amount needed to pull the tree level value up to what is experimentally observed is easily achieved in mSUGRA. Further, a detailed analyses indicates that a sizableA ishelpfulingeneratingalargeloopcorrection. 0 Since a large higgs boson mass implies a large SUSY scale it helps suppression of FCNC processes such as b sγ [43, 44] and B µ+µ−. Specifically s it exp→lains why no deviations→in B µ+µ− from s → the Standard Model result has been seen. Thus the LHCb collaboration [45] determines the branching ratio r(cid:0)B0 µ+µ−(cid:1) = (3.2+1.5) 10−9, which is in excel- B s → −1.2 × lent agreement with the Standard Model, which implies that the supersymmetric contribution [46–49] to this FIG. 3. The maximal Higgs mass as a function of tanβ in decay be very small. We note that the supersymmetric mGMSB, mAMSB, and mSUGRA and some of its variants. contribution to this decay is mediated by the neutral The top quark mass is fixed at Mt =173 GeV. From [36]. Higgs bosons and involve a flavor-changing scalar quark loop. It is also sensitive to CP violation [50, 51]. If the SUSY scale is large, the flavor-changing squark loop is i.e., as large as 50 tend to significantly enhance the ∼ suppressed. Further, the supersymmetric contribution supersymmetric contribution. For the same reason more is proportional to tan6β and large values of tanβ, moderate values of tanβ would rapidly bring down the 3 1036 Curve1 tor [54–61]. These contributions arise from the χ± ν(cid:101)µ CCExuuprrvveeerim23ent(LowerLimit) and from the χ0 µ(cid:101) loops. While the detailed analys−is is (yrs)1035 involved, a rough−approximation of the supersymmetric me correction is given by Lifeti Proton1034 δaµ sgn(M2µ)(cid:0)130 10−11(cid:1)(cid:18)100GeV(cid:19)2tanβ , (3) (cid:39) × M s 103131 5 120 125 130 Higgsbosonmassmh0(GeV) where M is the average SUSY scale that enters the s loops. From Eq. (3) one finds that the average SUSY FIG. 4. Dependence of the partial proton decay lifetime τ(p → ν¯K+) arising from baryon and lepton num- scaleMs mustberelativelysmalltomakeacontribution ber violating dimension five operators on m . Top curve: of the size given by Eq. (2). h0 m = 4207 GeV, A = 20823GeV, tanβ = 7.3. Mid- 1/2 0 dle: m1/2 = 2035GeV, A0 = 16336GeV, tanβ = 8, Bottom: The above discussion points to an apparent tension m = 3048GeV, A /m = −0.5, tanβ = 6.5. For all cases 1/2 0 0 between the SUSY scale indicated by the LHC measure- MHeff3/MG = 50 where MHeff3 is the Higgs triplet mass. From mentoftheHiggsbosonandtheBrookhavenobservation [53]. of a 3σ deviation. The following possibilities arise to reconciletheabovetworesults. Firstitcouldbethatthe Higgs boson mass receives corrections from extra matter supersymmetric contribution. Thus a lack of a small (see, e.g., [42] and the references there in). There is deviation of the B µ+µ− branching ratio from the another possibility which is that the Higgs boson could s Standard Model resu→lt is easily understood in the con- receive D term contributions from an extra U(1) which textofalargeSUSYscaleandamoderatevalueoftanβ. is present in many extensions of the Standard Model. In principle this would allow one to have a low SUSY scale. Further, a large SUSY scale helps stabilize the pro- However, one must also fold in the fact that the LHC ton against decays from the baryon and lepton number hasnotobservedanysparticlesthusfar. Specificallythis violating dimension five operators. This is so because putsthesquarksandthegluinomassesintheTeVrange. protondecayviabaryonandleptonnumberviolatingdi- mension five operators involves dressing loop diagrams Wediscussnowamechanismbywhichonecanresolve with sparticle exchanges. Very crudely the proton decay the tension between the LHC result and the Brookhaven from these is proportional to m2 /m4 where χ± is the experiment. This can be accomplished by a minimal ex- χ1 q˜ 1 chargino and the q˜is the squark. Thus a large sfermion tension of the supergravity model with universal bound- mass will lead to a desirable suppression of proton decay aryconditions. Thussupposeweconsiderasupergravity and an enhancement of its lifetime. As indicated in the model with universal scalar mass and universal trilinear precedingdiscussionthereisastrongcorrelationbetween couplingbutwithnon-universalityinthegauginosector. theSUSYscaleandtheHiggsmass. Thisstrongcorrela- Specifically we consider the boundary conditions on soft tion also implies a strong correlation between the proton parameters to be given by [62] lifetime from dimension five operators and the Higgs boson mass. This