Status of low mass LSP in SUSY
EEPJ manuscript No. (will be inserted by the editor)
Status of low mass LSP in SUSY.
Rahool Kumar Barman , a Genevieve Belanger , b and Rohini M. Godbole , c Indian Association for the cultivation of Science, Jadavpur, Kolkata 700032, India. LAPTh, Universit´e Savoie Mont Blanc, CNRS, B.P. 110, F-74941 Annecy Cedex, France. Centre for High Energy Physics, Indian Institute of Science, Bangalore, 560012, India.
Abstract.
In this article we review the case for a light ( < m h / Particle physics finds itself currently at a very curious juncture. It has been now almosta decade since the Higgs discovery [1]. Measurements of the various properties of theHiggs such as its mass and couplings with all the SM particles are now available. Themeasurements are consistent with the observed state being SM-like. The observationof a SM-like Higgs with a mass close to the electroweak (EW) scale was expected to beaccompanied by evidence for the TeV scale physics which would explain stabilisationof the Higgs mass around the EW scale. Absence of any evidence of such physicsbeyond the SM (BSM) is what one can call the LHC paradox. This situation is quiteunusual in the field of particle physics where the development in the past six to seven a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] a r X i v : . [ h e p - ph ] O c t Will be inserted by the editor decades had been particularly propelled by close cooperation/competition betweenthe theory and experimental community where each set new goal posts for the other.Weak scale Supersymmetry (SUSY) [2, 3] has been one of the most attractivesolution to the problem of the instability of the Higgs mass to radiative corrections andhence had been a template of BSM physics to be searched at the LHC. Absence of anyevidence for any of the BSM physics at the TeV scale in the current LHC results [1],points toward generically heavy and/or compressed supersymmetric spectra in thestrong sector. The limits are generically lower in the electroweakino (EWeakino) sectordue to the lower EW production cross-sections as well as compressed spectra [4, 5].Experiments at the LHC have begun to probe such scenarios. The high luminosityLHC run, with an expected luminosity of 3000 fb − , will explore the EWeakino sectorin detail. In view of this and also the ever increasing lower limits on the stronglyinteracting sparticles, it is therefore a matter of great interest to investigate howlight the EWeakino sector of the Supersymmetric theories can really be, remainingconsistent with all the current available information and further what would be theprospects of current/future facilities to search for them.Further the EW sector of supersymmetric theories involves ’naturally’ a readymade candidate for the Dark Matter (DM), which is known to constitute about 26 . Ω P L h = 0 . ± . , (1)where h denotes the Hubble parameter in units of 100 km s − M pc − . Thus theupper limit on the Ωh at 95% C.L., Ω maxobs h is 0 . SU (2) L × U (1) Y quantum numbers) ofappropriate strength to provide the correct order of magnitude of the relic densityfor masses of ∼ O (100) GeV, such that they are non relativistic at the time of freeze-out in the early universe [9]. Thus they are ideal WIMP (Weakly Interacting MassiveParticle) DM candidates. Early comprehensive discussions of SUSY DM can be found,for example, in [10, 11, 2] .A constraining and hence interesting aspect of the SUSY DM solution is as fol-lows. The relic density predictions are obviously correlated with the DM detection(direct/indirect) rates and DM searches at the colliders as they involve the same cou-plings and masses, but interestingly enough they are also correlated with the resultsof the searches for sparticles and Higgs bosons at the various colliders, studies of Higgsproperties and precision measurements in flavour physics. This happens because thesame parameters of the SUSY model which determine the mass of the DM particlesand its couplings with SM particles, also impact the spectrum and couplings of theHiggses for example. As we will discuss in the next section in the simplest version ofSUSY theories, the so called constrained Minimal Supersymmetric Standard Model(cMSSM), consistency with the non-observation of SUSY particles at the LHC andabsence of a signal in the direct/indirect detection so far, coupled with the demandthat the LSP DM has a relic density which can account for the DM in the Universe, For a recent mini review of thermal and non thermal dark matter see [12]. For a recent,detailed discussion of cosmological constraints on light, scalar dark matter see reference [13].ill be inserted by the editor 3 all push the LSP mass to high values. A high mass LSP is in tension with the ’natu-ralness’ of the SUSY solution. In addition, a low mass LSP can still be consistent withall the experimental constraints in other versions of MSSM such as the one with nonuniversal Higgs masses (NUHM) or the phenomenological MSSM (pMSSM) where theassumptions made to reduce the number of parameters in the cMSSM are relaxed.On the observational side, over more than a decade, there have been differentclaims of experimental evidence for ’light’ DM in the mass range ∼ O (10) GeV [14] .Further, the reach of major DD experiments deteriorates in lower mass region andmany new ones are being constructed to probe even the sub-GeV region [15, 16]. Allthis indicates that the region of light LSP’s is not without theoretical and observa-tional interest.All the above makes it clear why investigating the status of a light LSP which canbe (at least partially) responsible for the relic DM in the Universe, is very important.Within the context of SUSY, this is the one window that needs to be thoroughlyexplored, to be able to draw firm conclusions about the WIMP paradigm, which isunder great scrutiny [12, 17].In this article we will mainly discuss the case of a low mass neutralino as theSUSY DM, and we will also mention briefly the status of sneutrino DM. In Section 2we will summarise the issues about the calculation of relic density of DM, its directand indirect detection as well as some aspects of the collider phenomenology of theDM. After this we will discuss generic aspects of the phenomenology of a light SUSYDM. We will show that a light neutralino LSP DM, is all but ruled out in the mostconstrained SUSY models and is under tension in some of the variants. There arethree ways to relax some of the tight constraints on the light LSP : 1) modifyingthe high scale relation among the gaugino masses or the Higgs mass parameters, 2)adding extra EW particles (and hence EW sparticles) in the spectrum while keepingthe same gauge group, e.g adding a singlet Higgs in the NMSSM and/or a righthanded neutrino and 3) extending the gauge group. All three can lead to a change inthe composition of the LSP and the latter two can change the number of interactioneigenstates of neutralinos and hence the nature of the LSP. Here we will discuss onlythe first two possibilities. Let us begin here briefly by summarising the relevant details of the relic densitycalculation. In the standard model of cosmology, we assume that the early universecan be described by a radiation dominated medium that is in thermal equilibrium.Over time, the number density, n , of particles of a certain species within this mediumdepends on three rates: the expansion rate of the universe, the rate at which newparticles are created, and the rate at which they are annihilated. The time evolutionof the number density can be described, under a few simplifying assumptions, by aBoltzmann evolution equation [9]: dndt = − Hn − (cid:104) σ ann v (cid:105) ( n − n eq ) . (2)where H is the Hubble parameter governing the expansion rate of the Universe, (cid:104) σ ann v (cid:105) is the velocity weighted annihilation cross-section and n eq stands for the We will summarise the current experimental situation in some detail in the appropriatesection. We consider the region < m h / equilibrium number density. If