correlation is illustrated in Fig. 4. The m ,m˜ ,m ,A ,tanβ,sign(µ), (4) 0 1/2 3 0 current data also puts a lower limit on the heavier Higgs boson mass (see, e.g., [40, 52]). where m << m ,m = m = m˜ << m . As an il- 0 3 1 2 1/2 3 lustrative example we choose m /m = 10. In this case 3 1 III. HIGGS BOSON MASS AND g −2 thegluinomassentersintheRGevolutionofthesquarks µ andbeingthelargestmassdrivestheRGevolutionwhich results in radiative breaking of the electroweak symme- While the Higgs boson mass of 126 GeV indicates a try(Forareviewsee[63]). Welabelthismodelg˜SUGRA high SUSY scale in the TeV region, the Brookhaven ex- since REWSB is driven by the gluino mass. Specifically periment on g 2 points to a rather low SUSY scale. µ − we exhibit the evolution of the masses of the third gen- Thus the Brookhaven Experiment E821 [9] finds that eration squarks U˜, Q˜ and the Higgs H which form a a = 1(g 2)deviatesfromtheStandardModelpredic- 2 µ 2 µ− coupled set due to the large Yukawa coupling as shown tion [10, 11] at the 3σ level. Supposing that the entire in Eq. (5). deviationcomesfromasupersymmetriccontributionone finds        m2 3 3 3 m2 3 It has lonagSµUSbYee=n δkaneµoxwpn=t(h2a8t7±siz8a0b)l×e c1o0n−t1r1ib.utions(t2o) ddt mH2U˜2 =−Yt2 2 2 mH2U˜2 −YtA2t 2 g 2canarisefromthesupersymmetricelectroweaksec- m2 1 1 1 m2 1 µ− Q˜ Q˜ 4   3α˜ m2+α˜ m2 PosteriorMean 2 2 1 1 1σCredibleInterval + 16α˜ m2+ 16α˜ m2 . (5) 20 2σCredibleInterval  3 3 3 9 1 1  ) 136α˜3m23+3α˜2m22+ 19α˜1m21 TeV15 ( s s a10 M Here Y =h2/(4π2) where h is the top Yukawa coupling t t t 5 and A is the trilinear coupling in the top sector. Sup- t pose m3 is in the TeV range but m0,m1,m2 = O(100) H0 χ˜±2 t˜1 q˜ g˜ GeV. In this case the RG evolution drives squarks to be- 1200 PosteriorMean come heavy with masses in the several TeV region while 1σCredibleInterval 1000 the sleptons remain light. A numerical analysis of the 2σCredibleInterval RG evolution is given in Fig. 5. Here one finds that the V) 800 evolution of sfermion masses which start with a univer- Ge sal scalar mass at the GUT scale generates a significant ( 600 s s split as the masses evolve towards the electroweak scale. Ma 400 Thus at the electroweak scale the squark masses lie in the several TeV region due to the large contributions of 200 thegluinomasstermintheRGevolutionwhiletheslep- ton masses do not receive large contributions from the χ˜01 χ˜±1 τ˜1 τ˜2 ℓ˜ gluino mass and remain relatively light. Further, since m ,m <<m theelectroweakgauginosallremainlight. 1 2 3 FIG.6. Toppanel: Anexhibitionoftheheavysparticlespec- Thus one has a split scale SUSY which is not to be con- trum in the g˜SUGRA model. Bottom panel: An exhibition fused with the split SUSY model [64]. The spectrum of of the light sparticle spectrum in the g˜SUGRA model. From the split scale SUSY is exhibited in Fig. 6. The analy- [62]. sis Fig. 6 was done using a Bayesian statistical analysis (for other works using statistical approach see [65–67]). From the lower panel of Fig. 6 we see that the elec- IV. HIGGS BOSON MASS AND REWSB troweak gauginos χ˜0 and χ˜± as well as the sleptons are 1 1 GEOMETRY all light. This light spectrum allows one to have sizable supersymmetric electroweak contributions to g 2. At µ − TheHiggsbosonat 126GeVanditsimplicationthat the same time since the squarks are heavy as seen from ∼ theSUSYscaleishighhasimportantimplicationsforthe theupperpanelofFig.6theSUSYscalethatentersinthe geometry of radiative breaking of the electroweak sym- loop correction to the Higgs boson is substantial which metry. It was pointed out long time ago that REWSB produces the desired size correction to the Higgs boson in general contains two main branches, the ellipsoidal mass. For related works see [68–72]. branch(EB)andthehyperbolicbranch(HB)[73–75](For related works see [76–78]). To understand the relation- shipitisconvenienttowritetheREWSBconstraintthat 104 determines µ2 in the following form M3 H1 ¡m20+µ2¢1/2   eV) H2 q +1 (EB) ss(G103 e µ2 = 0 (FP) m20 |C1|+∆(m1/2,AO,tanβ), Ma M2 ℓe M1 mm0e1/2 −1 (HB) (6) 102 105 1010 1015 +1:Euclidean geometry EB of REWSB, (7) RGEScaleQ(GeV) ⇒ 1:Hyperbolic geometry HB of REWSB, (8) − ⇒ where ∆ is typically positive and where C is a function 1 FIG.5. Anillustrationoftheevolutionofsparticlemassesin that depends only on tanβ,Mt and the renormalization the g˜SUGRA model. The analysis shows that starting with groupscaleQbutdoesnotdependonm0,m1/2,A0. The a universal scalar mass at the GUT scale, the renormaliza- signs ( ) in Eq. (6) are determined by the sign of C1(Q) ± tiongroupevolutionsplitsthesquarkmassesfromtheslepton withdependsontherenormalizationgroupscaleQ. The masses by huge amounts. From [62]. RG scale Q is chosen so that the two loop correction to the scalar potential is minimized. Typically Q M s ∼ where Ms =√mt˜1mt˜2 . 5 fine tuning which we address below (for a related work see [80]). It should be kept in mind, however, that the Let us discuss now the implications of Eq. (6). First issue of what constitutes fine tuning is a rather subjec- consider the case when C = 0. In this case one finds tive one and depends in part on what phenomena are 1 that at the one loop level, µ2 no longer depends on m . included in the analysis. Generally, fine tuning analyses 0 Thus here m can get large without affecting µ. This is include just the constraints of radiative breaking of the 0 the focus point region (FP) [76]. However, a small µ can electroweak symmetry. However, it is not unreasonable be gotten in other ways even when C is non-vanishing. toincludeotherphenomenasuchassuppressionofflavor 1 Thus suppose C is non-vanishing and negative. In this changing neutral currents and CP violating effects [81] 1 case one can have cancellation between the C term and and suppression of proton decay from dimension five 1 the ∆ term so that µ2 is still small. In fact the curves operators [53, 82] within the framework of grand unified of fixed µ2 in the plane of two of the other parameters theories. As an illustration of how the fine tuning is af- are hyperbolic curves or focal curves. An illustration is fected by including more than just REWSB constraints, given in the upper panel of Fig. 7. An illustration of the we considerafine tuninganalysisincluding twodifferent focal surface region of the hyperbolic branch when one phenomena, i.e., REWSB and proton stability. We will considers the 3-d region of m ,m ,A is given in the consider fine tuning for these two phenomena separately 0 1/2 0 upper panel of Fig. 7. Finally suppose C is positive. and then combine them to produce a composite fine 1 In this case as m gets large µ also gets large since ∆ tuning. 0 is typically positive. Thus the region of small µ is not achievedinthiscase. Thisistheellipsoidalbranch(EB). Thusto definefinetuningforthe REWSBoneconsid- In summary on EB a large m implies a large µ. On ers the minimization of the scalar potential that deter- 0 FP and on HB a small µ can be consistent with a large mines the Z -boson mass and one has m . Phenomenologically a small µ is desirable since it 0 1 allows one to have all the EW gauginos in the sub TeV M2 = µ2+ m 2+ (9) range. A small µ is also desirablefor observationof dark 2 Z − | Hu| ··· matter. Hereonenoticesthatasµor m getslarge,oneneeds | Hu| afinetuningtogettheZ massdowntotheexperimental value. An obvious way to define fine tuning then is via the ratio F given by 10 µ(TeV) m1/2=0.5TeV 0.49 2m 2 5 0.48 F ∼ |MH2u| . (10) (TeV) 0 HB/FC1 0.47 Z A0 0.46 Eq. (10) indicates that low values of mHu and thus low −5 0.45 values of soft masses O(MZ) will lead to low values of µ=(0.465±0.035)TeV 0.44 fine tuning. −100 2 4 6 8 10 m0(TeV) However,lowvaluesofsoftmassescancreateproblems as they lead to large FCNC and CP violating effects. Further, low values of soft masses will in general lead to rapid proton decay from baryon and lepton number violating dimension five operators in unified models of particleinteractions(forrecentreviewssee[83–85]). The fine tunings using FCNC and CP violating effects has been discussed specifically in [81] and here we focus on proton decay. Thus to get the proton lifetime prediction from baryon and lepton number violating dimension five operators to be consistent with the experimental upper FIG. 7. Top panel: An illustration of the Focal Curve region limitonp ν¯K+ partiallifetimeoneneedsafinetuning of the hyperbolic branch. Bottom panel: An illustration of → of input parameters and in this case one may define fine theFocalSurfaceregionofthehyperbolicbranch. From[79]. tuning so that 4 1033yr F = × . (11) pd τ(p ν¯K+)yr → V. FINE TUNING As indicated in Section II very roughly τ(p ν¯K+) → ∼ The Higgs boson mass of 126 GeV and the large C(mχ±/m2q˜MHef3f)−2 where MHef3f is the Higgs triplet SUSY scale it implies raise the issue of naturalness and mass. Eq. (11) makes clear that larger squark masses 6 will lead to a larger proton lifetime and a smaller value PatternLabel MassHierarchy % of fine tuning parameter F . In general one may have several such fine tuning parpadmeters F , where i takes on nuSP2[C1a] χ±1 <χ02<χ03<χ04 35.71 i the values 