the second term on the right-hand side dominates, n will approach the equilibrium number density n eq . When n reaches n eq , the creation(proportional to n eq ) and annihilation (proportional to n ) processes are in equilib-rium, and the number density only changes over time because of the expansion ofthe universe. Therefore, the Boltzmann equation will always drive towards an equi-librium. During the inflationary era of the universe, the hot, dense medium of theearly universe cools quickly and the number density of particles rapidly drops. Par-ticle annihilations still occur during this stage, but the creation of heavier particlestates becomes improbable because the thermal velocities of particles are too low.The number density therefore depletes. At some point, the density of the particlesgets too low such that the annihilation mechanism also stops working: the universeis simply too dilute for particles to find each other. The creation and annihilationprocesses freeze out, and the number density approaches a constant value: the relicdensity Ω DM h . The relic density for a particular species would be decided by thethermal average (cid:104) σ ann v (cid:105) and of course the mass of the DM candidate.In fact for a ’cold’ DM particle (call it (cid:101) χ ), an approximate estimate of the relicdensity can be obtained for standard thermal history of the Universe, which is inde-pendent of its mass, barring logarithmic corrections. The expression, neglecting thesecorrections, can be written as [10]: Ω (cid:101) χ h = m (cid:101) χ n (cid:101) χ ρ c (cid:39) × − c m s − (cid:104) σ ann v (cid:105) , (3)where ρ c is the critical density. The velocity dependence of the annihilation cross-section has been neglected in arriving at this. We see that if the velocity averagedannihilation cross-section is ∼ − c m s − , one can have relic density with the rightorder of magnitude. This is ’naturally’ achieved for a weakly interacting massive par-ticle with mass around 100 GeV. It is in this sense that the supersymmetric theoriescan present a ready made DM candidate which could have the correct relic density.Note, however, that this is also achieved for a range of weakly interacting particlemasses with the coupling strengths, g (cid:101) χ , varying appropriately such that the ratio g (cid:101) χ /m (cid:101) χ is kept fixed, because assuming m (cid:101) χ to be the only mass scale, on dimensionalgrounds we have σ ann ∼ g (cid:101) χ /m (cid:101) χ . We will see effects of this in our discussions of SUSYDM as well.Of course, most generally (cid:104) σv (cid:105) is not velocity independent. On solving the Boltz-man equation one finds that the freeze-out occurs roughly at a temperature T f suchthat m (cid:101) χ (cid:39) − T f if one wishes to have the relic density Ω obs (cid:101) χ h = 0 . ± . (cid:101) χ has small velocities at the freeze-out. Hence while calculating therelic density it is sufficient to expand the annihilation cross-section in powers of v as σv = a + bv + · · · . (4)For s -channel annihilation the cross-section will be constant and hence the first termcan be enough. However, when (cid:101) χ are Majorana particles, as they are in SUSY, thes-channel annihilation into light fermions, for example, will be helicity suppressed andthe b term HAS to be taken into account as well. In general, it is sufficient to keeponly the first two terms in the expansion and approximate analytical expressionscan be obtained in terms of a, b [10]. Of course, the state of the art relic densitycalculations are done by solving the Boltzman equation numerically and considering By Cold Dark Matter (CDM) one means that the DM particle is moving with non-relativistic speeds at the time of decoupling and freeze-out. If the DM particle is movingwith relativistic speeds at the time of the freeze-out, it is called a Hot Dark Matter (HDM)candidate.ill be inserted by the editor 5 all the annihilation channels [18, 19, 20, 21]. Note that if the annihilation proceedsthrough a resonance then these rules of thumb are not enough to understand theresults one gets numerically.If for a particular DM species, say (cid:101) χ , the computed relic density Ω (cid:101) χ h is lessthan the observed one Ω P L h then that species is said to be under-abundant, as itdoes not account for all the DM that is observed. Likewise, if one has Ω (cid:101) χ > Ω P L thecorresponding DM species is said to be over-abundant. Recall here also that while thevelocities of the DM particles at the freeze-out are ∼ . − . c , those in the galactichalos are much smaller ∼
200 k m s − ∼ − c . This will have to be kept in mindwhen one tries to understand in a collective manner the implications of parametersof a model for the relic density as well as those for the direct/indirect detectionexperiments in a given model. It should also make it clear why the issue of velocitydependence of (cid:104) σ ann v (cid:105) is a crucial one.It is also possible, as in Supersymmetric theories, that there exist other BSMparticles in the spectrum. If there exists the next to lightest supersymmetric particle(NLSP) (say (cid:101) χ ) which is close in mass to the LSP (which we have called (cid:101) χ ), thenin addition to the self annihilation via (cid:101) χ + (cid:101) χ → SM + SM , (cid:101) χ can be depleted alsoby the co-annihilation process (cid:101) χ + (cid:101) χ → SM + SM . If the masses of (cid:101) χ and (cid:101) χ areclose then the number density of (cid:101) χ is appreciable at the time (cid:101) χ freezes out. Thenthis depletion needs to be added in the Boltzman equation(Eq. 2).Further sometimes the LSP interacts so weakly with the SM particles that itcannot reach thermal equilibrium. In this case DM can be created either from thedecay of some heavy particle that decays into the LSP while in equilibrium or fromthe annihilation of pair of SM particles. This is called the freeze-in mechanism [22, 23].Another possibility is that the NLSP decays on a long time scale, either due tocompressed spectra or small couplings, into a final state containing the LSP. Whenthis decay occurs after the freeze-out of the NLSP, the relic density of the LSP issimply related to that of the NLSPThere exists of course the possibility that the early universe cosmology is non stan-dard. In the above discussion, one has assumed that the Universe must have evolvedadiabatically after the (cid:101) χ decoupled. If there was a period of entropy production, e.g.due to the out–of–equilibrium decay of another massive particle, only a small frac-tion of today’s CMB photons would originate from the SM plasma at T f which isthe freeze-out temperature. Only this fraction should be used in computing n (cid:101) χ andthen the prediction of Ω (cid:101) χ h will be diluted accordingly. One example of such a latedecaying particle, is a SUSY modulus scalar. For every value of DM mass, severalcombinations of reheating temperature and heavy scalar mass can lead to a relic den-sity compatible with the observed value [24, 25, 26]. One phenomenological approachto analyse the over-abundnant scenarios would therefore be to simply assume that itis possible to find a mechanism that brings the DM relic density in agreement withobservations. Thus, in practice one can analyse all the parameter space points of themodel, for which the relic density value computed assuming thermal freeze-out witha standard cosmological model is above Ω P L h and ask the question how these pa-rameter space points may be explored by the direct/indirect detection experimentsor the collider ones.In the next two sub sections we first discuss the (model independent) aspects of allthe three types of DM detection experiments and then discuss their interpretation aswell as implication in the context of SUSY model parameters in the last subsection. Let us briefly summarise the (model independent) information about Direct and In-direct detection of the DM. Direct detection experiments aim to detect small pertur-
Will be inserted by the editor
Fig. 1.