1 n. In this case a more appropriate object nuSP2[C1b] χ±1 <χ02<χ03<χ±2 14.57 ··· to consider is a composite fine tuning F defined by [53] nuSP2[C2a] χ±1 <χ02<τ1<ντ 12.25 (cid:32) (cid:33)1 nuSP2[C3a] χ±1 <χ02<g<χ03 6.237 = (cid:89)n F n . (12) nuSP2[C3b] χ±1 <χ02<g<t1 4.820 i F i=i nuSP2[C4a] χ±1 <χ02<H0<A0 2.767 nuSP2[C5b] χ±1 <χ02<t1<τ1 2.746 An analysis of fine tunings defined by Eq. (10), Eq. (11) and Eq. (12) is given in Fig. 8 of [53]. Here the red re- nuSP2[N1a] χ02<χ±1 <g<χ03 2.246 gionindicatesfinetuningwhenoneconsidersjustthera- diativeelectroweaksymmetrybreaking. Asexpectedthe TABLEII. Asampleofsparticlemasshierarchiesforthenon- finetuningincreaseswithincreasingm0. Theblueregion universal SUGRA (nuSUGRA) model with a light chargino. givesthefinetuningfortheprotondecayarisingfromdi- Thehighscaleparameterslieintherangem ∈[0.1,10]TeV, 0 mensionfiveoperators. As expectedthefine-tuninghere M = M = m ∈ [0.1,1.5]TeV, M = αm , α ∈ [1,1], 1 3 (cid:101)1/2 2 (cid:101)1/2 2 is a falling function of m0. The composite fine tuning A0 ∈ [−5,5], tanβ ∈ [2,50], µ > 0, with the constraints defined via Eq. (12) is given by the black region. One Ωmh02 <0.12, m >120GeV. From [86] h0 finds that the overall fine tuning decreases with a large m and thus a smaller fine tuning occurs at large m . 0 0 This result is in contrast to the conventional view that a smallSUSYscaleO(M )constitutesasmallfinetuning. Z mass hierarchies is even larger since the mass gaps Theanalysisaboveshowsthatinclusionofflavorandpro- among the sparticle masses can vary continuously which tonstabilityconstraintsargueforanoveralllargerSUSY makes the allowed sparticle landscape even larger than scale. the string landscape of 10500 string vacua. Truncated ∼ hierarchies (e.g., n=3,4) are much smaller and one can Pattern Label Mass Hierarchy % generate a list of simplified models from these. In pre- mSP[C1a] χ± <χ0 <χ0 <χ0 83.8 vious works an analysis of the sparticle mass hierarchies 1 2 3 4 was carried out where the experimental lower limits of mSP[C1b] χ± <χ0 <χ0 <H0 2.49 1 2 3 the Higgs mass constraint given by LEP II was used. mSP[τ1a] τ <χ0 <χ± <H0 3.89 The observation of the Higgs boson mass at 126 GeV 1 2 1 ∼ imposes a much more severe constraint and one might mSP[N1a] χ0 <χ± <H0 <A0 3.31 2 1 ask what the set of allowed mass hierarchies is in this case. A full analysis of this issue is given in [86] where TABLE I. A sample of sparticle mass hierarchies for mSUGRA, where χ0 is the LSP. The input at the GUT the implications for the mSUGRA case as well as for 1 scale consists of m ∈ [0.1,10]TeV, m ∈ [0.1,1.5]TeV, the SUGRA models with non-universalities (nuSUGRA) 0 1/2 A0 ∈ [−5,5], tanβ ∈ [2,50], µ > 0, with the constraints are investigated [The literature on non-universalities m0 in supergravity models is extensive. For a sample see Ωh2 < 0.12, m > 120GeV. Here and in Table II and Ta- h0 [93–107] and for a review see [108]]. Here we give a brief ble III the last column gives the percentage with which the patterns appear in the scans. From [86]. description of the main results. The analysis of mass hierarchies under the Higgs boson mass constraint for the mSUGRA model is given in Table 1 where we display only those mass hierarchies VI. HIGGS AND THE SPARTICLE which have a frequency of occurrences larger than 2%. LANDSCAPE The sequence χ± < χ0 < χ0 < χ0 implies that the 1 2 3 4 mass of χ0 is smaller than the mass of χ0, the mass of 1 2 It has been demonstrated in several previous χ02 is smaller than the mass of χ03 and so on. Here the works that sparticle mass hierarchies can be used as constrain on the relic density of Ωh2 < 0.12, and on the discriminants of the underlying models of SUSY break- Higgs boson mass of mh0 > 120GeV were imposed. A ing [87–92]. However, the landscape of mass hierarchies similar analysis for the non-universal supergravity mod- is large. Thus there are 31 additional particles beyond els with non-universality in the SU(2)L gaugino masses the spectrum of the Standard Model and there are a is displayed in Table 2, while the analysis with non- priori 31! ways in which these particles can hierarchi- universalityinthegluinomassesisdisplayedinTableIII. cally arrange themselves. Using Sterling’s formulae, i.e.. n! √2πn(n/e)n,onefindsthatn=31gives 8 1033 One may note that the so called simplified mod- ∼ ∼ × possibilities. Actually the possible landscape of sparticle els [109–116] can be generated from the analysis of UV 7 PatternLabel MassHierarchy % mass is given in Fig. 9 where the parameter points are colored according to the Higgs boson mass in the mass nuSP3[C1a] χ±1 <χ02<χ03<χ04 63.273 range120GeV-129GeV.Herethedeepbluecorresponds nuSP3[C1b] χ±1 <χ02<χ03<g 10.263 to the smallest and the deep red to the largest Higgs bo- nuSP3[C1c] χ±1 <χ02<χ03<H0 4.587 son mass. One may notice that most of the parameter nuSP3[C1d] χ±1 <χ02<χ03<τ1 4.243 points with the Higgs mass in the vicinity of the values measured by the ATLAS and CMS experiments lie be- nuSP3[C1e] χ±1 <χ02<χ03<t1 4.549 low the current lower limit of the LUX experiment [118]. nuSP3[g1a] g<χ02<χ±1 <χ03 3.940 The analysis further shows that future dark matter ex- nuSP3[g1b] g<χ02<χ±1 <t1 3.031 perimentssuchasXENON1T[119]willbeabletoexplore a large part of the parameter space consistent with the measured Higgs boson mass. TABLE III. A sample of sparticle mass hierarchies for the nuSUGRA model with a light gluino. The high scale parameters lie in the range m ∈ [0.1,10]TeV, M = M = 0 1 2 m ∈ [0.1,1.5]TeV, M = αm , α ∈ [1,1], A0 ∈ [−5,5], (cid:101)1/2 3 (cid:101)1/2 6 m0 tanβ ∈ [2,50], µ > 0, with the constraints Ωh2 < 0.12, m >120GeV. From [86]. h0 FIG. 9. An exhibition of the spin independent neutralino- proton cross section R × σSI vs the neutralino mass for p,χ0 1 mSUGRA where the colors exhibit the Higgs boson mass. From [86]. FIG. 8. An illustration of three simplified models that arise from truncation of UV complete models. From [86]. VIII. FUTURE PROSPECTS complete models presented in Tables I-III and those discussed in [86] by a truncation. Thus a truncation of In view of the TeV size SUSY scale indicated by the SUGRA GUTs keeping a few lowest mass particles gen- Higgsbosonmass,LHCRUNII,whichwilllikelyoperate erates a large number of simplified models. An illustra- at √s = 13 TeV, has a better chance of observing tion is given in Fig. 8 where three simplified models are sparticles than LHC7+8, at least those sparticles which shown that arise from UV complete models under the are low lying. These low lying sparticles are mostly Higgs boson mass constraint and under the relic density uncolored particles, and in addition the gluino and the constraint. Currently many experimental analyses are lightestsquarksarealsopossiblecandidatesfordiscover. being done using simplified models. However, it should Recent analyses have shown that LHC RUN II could bekeptinmindthatthesemodelsareonlytruncationsof observe gluinos up to 2 TeV [120, 121] and the CP ∼ themorecompletemodelswhichshouldbeusedforcom- odd Higgs up to around a TeV [122]. Further hints of parison with the underlying theory that generates these new physics beyond the Standard Model can come from mass hierarchies. precision measurement of the Higgs boson couplings to fermions at the International Linear Collider, a high energy e+e− machine which can measure most of the Higgs-fermion couplings to an accuracy of up to 5% VII. HIGGS AND DARK MATTER [123]. Forthedirectobservationofheaviersparticlesone will require a hadron collider with much larger energies The Higgs boson mass constraint also has significant than those at LHC RUNII, such as a 100 TeV hadron implications for dark matter detection (for a related collider. Analyses indicate that such a machine could work see [117]). An analysis of the spin independent detect a gluino up to as much as 10 TeV as indicated neutralino-proton cross section R σSI , where R = ∼ × p,χ(cid:101)01 by simulations based on simplified models [121]. (Ωh2) /(Ωh2) , as a function of the neutralino theory WMAP 8 vacuum unstable provides yet another reason why new physics beyond the Standard Model must exist. The most promising candidate for such physics is supersymmetry. Specifically within the concrete framework of supergravity grand unification one finds that the Higgs bosonmassispredictedtoliebelow 130GeV.Thefact ∼ that the observed HIggs boson mass respects this bound is a significant support for SUGRA GUT. Further, the Higgs boson mass of 126 GeV requires the average ∼ SUSYscaletobehigh, i.e., intheTeVregion. Thishigh scale explains why we have seen no significant deviation FIG. 10. An illustration of the probe of high SUSY scales from the Standard Model prediction in FCNC processes using the electron EDM. The plot exhibits the electron such as b sγ and B µ+µ−. Further, the same high s → → EDM as a function of m0 for different values of the phase SUSY scale explains the non-observation of sparticles in αµ of the Higgs mixing parameter µ. The curves are √s =7TeVand√s =8TeVdataatRUNIoftheLHC. for the cases α = −3 (small-dashed, red), α = −0.5 µ µ (solid), α = 1 (medium-dashed, orange), and α = 2.5 µ µ AsdiscussedinSectionIIIoneimportantissuepertains (long-dashed, green). The other parameters are |µ| = 4.1× 102 , |M | = 2.8 × 102 , |M | = 3.4 × 102 , |A | = 3 × to the Brookhaven experiment which sees a 3σ deviation 1 2 e 106 , mν0˜ = 4×106 , |Aν0˜| = 5×106 , tanβ = 30. Allmasses ingµ−2fromtheStandardModelprediction. Thiseffect are in GeV, phases in rad and EDM in ecm.The analysis is difficult to understand within the supergravity model shows that improvements in the electron EDM constraint with universal boundary conditions. However, it is not can probe scalar masses in the 100 TeV- 1 PeV region and difficult to explain the observed phenomenon within su- beyond. The top horizontal line is the current experimental pergravity unified models with non-universal boundary limit from the ACME Collaboration [124]. From [125]. conditions. Here it is possible to have light electroweak gauginos and light sleptons while the squarks are heavy. InthiscaseonecanexplaintheBrookhaveng 2result µ − as well as achieve a Higgs boson mass consistent with Further precision experiments can allow one to probe experiment. The discovery of the Higgs boson mass is even higher SUSY mass scales. [125–129]. One example important not only because one has found the last miss- is to use EDMs as a probe of high SUSY scales. Thus ing piece of the Standard Model but also because it is the electron EDM is most stringently constrained by the likely the first piece of a new class of models such as ACME Collaboration [124] which gives supersymmetric models which require the existence of a d <8.7 10−29 ecm . (13) wholenewsetofparticles. ItishopedthatLHCRUNII e | | × will reveal some of these. Fig. 10 exhibits the dependence of the electron EDM on m for a number of CP phases of the Higgs mixing 0 parameter. The electron EDM limit is likely to improve by an order of magnitude in the coming years and thus the future EDM measurements will allow one to extend the probe of new physics up to a PeV or more as shown ACKNOWLEDGMENTS in Fig. 10. One can also use the precision measurement of g 2 of the electron as a sensitive probe of new − physics [130, 131]. This research is supported in part by grants NSF grants PHY-1314774 and PHY-0969739, and by XSEDE In summary the discovery of the Higgs boson and grant TG-PHY110015. This research used resources of the measurement of its mass at 126 GeV has very theNationalEnergyResearchScientificComputingCen- ∼ significant implications for new physics beyond the ter,whichissupportedbytheOfficeofScienceoftheU.S. Standard Model. The fact that a 126 GeV Higgs boson Department of Energy under Contract No. DE-AC02- massintheframeworkoftheStandardModelmakesthe 05CH11231 [1] CMS Collaboration, Phys. Lett. B 716 (2012) 30–61, [4] ATLAS Collaboration, Science 338 (2012) arXiv:1207.7235. 1576–1582. [2] ATLAS Collaboration, Phys. Lett. B 716 (2012) [5] F. Englert and R. Brout, Phys. Rev. Lett. 13 (1964) 1–29, arXiv:1207.7214. 321–323. [3] CMS Collaboration, Science 338 (2012) 1569–1575. [6] P. W. Higgs, Phys. Lett. 12 (1964) 132–133. 9 [7] P. W. Higgs, Phys. Rev. Lett. 13 (1964) 508–509. [39] O. Buchmueller, M. Dolan, J. Ellis et al., Eur.Phys.J. [8] G. Guralnik, C. Hagen, and T. Kibble, Phys. Rev. C74 (2014), no. 3, 2809, arXiv:1312.5233. Lett. 13 (1964) 585–587. [40] P. Nath, Int.J.Mod.Phys. A27 (2012) 1230029, [9] Muon G-2 Collaboration, Phys. Rev. D 73 (2006) arXiv:1210.0520. 072003, arXiv:hep-ex/0602035. [41] P. Nath, Front.Phys.China 8 (2013) 294–301, [10] K. Hagiwara, R. Liao, A. D. Martin et al., J. Phys. G arXiv:1302.1863. 38 (2011) 085003, arXiv:1105.3149. [42] W.-Z. Feng and P. Nath, Phys.Rev. D87 (2013), [11] M. Davier, A. Hoecker, B. Malaescu et al., Eur. Phys. no. 7, 075018, arXiv:1303.0289. J. C 71 (2011) 1515, arXiv:1010.4180. [43] S. Bertolini, F. Borzumati, A. Masiero et al., Nucl. [12] G. Degrassi, S. Di Vita, J. Elias-Miro et al., JHEP Phys. B 353 (1991) 591–649. 