Upper limits on the spin-independent WIMP-nucleon cross section ( σ SI ), derivedby Xenon-1T, at 90% C.L. (from [30]). bations of atoms within the detectors, which are caused by WIMPs of astrophysicalorigin that pass the detector. Since the velocity of these particles is generally non-relativistic, the WIMP scattering occurs elastically and at most causes excitation orionization of detector material. As we do not know the mass, the type of interaction,or the interaction strength of the WIMPs, it is important to have several detectorswith different detector materials. Furthermore, to reduce the background as much aspossible, direct detection experiments are often placed in deep-underground labora-tories. The goal of these highly sensitive experiments is to measure the amount ofenergy deposited when a WIMP DM scatters off the target nuclei inside the detec-tor in a background-free environment. The scattering rate between the WIMP andtarget nuclei ( dN/dE ) can be obtained [27, 28, 29]. This of course depends on theWIMP-nuclei differential cross section which, in turn depends, among other things,on the distribution of the WIMP DM particles in the relative velocity v betweenthe DM and the earth. The interaction cross-section has two parts: spin-independent σ SI and the spin-dependent σ SD . Note that the spin-independent interactions arecoherent as they couple to the entire nucleus whereas the spin dependent interactionsare not, because the spin of the nucleus does not increase with its mass. Hence, forheavier nuclei the spin-independent interactions dominate. The calculation requiresknowledge of the spin content of the nuclei as well as degree of coherence betweendifferent nucleons. The latter is encoded in the form factors calculated in [29]. Thenon-observation of WIMPs at direct detection experiments places limits on the in-teraction strength between a WIMP and the proton/neutron as a function of theWIMP mass. Fig. 1 (taken from [30]) summarises the current upper limits on thespin-independent WIMP-nucleon cross section from the Xenon-1T experiment. Notealso that even though there exist considerable uncertainties in the theoretical pre-dictions of the expected cross-sections, coming from astrophysical inputs as well aslimitations in the knowledge of the parton content of the nucleus, they are under rea-sonable control [27, 28]. The DD detectors have a threshold energy, below which theycannot measure the recoil induced by the DM particle. This means that the DD detec-tors have low sensitivity for low-mass DM particles. As the mass of the DM particlebecomes higher, the number density and therefore the flux decreases, so we expecta lower rate. This explains the observed shape of the limits on the WIMP-nucleuscross-section seen in Fig. 1. In fact, below O (10) GeV (depending on the detector ma-terial) there is low sensitivity. Above O (10) GeV, the sensitivity increases till about ill be inserted by the editor 7 O (50) GeV and then reduces again due to the limited statistics for high-mass DMparticles.A short comment on the evidence for light WIMP (in the mass range from 7 to30 GeV) that was mentioned in the introduction, is in order here. The results fromLUX [31] and Xenon-1T [30] cover, with much higher sensitivity, the same regionwhere signals were reported by CoGenT [32], CRESST [33], CDMS-Si [34, 35] andDAMA/LIBRA [36, 37]. The absence of signal by these two experiments in this regionimplies that the earlier experimental results are either fluctuations or not relatedto DM. Results by an improved version of CDMS, the SuperCDMS, does not seeany signal in the region favoured by earlier sightings either [38]. It should be notedhere that the region of small DM masses (smaller than 6 GeV or so ) is actuallyquite unconstrained even after the very remarkable result from Xenon-1T, shown inFig. 1, has become available. It is an interesting question to ask that if a light (cid:101) χ isdetected and if one manages to construct a model such that it is allowed from relicdensity considerations, whether other cosmological considerations will allow it. Thiswas answered in the affirmative [39]. Using the bound on effective number of ν species( N eff ), one can in fact show that, on cosmological grounds even a Cold Dark Matter(CDM) of mass ∼ O (MeV) is allowed [40].Indirect detection experiments look for annihilation products that originate fromastrophysical WIMP–WIMP scattering. These products include (anti-)protons, pho-tons, (anti-)electrons, and neutrinos. The rate at which these particles are createddepends on the density of dark matter squared. Furthermore, the velocities of theWIMPs need to be high enough, such that the WIMPs can scatter inelastically.These facts combined mean that these annihilations occur in dense areas, such asthe dwarf spheroidal (dSph) galaxies which are rich in DM or the center of the sunor the galaxy. The non-observation of the annihilation products results in limits onthe present-day velocity-weighted annihilation cross section. These limits depend onthe WIMP mass and the annihilation scenario. However, WIMP–WIMP scatteringis not the only process that could create (anti-)protons, photons, (anti-)electrons orneutrinos. It follows that a good knowledge of the environments where the annihila-tions could occur is needed, and this knowledge is not always available. An exampleof the foregoing is the notorious Galactic Center excess of the spectrum of high ener-getic photons (gamma rays), as observed by the Fermi-LAT satellite [41]. A possibleexplanation for such excesses includes annihilations of light ( < −
70 GeV) DMparticles, see for example, [42, 43, 44, 45]. But given the many uncertainties, theseexplanations are heavily debated.