1208 (2012) 098, arXiv:1205.6497. [44] R. Barbieri and G. Giudice, Phys. Lett. B 309 [13] I. Masina, Phys.Rev. D87 (2013), no. 5, 053001, (1993) 86–90, arXiv:hep-ph/9303270. arXiv:1209.0393. [45] LHCb Collaboration, Phys. Rev. Lett. 110 (2013) [14] D. Chowdhury, R. M. Godbole, K. A. Mohan et al., 021801, arXiv:1211.2674. JHEP 1402 (2014) 110, arXiv:1310.1932. [46] S. R. Choudhury and N. Gaur, Phys. Lett. B 451 [15] P. Nath, R. L. Arnowitt, and A. H. Chamseddine, (1999) 86–92, arXiv:hep-ph/9810307. “Applied N =1 Supergravity”, volume 1 of ICTP [47] K. Babu and C. F. Kolda, Phys. Rev. Lett. 84 (2000) Series in Theoretical Physics. World Scientific, 228–231, arXiv:hep-ph/9909476. Singapore, 1984. [48] C. Bobeth, T. Ewerth, F. Kruger et al., Phys. Rev. D [16] J. F. Gunion, H. E. Haber, G. L. Kane et al., 64 (2001) 074014, arXiv:hep-ph/0104284. Front.Phys. 80 (2000) 1–448. [49] R. L. Arnowitt, B. Dutta, T. Kamon et al., Phys.Lett. [17] A. Djouadi, Phys. Rept. 459 (2008) 1–241, B538 (2002) 121–129, arXiv:hep-ph/0203069. arXiv:hep-ph/0503173. [50] T. Ibrahim and P. Nath, Phys. Rev. D 67 (2003) [18] M. S. Carena and H. E. Haber, Prog.Part.Nucl.Phys. 016005, arXiv:hep-ph/0208142. 50 (2003) 63–152, arXiv:hep-ph/0208209. [51] T. Ibrahim and P. Nath, Rev. Mod. Phys. 80 (2008) [19] M. S. Berger, Phys.Rev. D41 (1990) 225. 577–631, arXiv:0705.2008. [20] J. R. Ellis, G. Ridolfi, and F. Zwirner, Phys.Lett. [52] L. Maiani, A. Polosa, and V. Riquer, Phys. Lett. B B257 (1991) 83–91. 718 (2012) 465–468, arXiv:1209.4816. [21] H. E. Haber and R. Hempfling, Phys.Rev.Lett. 66 [53] M. Liu and P. Nath, Phys.Rev. D87 (2013), no. 9, (1991) 1815–1818. 095012, arXiv:1303.7472. [22] Y. Okada, M. Yamaguchi, and T. Yanagida, [54] T. Yuan, R. L. Arnowitt, A. H. Chamseddine et al., Prog.Theor.Phys. 85 (1991) 1–6. Z. Phys. C 26 (1984) 407. [23] J. R. Espinosa and R.-J. Zhang, Nucl.Phys. B586 [55] D. A. Kosower, L. M. Krauss, and N. Sakai, Phys. (2000) 3–38, arXiv:hep-ph/0003246. Lett. B 133 (1983) 305. [24] H. Baer, V. Barger, and A. Mustafayev, Phys. Rev. D [56] J. L. Lopez, D. V. Nanopoulos, and X. Wang, Phys. 85 (2012) 075010, arXiv:1112.3017. Rev. D 49 (1994) 366–372, arXiv:hep-ph/9308336. [25] A. Arbey, M. Battaglia, A. Djouadi et al., Phys. Lett. [57] U. Chattopadhyay and P. Nath, Phys. Rev. D 53 B 708 (2012) 162–169, arXiv:1112.3028. (1996) 1648–1657, arXiv:hep-ph/9507386. [26] P. Draper, P. Meade, M. Reece et al., Phys. Rev. D [58] T. Moroi, Phys. Rev. D 53 (1996) 6565–6575, 85 (2012) 095007, arXiv:1112.3068. arXiv:hep-ph/9512396. [27] M. Carena, S. Gori, N. R. Shah et al., JHEP 1203 [59] T. Ibrahim and P. Nath, Phys. Rev. D 62 (2000) (2012) 014, arXiv:1112.3336. 015004, arXiv:hep-ph/9908443. [28] S. Akula, B. Altunkaynak, D. Feldman et al., Phys. [60] S. Heinemeyer, D. Stockinger, and G. Weiglein, Nucl. Rev. D 85 (2012) 075001, arXiv:1112.3645. Phys. B 690 (2004) 62–80, arXiv:hep-ph/0312264. [29] S. Akula, P. Nath, and G. Peim, Phys. Lett. B 717 [61] A. Sirlin and A. Ferroglia, arXiv:1210.5296. (2012) 188–192, arXiv:1207.1839. [62] S. Akula and P. Nath, Phys.Rev. D87 (2013), no. 11, [30] C. Strege, G. Bertone, F. Feroz et al., JCAP 1304 115022, arXiv:1304.5526. (2013) 013, arXiv:1212.2636. [63] L. Ibanez and G. Ross, Comptes Rendus Physique 8 [31] A. H. Chamseddine, R. L. Arnowitt, and P. Nath, (2007) 1013–1028, arXiv:hep-ph/0702046. Phys. Rev. Lett. 49 (1982) 970. [64] N. Arkani-Hamed and S. Dimopoulos, JHEP 0506 [32] P. Nath, R. L. Arnowitt, and A. H. Chamseddine, (2005) 073, arXiv:hep-th/0405159. Nucl. Phys. B 227 (1983) 121. [65] R. R. de Austri, R. Trotta, and L. Roszkowski, JHEP [33] L. J. Hall, J. D. Lykken, and S. Weinberg, Phys. Rev. 0605 (2006) 002, arXiv:hep-ph/0602028. D 27 (1983) 2359–2378. [66] F.Feroz, M.Hobson,andM.Bridges, Mon. Not. Roy. [34] R. L. Arnowitt and P. Nath, Phys. Rev. Lett. 69 Astron. Soc. 398 (2009) 1601–1614, (1992) 725–728. arXiv:0809.3437. [35] G. Kane, P. Kumar, R. Lu et al., Phys.Rev. D85 [67] D. Kim, P. Athron, C. Balzs et al., Phys.Rev. D90 (2012) 075026, arXiv:1112.1059. (2014) 055008, arXiv:1312.4150. [36] A. Arbey, M. Battaglia, A. Djouadi et al., JHEP [68] G. F. Giudice, P. Paradisi, A. Strumia et al., JHEP 1209 (2012) 107, arXiv:1207.1348. 1210 (2012) 186, arXiv:1207.6393. [37] J. Ellis and K. A. Olive, Eur. Phys. J. C 72 (2012) [69] M. Ibe, T. T. Yanagida, and N. Yokozaki, JHEP 2005, arXiv:1202.3262. 1308 (2013) 067, arXiv:1303.6995. [38] H. Baer, V. Barger, P. Huang et al., Phys.Rev. D87 [70] S. Mohanty, S. Rao, and D. Roy, JHEP 1309 (2013) (2013), no. 3, 035017, arXiv:1210.3019. 027, arXiv:1303.5830. 10 [71] G. Bhattacharyya, B. Bhattacherjee, T. T. Yanagida (2002) 075009, arXiv:hep-ph/0110341. et al., Phys.Lett. B725 (2013) 339–343, [102] U. Chattopadhyay, A. Corsetti, and P. Nath, Phys. arXiv:1304.2508. Rev. D 66 (2002) 035003, arXiv:hep-ph/0201001. [72] K. Babu, I. Gogoladze, Q. Shafi et al., Phys.Rev. [103] S. P. Martin, Phys. Rev. D 79 (2009) 095019, D90 (2014) 116002, arXiv:1406.6965. arXiv:0903.3568. [73] K. L. Chan, U. Chattopadhyay, and P. Nath, Phys. [104] D. Feldman, Z. Liu, and P. Nath, Phys. Rev. D 80 Rev. D 58 (1998) 096004, arXiv:hep-ph/9710473. (2009) 015007, arXiv:0905.1148. [74] U. Chattopadhyay, A. Corsetti, and P. Nath, Phys. [105] I. Gogoladze, F. Nasir, and Q. Shafi, Int.J.Mod.Phys. Rev. D 68 (2003) 035005, arXiv:hep-ph/0303201. A28 (2013) 1350046, arXiv:1212.2593. [75] H. Baer, C. Balazs, A. Belyaev et al., JHEP 0306 [106] M. Adeel Ajaib, I. Gogoladze, Q. Shafi et al., JHEP (2003) 054, arXiv:hep-ph/0304303. 