The dark matter particles are assumed to interact weakly with the observed matter,are stable at the time scale of the universe, and, are assumed to be charge neu-tral. Correspondingly, the DM particles manifest themselves as missing energy in thecolliders. Hence the collider-based experiments, such as ATLAS and CMS, look formissing transverse energy (E / T ) in their detectors, which may be a sign of an un-detected particle that is produced during the inelastic scattering process of the twocolliding protons. Dark matter searches at the colliders are therefore mostly based onidentifying the visible counterparts produced in association with the DM candidate viz mono-jet + E / T [46, 47], mono- Z/W ± /H + E / T [48, 49]. DM particles can alsobe present in decay chain of sparticles, should they be produced in the pp collisions.These then can give rise to events containing E / T along with SM particles. This hap-pens to be an important channel for SUSY searches as well. None of these searcheshave reported a clear signature over the SM expectation at the LHC so far. Will be inserted by the editor
Another category of collider probes for the case of light DM ( m (cid:101) χ ≤ m h / ∼ . ggF , V BF and
V h modes. The most recent measurement of Br ( h → invisible ), performedby ATLAS using the Run-II LHC data ( L = 140 fb − ) in the V BF
Higgs productionmode, has set the upper limit at 13% at 95% CL [54]. Note here that the observedHiggs signal strengths also imply an direct, albeit model dependent, constraint onthis branching ratio.In the context of a specific model like SUSY the DM may also be searched at thecollider in terms of production of just the EWeakinos which we will discuss in detailin the next sections.An important aspect regarding the collider searches of DM is that any neutralparticle which interacts weakly with the detector or which decays outside the detectorwould also result in a missing energy signature similar to that of a DM particle. Undersuch circumstances, it would not be feasible to resolve the DM contribution to E / T .Therefore, the collider searches for DM of this variety do not provide the most efficientprobes for DM detection, rather, they provide complementary probes in associationwith the direct and indirect DM detection modes. In the MSSM there are two neutral LSP candidates in the observable sector, thelightest neutralino (cid:101) χ and a (cid:101) ν . While in most models the (cid:101) χ is the LSP we willbriefly entertain the possibility of the (cid:101) ν DM. We will not discuss the case of the lightgravitino as the DM in this article.Due to the absence of positive results in the search for DM at the colliders as wellas in the high sensitivity DM experiments, for a light (cid:101) χ , the focus shifted away fromthe constrained SUSY model cMSSM with its limited number of parameters, quiteearly on. The interest, since then, has been in SUSY models where the constrainingassumptions are relaxed or the particle content is augmented, with a view to obtaina SUSY DM candidate which 1)can provide adequate relic DM either via freeze-outor freeze-in and 2)is consistent with the non-observation in the DD experiments. Thetight connection between the DD rates and the size of the σ ann v makes this exercisemore tricky. The focus of the activity is to see how one can explore these models atthe LHC not just through the DM searches but also via associated phenomenologyof the Higgs and also that of the sparticles other than the LSP. Of course, the latterhas meaning only in the context of a particular model. (cid:101) ν DM Even though (cid:101) χ is the LSP in most SUSY models, let us briefly discuss the possi-bility of a (cid:101) ν LSP. In this case the most important contributions to the annihilationcross section come from (1) (cid:101) ν (cid:101) ¯ ν → f ¯ f through the exchange of a Z boson in the s − channel, where f is an SM fermion, (2) (cid:101) ν (cid:101) ¯ ν → l ¯ l through the exchange of a neu-tralino or chargino in the t − channel and (3) (cid:101) ν (cid:101) ¯ ν → V ¯ V ( V = W ± , Z ) for m (cid:101) ν ≥ m V .With the exception of the l ¯ l final states other final states do not require exchange ofany particles that are possibly heavy. The relevant couplings are electroweak gauge ill be inserted by the editor 9 couplings, unsuppressed by any mixing angles. Thus the annihilation cross-sectionsare rather large and hence by Eq. 3 the resulting relic is small unless the (cid:101) ν is quiteheavy. Moreover, direct dark matter searches exclude the possibility that (cid:101) ν ’s form amajor part of the dark halo of our galaxy [10]. The reason is again the full strengthcouplings of (cid:101) ν with the Z boson, which leads to a large scattering cross-section, biggerby a factor 4 compared to a Dirac neutrino. Nevertheless the sneutrino could be theLSP. In this case the only model independent limit on m ˜ ν L comes from the invisiblewidth of the Z and is 41 GeV as quoted in reference [1] and obtained in [55]. Sincethe (cid:101) ν L couples only to the Z , this limit could not be improved by the ’mono’ photonanalysis at LEP-II with its limited luminosity. Situation can be different at the future e + e − colliders. Above mentioned direct detection constraints can be avoided if oneconsiders additional DM candidates, as was revisited recently in reference [58] whereit was also shown that some parameter space may be made viable by consideringinelastic DM in the mixed (cid:101) ν scenario.Within this scenario, after recasting the current analysis of the mono-W/Z fromthe LHC Run-II and coupling this with the upper bound on the invisible width ofthe Higgs boson, reference [58] obtains a lower limit of 55 GeV on m (cid:101) ν , assuming acompressed spectrum with ∆m = m (cid:101) e − m (cid:101) ν = 5 GeV. In the absence of a compressedspectra, the (cid:101) ν cannot be light. Moreover the light sneutrino scenario is expected tobe fully covered by the HL-LHC assuming that the leptons for the (cid:101) e decay will be’invisible’, ie. for the same compressed spectra. Another option, that we will notentertain here, is that the sneutrino is the NLSP and DM consists of a gravitino or anaxino. It is not clear, however, whether any regions of the parameter space of differentmodels described in Refs. 42 to 54 in [58] still remain viable to keep (cid:101) ν as the LSP sinceboth the collider constraints as well as cosmological ones have changed substantiallysince the original models were constructed. The issue needs to be revisited too!Adding a right handed (RH) neutrino and sneutrino (cid:101) ν R provides a well motivatedextension of minimal SUSY that allows to account for neutrino masses. This alsoenlarges the possibilities for sneutrino DM. Indeed the DM could now be the (cid:101) ν R ora mixed state. In the latter case one will still suffer from strong bounds from directdetection that enters through the small (cid:101) ν L component. Those can be best avoidedif the (cid:101) ν LSP lies in the region where DD experiments loose sensitivity (less than 10GeV) [59]. Obtaining a light mixed sneutrino, however, requires a very large A termin the sneutrino mass matrix. This is hard to achieve in the pMSSM with parametersdefined at the high scale. Thus in this framework the light sneutrino has been shownto be no longer viable after taking into account LHC constraints [60].The case of a pure (cid:101) ν R has been discussed within various models, for example thecMSSM, the pMSSM [61, 62] or the NMSSM [63, 64, 65] extended with (cid:101) ν R . In theMSSM one adds three generations of right handed singlet (cid:101) ν and the superpotentialcan be written as W (cid:101) νmssm = W mssm + y ν ˆ H u · ˆ L ˆ N . (5)where N is a the singlet neutrino field and y ν is the Yukawa