1307 (2013) 139, arXiv:1303.6964. [76] J. L. Feng, K. T. Matchev, and T. Moroi, Phys. Rev. [107] B. Kaufman and B. D. Nelson, Phys.Rev. D89 Lett. 84 (2000) 2322–2325, arXiv:hep-ph/9908309. (2014) 085029, arXiv:1312.6621. [77] S. Cassel, D. Ghilencea, and G. Ross, Nucl.Phys. [108] P. Nath, B. D. Nelson, H. Davoudiasl et al., B825 (2010) 203–221, arXiv:0903.1115. Nucl.Phys.Proc.Suppl. 200-202 (2010) 185–417, [78] D. Feldman, G. Kane, E. Kuflik et al., Phys. Lett. B arXiv:1001.2693. 704 (2011) 56–61, arXiv:1105.3765. [109] N. Arkani-Hamed, P. Schuster, N. Toro et al., [79] S. Akula, M. Liu, P. Nath et al., Phys. Lett. B 709 arXiv:hep-ph/0703088. (2012) 192–199, arXiv:1111.4589. [110] J. Alwall, P. Schuster, and N. Toro, Phys.Rev. D79 [80] H. Baer, V. Barger, P. Huang et al., Phys.Rev. D87 (2009) 075020, arXiv:0810.3921. (2013), no. 11, 115028, arXiv:1212.2655. [111] J. Alwall, M.-P. Le, M. Lisanti et al., Phys.Rev. D79 [81] J.JaeckelandV.V.Khoze, JHEP 1211(2012)115, (2009) 015005, arXiv:0809.3264. arXiv:1205.7091. [112] D. S. Alves, E. Izaguirre, and J. G. Wacker, JHEP [82] R. L. Arnowitt and P. Nath, Phys.Rev. D49 (1994) 1110 (2011) 012, arXiv:1102.5338. 1479–1485, arXiv:hep-ph/9309252. [113] LHC New Physics Working Group, J.Phys. G39 [83] P. Nath and P. Fileviez Perez, Phys.Rept. 441 (2007) (2012) 105005, arXiv:1105.2838. 191–317, arXiv:hep-ph/0601023. [114] J. Barnard and B. Farmer, JHEP 1406 (2014) 132, [84] S.Raby,T.Walker,K.Babuetal., arXiv:0810.4551. arXiv:1402.3298. [85] K. Babu, E. Kearns, U. Al-Binni et al., [115] S. Kraml, S. Kulkarni, U. Laa et al., Eur.Phys.J. arXiv:1311.5285. C74 (2014) 2868, arXiv:1312.4175. [86] D. Francescone, S. Akula, B. Altunkaynak et al., [116] L. Edelhuser, J. Heisig, M. Krmer et al., JHEP 1412 arXiv:1410.4999. (2014) 022, arXiv:1410.0965. [87] D. Feldman, Z. Liu, and P. Nath, JHEP 0804 (2008) [117] L. Roszkowski, E. M. Sessolo, and A. J. Williams, 054, arXiv:0802.4085. JHEP 1408 (2014) 067, arXiv:1405.4289. [88] D. Feldman, Z. Liu, and P. Nath, Phys.Lett. B662 [118] C. Ghag, arXiv:1412.4660. (2008) 190–198, arXiv:0711.4591. [119] XENON1T collaboration, arXiv:1206.6288. [89] N. Chen, D. Feldman, Z. Liu et al., Phys.Rev. D83 [120] H. Baer, V. Barger, A. Lessa et al., JHEP 0909 (2011) 035005, arXiv:1011.1246. (2009) 063, arXiv:0907.1922. [90] D. Feldman, Z. Liu, and P. Nath, Phys.Rev.Lett. 99 [121] T. Cohen, T. Golling, M. Hance et al., JHEP 1404 (2007) 251802, arXiv:0707.1873. (2014) 117, arXiv:1311.6480. [91] J. A. Conley, J. S. Gainer, J. L. Hewett et al., [122] B. Altunkaynak, C. Kao, and K. Yang, Eur.Phys.J. C71 (2011) 1697, arXiv:1009.2539. arXiv:1312.3011. [92] B. Altunkaynak, B. D. Nelson, L. L. Everett et al., [123] M. E. Peskin, arXiv:1207.2516. Eur.Phys.J.Plus 127 (2012) 2, arXiv:1011.1439. [124] ACME Collaboration, Science 343 (2014), no. 6168, [93] J. R. Ellis, K. Enqvist, D. V. Nanopoulos et al., Phys. 269–272, arXiv:1310.7534. Lett. B 155 (1985) 381. [125] T. Ibrahim, A. Itani, and P. Nath, Phys.Rev. D90 [94] M. Drees, Phys. Lett. B 158 (1985) 409. (2014), no. 5, 055006. [95] P. Nath and R. L. Arnowitt, Phys. Rev. D 56 (1997) [126] D. McKeen, M. Pospelov, and A. Ritz, Phys.Rev. 2820–2832, arXiv:hep-ph/9701301. D87 (2013), no. 11, 113002, arXiv:1303.1172. [96] J. R. Ellis, K. A. Olive, and Y. Santoso, Phys. Lett. B [127] T. Moroi and M. Nagai, Phys.Lett. B723 (2013) 539 (2002) 107–118, arXiv:hep-ph/0204192. 107–112, arXiv:1303.0668. [97] G.Anderson,H.Baer,C.-h.Chenetal., Phys. Rev. D [128] W. Altmannshofer, R. Harnik, and J. Zupan, JHEP 61 (2000) 095005, arXiv:hep-ph/9903370. 1311 (2013) 202, arXiv:1308.3653. [98] G. Anderson, C. Chen, J. Gunion et al., eConf [129] M. Dhuria and A. Misra, Phys.Rev. D90 (2014), C960625 (1996) SUP107, arXiv:hep-ph/9609457. no. 8, 085023, arXiv:1308.3233. [99] K. Huitu, Y. Kawamura, T. Kobayashi et al., Phys. [130] G. Giudice, P. Paradisi, and M. Passera, JHEP 1211 Rev. D 61 (2000) 035001, arXiv:hep-ph/9903528. (2012) 113, arXiv:1208.6583. [100] A. Corsetti and P. Nath, Phys. Rev. D 64 (2001) [131] A. Aboubrahim, T. Ibrahim, and P. Nath, 125010, arXiv:hep-ph/0003186. arXiv:1403.6448. [101] U. Chattopadhyay and P. Nath, Phys. Rev. D 65