coupling producingDirac masses for the ν ’s. The only interaction between the (cid:101) ν R and the SM particles iscontrolled by the small y ν . This smallness has various implications. Firstly the veryweak interaction allows to completely avoid the strong constraints from DD cross-sections. Moreover it means that the (cid:101) ν R might not achieve thermal equilibrium inthe early Universe, two mechanisms can then contribute to the relic formation, thefreeze-in production of (cid:101) ν R through the decay of some SM or SUSY particle, or theproduction of (cid:101) ν R from the decay of the long-lived NLSP after it freezes out. As a result The limits of 84 GeV [56] and 94 GeV [57] on the mass of (cid:101) ν L , obtained using an analysisof slepton production by the ALEPH and DELPHI collaborations respectively, are valid forthe case of the LSP being (cid:101) χ and more over are in the framework of the cMSSM.0 Will be inserted by the editor of the small y ν , after the RG evolutions the (cid:101) ν R emerges quite often as the LSP and (cid:101) τ as the NLSP. The (cid:101) ν L also can be quite often light but does not contribute to therelic DM in any appreciable manner for reasons explained in the first paragraph. In[66], it is shown that it is possible to get Ω (cid:101) ν R h for m (cid:101) ν R ∼ −
40 GeV, in agreementwith the measurement by PLANCK collaboration [6], with all the strongly interactingsparticles in the TeV range and the EW sparticles in the range ∼ − (cid:101) τ doesnot create problems with Big Bang Nucleosynthesis (BBN), that its mass is above thelimit imposed on the quasi-stable charged particle from LHC searches and that themass of the light Higgs as well as the rates observed in various channels are consistentwith measurements [67, 68]. This just shows the tight rope one has to walk before aSUSY DM candidate is acceptable. These are the correlations that were talked aboutin the introduction.A light (cid:101) ν R can also behave as a WIMP if it couples to other new particles, in thatcase it could have detectable cross-section in DD experiments, such is the case forexample is an extension of the NMSSM with the superpotential W (cid:101) νnmssm = W nmssm + λ N ˆ S ˆ N ˆ N + y ν ˆ L · ˆ H u ˆ N , (6)where W nmssm = W mssm ( µ = 0) + λ ˆ S ˆ H u · ˆ H d + κ S (7)and W mssm ( µ = 0) refers to the MSSM super potential without the µ -term, while λ and κ are dimensionless parameters. Thus, compared with the NMSSM the modelcontains the trilinear interaction between the singlet superfield S and one more addi-tional singlet Neutrino super field N . Here again the Yukawa coupling y ν is a rathersmall number as it gives rise to the small Dirac neutrino mass term. But this inter-action does not play any role, rather it is the trilinear interaction between the singletfields S and N which gives rise to interactions of the (cid:101) ν R with the Higgs sector andhence with the SM particles. Thus, it is possible to have a (cid:101) ν R as a satisfactory ther-mal DM candidate over a wide range of parameters and in particular to have a lightDM candidate [63]. Let us just mention in the end that the invisible decays of the h play an important role in the light (cid:101) ν R DM phenomenology mentioned and has beenstudied, eg. in [69]. (cid:101) χ DM Next we move to the much more widely studied case of the LSP neutralino DM.To discuss this let us just summarise the parameter choice that is used normallyfor phenomenological discussions. Assuming no CP violation other than the onein the SM, in the framework of pMSSM one has in fact 19 parameters, definedat the EW scale. These are: the gaugino masses M , M , M , the Higgs sector pa-rameters µ, tan β = v u /v d , m A , the masses of the first two generations of sfermions m ˜ e R , m ˜ L , m ˜ Q , m ˜ u R , m ˜ d R , those of the third generation m ˜ τ R , m ˜ L , m ˜ Q , m ˜ b R , m ˜ t R and the trilinear couplings A t , A τ , A b . For the case of cMSSM, one has only four freeparameters : the common scalar mass m , the common gaugino mass M / , a commontrilinear term A , Higgs sector parameters tan β and sign of µ . Values of µ, m A and allthe other above mentioned parameters at the EW scale are then calculated in termsof these high scale parameters. In the non-universal gaugino models the equality ofgaugino masses at high scale is broken and all the other remains the same as cMSSM. ill be inserted by the editor 11 The neutralino and chargino mass matrix can be written in terms of the pMSSMparameters as: M n = M − M Z c β s W M Z s β s W M M Z c β c W − M Z s β c W − M Z c β s W M Z c β c W − µM Z s β s W − M Z s β c W − µ , (8) where s W ≡ sin θ W , c W ≡ cos θ W , s β ≡ sin β , c β ≡ cos β and X = M √ M W sin β √ M W cos β µ . (9) The neutralino mass matrix M n is written in the interaction eigenstate ( ˜ B, ˜ W , ˜ h d , ˜ h u )basis, ie. the bino-wino-higgsino basis and the chargino mass matrix is written in thewino-higgsino basis. The mass eigenstates of these two matrices, denoted by (cid:101) χ i , (cid:101) χ ± j with i = 1 , j = 1 , (cid:101) χ is one choice for the LSP. Note from Eqs. 8, 9,that the masses and the gaugino-higgsino mixing of the EWeakinos are controlledby M , M , tan β and µ . The effect of tan β is somewhat mild. Thus the dominantcomponent of the lightest EWeakinos is decided by the relative values of M , M , µ :higgsinos if | µ | (cid:28) M , M and bino (wino) for M ( M ) (cid:28) | µ | . If µ, M and M areall comparable then (cid:101) χ i , (cid:101) χ ± j , i = 1 , j = 1 ,
2, are mixed states. In the cMSSM the (cid:101) χ is dominantly a bino.The couplings of the various EWeakino mass eigenstates with the SM particles,are controlled by the gaugino/higgsino content. The annihilation cross-sections arecontrolled by these as well as masses of the sparticles exchanged in the t -channelor the gauge bosons/higgses in the s -channel. Note that the masses of the variousEWeakinos and sfermions and the Higgses are controlled by the parameters in thelist of the 19 parameters mentioned for the pMSSM, whereas in the other versionsof SUSY models the values of these at the EW scale will be decided in terms of thefew parameters given at the high scale. Thus the dominant annihilation channel for agiven type of (cid:101) χ as well as whether there will be co-annihilations, all will be decidedby these parameters.Thus it is no surprise that, while the discussions after Eq. 3 showed that SUSY DM (cid:101) χ can have interactions and mass of the right order of magnitude required to give riseto the observed relic density Ω P L h , in reality as we scan over the parameter spaceof the SUSY models, the predictions for the relic density can vary by many orders ofmagnitude, controlled mainly, though not completely, by the LSP composition. Thesubject is complex and the literature on the subject truly vast. We refer the readerto [70] for a recent summary. However, the general strategy that has been chosen isto extract the essential features of the expected relic and the annihilation as well asinteraction cross-sections, in terms of the gaugino/higgsino content of the LSP. Ineach case, only a few of the many parameters are relevant and one can discuss theissue comprehensively and completely in terms of only those. We can specialise thenthe discussion to the case of interest here, viz. the light LSP.Pure winos (higgsinos) annihilate readily into gauge boson pairs and thus havelarge σ ann and hence are required to be very heavy ∼ . Ω P L h . Reference [71], for example, points out model parameterregions where the limits can be brought down upto a factor 2, but still not enoughto render them ’light’ enough for our consideration. Thus clearly these can not playvery important role for the discussions of the light (cid:101) χ DM.
On the other hand, let us take the case of a pure bino. The small size of the U (1) Y gauge coupling generally makes the annihilation cross-section small. This means thatthe (cid:101) χ will freeze out very early and hence the relic density will be too high. Thestrength of the cross-section also depends on the masses of sparticles exchanged inthe t/u channel for the production of pairs of longitudinal gauge bosons and f ¯ f pairsetc. Co-annihilation with sfermions can also provide some additional annihilationcross-section and decrease the relic density of binos. Hence these scenarios can thenhave implications for (and are impacted by), both the LHC searches and the DDexperiments. It is also not surprising that the LEP limits and the early days of LHCsearches which put limits on the masses of the charged EW sparticles like ˜ l iR , ˜ l iL and˜ χ ± , , already constrained considerably the viability of a pure light bino as a DM reliccapable of explaining the observed relic density. However, the situation can changesubstantially once the (cid:101) χ is of mixed nature, and even a small higgsino-bino mixingcan increase annihilation cross-section through scalars h, H or the pseudoscalar A ,in the s -channel. The annihilation into a f ¯ f pair by A resonance takes place via a s -wave, due to the Majorana nature of the (cid:101) χ while the annihilation by the scalars h, H happens via a p -wave.From the above discussions, it is clear that in MSSM (and its variant) the pos-sibility of having a light DM can be realised with a bino dominated (cid:101) χ . Since sucha (cid:101) χ was naturally expected in the low scale ’natural’ SUSY, even before the var-ious claims for light DM detection came on the scene, there was, in fact, a lot ofinterest in a light neutralino DM. Cosmological considerations implied rather smalllower bounds on the DM mass of O ( f ew ) GeV [39]. Discussions of [40] specialised toSUSY, also indicated a limit of 3 . m (cid:101) χ . In view of these lower bounds andalso a light dominant bino being an excellent thermal DM candidate, focus shifted toa general MSSM framework which consisted of various versions of the pMSSM oncethe LEP bound on the mass of a (cid:101) χ ± implied a lower bound on (cid:101) χ of 46 GeV in thecMSSM. The different versions of the pMSSM differed in the choice of free parame-ters, mainly relaxing the hypothesis of unification of gaugino masses in different ways.With the right thermal relic for a (dominantly) bino being facilitated by light sleptonmasses, this even had the potential of explaining the DM as well as the ( g − µ atone stroke and this was a favoured SUSY scenario considered in the early days bymany [72, 73, 74, 75] to quote a few. In the analysis of [75] which made use of aexistence of the pseudoscalar A and/or a light slepton, a lower bound was obtainedon the neutralino mass between 4-30 GeV, depending on values of m A and tan β . Thiswas consistent with the limit of about 18 GeV of reference [74] which was obtainedin a somewhat different scenario. It was shown that even an almost massless (cid:101) χ isallowed by the then available collider and cosmological data, as well as precision mea-surements of meson decays [76], if the relic was due to a HDM LSP, a hypothesis thatis not possible to sustain in view of the precision CMB measurements. The drivingforce on the constraints on (cid:101) χ masses in this period were the collider experiments andconsiderations of correct relic density setting goal posts for DD experiments. It shouldbe noted here that the contribution of a pseudoscalar to the DM-nucleon scatteringcross section is suppressed by the small momentum transfer. Hence DD experimentsare much more sensitive to a light scalar. Consequently they constrain a light scalarmuch more strongly than the pseudoscalar, for the same coupling and mass. In the MSSM extended to include a (cid:101) ν R which mixes with (cid:101) ν L , considerations of the N eff limits mentioned before, were used to find a lower limit of 3 . (cid:101) χ as CDM [40]. Herethe mixed (cid:101) ν R acts as an mediator for the annihilation of (cid:101) χ to ν ¯ ν . The Majorana natureof the (cid:101) χ make the annihilation to be a p wave process and hence there is no danger ofdistortion of the CMB radiation due to energy injection from the annihilation process.ill be inserted by the editor 13 With various claims of observation of light DM, both in direct and indirect de-tection experiments, the interest in light DM phenomenology really escalated with alarge number of investigations looking at the viability of light bino-dominated (cid:101) χ DM,with light sleptons particularly, (cid:101) τ R , with or without the resonant contribution of the h/H/A/Z [77, 78, 79, 80, 81, 82]. An analysis in the context of MSSM in [79] put alower limit of 28 GeV in the MSSM, which satisfied all the collider and flavour physicsconstraints available then. The importance of the constraints from b → sµ + µ − on the m A , tan β values in doing this analysis and for the limits on the mass of the (cid:101) χ waspointed out in [83]. The possibility of LHC signals that one may search for in caseof the light (cid:101) τ R which helps a light bino like (cid:101) χ good thermal DM, had also beeninvestigated [84].The mixed nature of (cid:101) χ not only has implications for the DM relic but also forthe Higgs decays. The implications of light (consistent with the LHC limits) (cid:101) χ , (cid:101) χ ± i for the Higgs decays h → γγ, h → (cid:101) χ i (cid:101) χ j etc. were already looked into (see for exam-ple [72, 73, 85, 86]) even before the Higgs discovery. These had already demonstratedthe correlations between the masses of the light EWeakinos and different branchingratios of a light Higgs. The invisible decay width of the h is controlled by the bino-higgsino mixing, apart from the masses of course. Since the same mixing also affectsthe thermal (cid:101) χ relic as well as the detection cross-sections, indeed this observableforms a very important part of the light (cid:101) χ phenomenology. Reference [87] discussedcomprehensively different aspects of a light (cid:101) χ for LHC, SUSY particle spectra andDM detection experiments, on the eve of the Higgs discovery.The discovery of the Higgs in 2012, removed one big unknown from the situationand thus gave a new direction for the phenomenological studies of the light (cid:101) χ case.So in addition to the earlier constraints one also had to now impose constraints onthe possible parameter space implied by the properties of the observed Higgs ( h )and the constraints on sparticle masses put by the non-observation of SUSY at theLHC. Particularly relevant parameters in the context of a light (cid:101) χ are of course theslepton masses, m A and the couplings of (cid:101) χ with h , A which are controlled by themixing in the neutralino sector as well as tan β . There were many investigations ofthe light (cid:101) χ case in light of the knolwedge of the properties of h and lack of SUSYsignals at the LHC [88, 89, 90, 91].The announcement of the Xenon100 results in 2013 was another game changer, asin one go it removed a part of the parameter space, where a light (cid:101) χ could be a goodthermal DM. For a nice summary of the situation which explored the case of m (cid:101) χ < (cid:101) χ , the Z and h exchange (called Z or h funnel) providing the necessary annihilation,possible light A being ruled out by consideration of the LEP/LHC searches. Oneshould add here that the bulk region where the slepton co-annihilation works andhence a light, bino-like (cid:101) χ is allowed, opens up if one relaxes the requirement ofgaugino mass unification, minimal flavour violation and CP conservation from theMSSM [97]. One should however also note that the last two are generally introducedso as to avoid problems with measurements in the flavour sector in MSSM and theirrelaxation is a bit of a tight rope walk in view of the ever more precise measurementsin the flavour sector.In summary, we notice that in the 19 parameter pMSSM, a light (cid:101) χ can be realisedin the region m (cid:101) χ ≤ . m (cid:101) χ ± ≥ . M , µ > ∼
100 GeV) andindeed the (cid:101) χ in the above mass region is dominantly a bino. There have been manyrecent investigations in this context [99, 100, 101, 102, 103], looking at the viability of light (cid:101) χ in light of the latest exclusions in the σ SI – m (cid:101) χ plane by the Xenon-1Texperiment as well as the latest EWeakino searches. The situation is summarised inSection 3.As a small digression let us note the following. The large values of the (cid:101) χ massesneeded in the SUSY models for a pure higgsino/wino case to explain the relic, havealso added to the questions about naturalness of the SUSY solution to DM. In ra-diative natural SUSY models [5], the requirement that their EW fine tuning(FT)measure ∆ EW be less than ∼
30, implies small values of µ which naturally indicates (cid:101) χ to be higgsino and ‘light’ (100 −
300 GeV). Of course such low mass higgsinocan not explain the total observed relic and one is forced to think of a multi compo-nent DM. However even that is not ’light’ enough by considerations of this article. Ageneric pMSSM discussion, however, investigating naturalness using the FT measure ∆ EW [104, 105], does find a cluster of points around m (cid:101) χ (cid:39) m Z / (cid:39) m h / ≤ Ω maxobs h .Next let us now turn to the case of the NMSSM. The NMSSM, described by thesuperpotential of Eq.7, is the simplest extension of the MSSM which was suggested asa mechanism which can explain why µ is small in a ’natural’ way. The NMSSM Higgssector is phenomenologically richer than that of MSSM and has an additional CP-even and a CP-odd Higgs state. Among the three CP-even Higgs bosons, h , h , h ,one is identified with h . In addition, the Higgs sector consists of two CP-oddpseudoscalar Higgs states, A , A , and two charged Higgs bosons. Along with tan β and µ , additional parameters of the Higgs sector are λ , κ , A λ , A κ , where A λ and A κ are the trilinear soft-breaking parameters [106]. The EWeakino sector also has anew ingredient viz. singlino ( ˆ S ). This results in 5 neutralinos and 2 charginos, and isparameterised by: M , M , µ, tan β, λ, κ . The 5 × M (cid:101) χ i = M − m Z sin θ W cos β m Z sin θ W sin β M m Z cos θ W cos β − m Z cos θ W sin β − m Z sin θ W cos β m Z cos θ W cos β − µ − λv sin βm Z sin θ W sin β − m Z cos θ W sin β − µ − λv cos β − λv sin β − λv cos β κv s (10) The mass eigenstates in this case are then a mixture of the ˜ B, ˜ W , ˜ h u , ˜ h d and the ˜ S .The singlino component will then modulate the interactions of the SM particles withthe (cid:101) χ i , i = 1 ,
5. Due to the presence of additional structure in the neutralino sector,additional mediators which can be involved in the (cid:101) χ annihilation processes and ininteractions with nuclei as well as the rich Higgs phenomenology at the colliders andin flavour physics, study of thermal DM in the NMSSM has been a very fertile field ofexploration[106, 108, 109]. The case of a light (cid:101) χ has been discussed in the literatureextensively [110, 111, 79, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123,124, 125, 126, 127] .In the NMSSM there exists a possibility of a light singlet dominated scalar orpseudoscalar which provides a good annihilation channel for a singlino-higgsino mixed (cid:101) χ , thus facilitating the correct relic abundance. Thus one can say that here one canhave h , A , Z and h funnel regions where an over dense universe can be avoided.Compatibility with the DD cross-section is obtained because the interactions of (cid:101) χ with quarks are weakened due to the singlino content.The case of light (cid:101) χ in theNMSSM was examined comprehensively in [79]. Due to difference between the DMvelocities at the freeze-out and in the galaxies and the flexibility in the couplings In addition to these we already discussed the extensions of the NMSSM where a (cid:101) ν R canbe a thermal DM candidate and leads to characteristic LHC signals.ill be inserted by the editor 15 of (cid:101) χ , it is possible to have both large or small DD cross-sections for light (cid:101) χ inthe NMSSM [79], for small masses of the mediator h , A . These can escape theconstraints from LEP and the LHC due to their singlet dominated nature.By virtue of the self coupling in the scalar sector, the h can decay into a pairof h /A which can then decay into a pair of fermions or a pair of light EWeakinos,thus giving rise to new exotic or invisible decays of the h . Thus these scenarios canbe probed through the properties of h , see for example [118, 125, 127]. In additionto these one can also probe them through direct production of the light higgsesand the light EWeakinos, at the LHC and future machines [109, 113, 116, 119, 120,121, 123, 124, 126, 128, 127]. This means that the allowed parameter space of theNMSSM is then constrained by the observed mass and measured signal strengthsof the h , current EWeakino searches, searches for light scalars at the LEP andthe LHC, the latter through the production in h decay. Of special importance arealso the constraints from flavour physics as was pointed in [110]. Further, for theselight (cid:101) χ ’s, the Indirect DM detection experiments, looking at the radio emission inthe Milky Way and in galaxy clusters, gamma rays in the dwarf spheroidal (dSph)galaxies and also the antiprotons in the milky way [111, 114, 118], can constrainthe NMSSM parameter space very effectively. The constraints from the Xenon-1Texperiment have again played an important role in constraining the parameter space.In fact, the direct and indirect detection experiments are pretty complementary inthis case [114]. Section 4 contains a detailed discussion of the current status of alight (cid:101) χ in NMSSM and discovery prospects at the LHC (HL/HE) , the future DMdetection experiments and the e + e − colliders: the Higgs and the B -factories. (cid:101) χ DM in pMSSM
The impetus of this section is the pMSSM scenario with a light neutralino DM andwith parameters defined at the electroweak scale. Let us first discuss the case where (cid:101) χ is a thermal relic ( Ω (cid:101) χ h ≤ Ω maxobs h ). Recent works in this direction [99, 103] (andthe references therein) have explored the impact of current limits from collider, as-trophysical and cosmological measurements. The analysis in reference [99] consideredthe following range of input parameters:1 GeV < M <
100 GeV ,
90 GeV < M < , < tan β < ,
70 GeV < µ < ,
800 GeV < M ˜ Q l <
10 TeV ,
800 GeV < M ˜ t R <
10 TeV ,
800 GeV < M ˜ b R <
10 TeV , < M < , −
10 TeV < A t <
10 TeV (11)The mass of the first and second generation squarks and the sleptons were fixed at3 TeV, while both A b and A τ were taken to be 0. The pseudoscalar mass was fixedat 1 TeV in order to decouple its effect from DM phenomenology and the lighterCP-even Higgs boson was identified with the 125 GeV Higgs boson of the StandardModel ( h ).The parameter space considered in reference [99] (Eqn. 11) was restricted to the µ > σ SI are more sensitive than their spin-dependentcounterparts. The current limits (projected reach) on σ SI from Xenon-1T [30] (Xenon-nT [129]) at 90% CL are illustrated as a solid (dashed) blue line in Fig. 2. The verticalaxis in Fig. 2 represents σ SI rescaled with ξ , defined as the ratio of the predicted relic density of (cid:101) χ ( Ω (cid:101) χ h ) to Ω maxobs h ξ = Ω (cid:101) χ h .
122 (12)Note that in the framework of the pMSSM considered here, the Higgs signal strength
Fig. 2.
SI DM-nucleon cross-section vs m (cid:101) χ for all points allowed by the collider and relicdensity constraints (modified from Ref. [99]). The reach of various DD experiments is shownby lines labelled accordingly. constraints impose an indirect upper limit on the Higgs to invisible branching frac-tion ( (cid:46) (cid:101) χ . The boundsfrom Xenon-1T excludes almost all the points in the Z funnel region and a significantfraction of points in the h funnel region. Note that the constraints from Xenon-1Texclude points which were otherwise allowed by the Higgs signal strength constraints.Let us next discuss the impact of current limits from direct EWeakino searches.For m (cid:101) χ ≤ . W Z mediated3 l + E / T channel, 2 l + E / T channel and the W h mediated 1 l + 2 b + E / T channel,performed using the LHC Run-II data ( L ∼
35 fb − ), is roughly 390 GeV [103] and650 GeV [130], respectively. We impose these limits conservatively by choosing onlyparameter space points which have higgsino- (wino-) dominated EWeakinos (withhiggsino (wino) admixture > . Only one point in the Z funnel region appears to avoid the current EWeakinoconstraints. A closer observation reveals that this particular point has µ ∼
240 GeVand M ∼
470 GeV resulting in higgsino-dominated (cid:101) χ , (cid:101) χ and (cid:101) χ ± with a mass smallerthan 390 GeV and wino-dominated (cid:101) χ and (cid:101) χ ± with a mass smaller than 650 GeV.However, the amount of higgsino admixture in (cid:101) χ and (cid:101) χ ± is around 88% and the Similar results have also been reported in reference [103].ill be inserted by the editor 17 amount of wino admixture in (cid:101) χ and (cid:101) χ ± is around 89%, thus, falling only marginallyoutside the conservative interpretation of the current reach of direct higgsino andwino searches. Fig. 2 also shows that the entire region of currently allowed parameterspace in the thermal scenario falls within the projected reach of the Xenon-nT.An ongoing work [131] has analysed the projected capability of the HL-LHC andthe HE-LHC ( √ s = 27 TeV, L = 15 ab − ) to probe the currently allowed parameterspace via direct EWeakino searches in the W Z and
W h mediated 3 l + E / T finalstate. The analysis in reference [131] utilises the signal regions and efficiency gridsobtained in reference [127] . The projected reach of the HL-LHC (HE-LHC) is shownin Fig. 3 left (right) panel for the currently allowed parameter space in the h funnel region. The currently allowed points are mostly concentrated in the ξ (cid:46) . ξ (cid:38) . ξ (cid:46) .
02 region have µ (cid:46)
150 GeV and M (cid:38)
650 GeV. Asa result, the amount of bino admixture in (cid:101) χ and (cid:101) χ increases which in turn leads toa reduction in the higgsino composition to values below 90%. These points, therefore,survive the current limits from direct higgsino searches. Since, M is also larger than ∼
650 GeV, the wino-like (cid:101) χ and (cid:101) χ ± evades the constraints from direct wino searches.The region with ξ (cid:38) . M (cid:38)
250 GeV and µ (cid:38)
400 GeV. Consequently, the heavier neutralinos and the charginos are either wino-higgsino mixed states or outside the current limits from direct EWeakino searches.Furthermore, the large mass difference between M and µ results in a relatively smaller h (cid:101) χ (cid:101) χ coupling leading to higher values of ξ . The intermediate ξ region (0.02 (cid:46) ξ (cid:46) (cid:46) µ (cid:46)
400 GeV and M (cid:46)
500 GeV.The points with M (cid:38)
500 GeV get excluded by the current limits from direct higgsinosearches since the amount of higgsino content in (cid:101) χ / (cid:101) χ and (cid:101) χ ± increases above 90%.The only allowed point in the Z funnel region also falls within the projected discoveryreach of direct EWeakino searches at the HL-LHC. Fig. 3. ξ vs m (cid:101) χ for the allowed parameter space points. Blue (Orange) coloured points fallwithin (outside) the projected discovery reach of direct searches in the 3 l + E / T channel atthe HL-LHC (left panel) and the HE-LHC (right panel) (from Ref. [131]). Details on the translation scheme can be found in reference [127]8 Will be inserted by the editor
In Fig. 3, the orange (blue) coloured points are outside (within) the projecteddiscovery reach. HE-LHC displays a much larger discovery reach compared to theHL-LHC. The orange points close to ξ ∼ − have a typically large M ( (cid:38) µ ( (cid:46)
150 GeV). As a result, the (cid:101) χ , (cid:101) χ and (cid:101) χ ± in these parameterspace points have a dominant higgsino composition, and pp → (cid:101) χ (cid:101) χ ± + (cid:101) χ (cid:101) χ ± are thedominant chargino-neutralino pair production modes. However, due to smaller valueof µ , the mass difference between (cid:101) χ / (cid:101) χ / (cid:101) χ ± and (cid:101) χ is either small or very close to the W / Z / h mass resulting in suppressed signal efficiencies in both W Z and
W h mediated channels. As a result, despite having large production rates, these pointsresult in a very small or zero signal significance. The orange points close to ξ ∼ M and µ and falls outside the projected discovery reach due tosmall production cross-section.There is also substantial motivation to consider the scenario, Ω (cid:101) χ h > Ω maxobs h ,where non-standard mechanisms enable the production of the observed relic den-sity (see Sec. 2.1). Considering the parameter space shown in equation 11, the workin reference [99] shows that such a scenario can lead to phenomenological featureswhich are distinct from the predictions of the thermal relic scenario. The lower limiton m (cid:101) χ is lifted in the non-standard scenario and allowed points are obtained with m (cid:101) χ as small as (cid:46) . h (cid:101) χ (cid:101) χ couplings since an efficient annihilation is no longerrequired. As a result, a wide range of Br ( h → (cid:101) χ (cid:101) χ ) is observed which can attainvalues as small as ∼ − . Fig. 4.
Points allowed by the collider and relic density constraints ( Ω (cid:101) χ h > . σ SI vs m (cid:101) χ plane. Left panel (from Ref. [131]): Grey points are excludedby the current Xenon-1T limits and the black points are excluded by the current limits fromdirect EWeakino searches. The colour palette shows the variation in ξ . Right panel (mod-ified from Ref. [99]): Grey points are excluded by the current Xenon-1T constraints and thecurrent LHC limits. Black coloured points have Br ( h → invisible ) < . Br ( h → invisible ). The reach of various DD experimentsis shown by lines labelled accordingly. The points corresponding to Ω (cid:101) χ h > .
122 and allowed by the collider constraintsare illustrated in the σ SI - m (cid:101) χ plane in Fig. 4. A significantly large population of pointsare allowed by the current DD constraints over the entire m (cid:101) χ range contrary to thethermal scenario. The black coloured points in the left panel of Fig. 4 are excludedby the combined limits from direct EWeakino searches [103, 130]. The colour palette ill be inserted by the editor 19 is used to illustrate the variation in ξ and the coloured points represent the currentlyallowed parameter points. The funnel regions correspond to smaller values of ξ due toannihilation via resonance and ξ attains larger values as one moves towards smaller m (cid:101) χ values.In Fig. 4 (right panel), the complementarity between the DD cross-sections andHiggs to invisible branching is highlighted. The grey points are excluded by the currentlimits from Xenon-1T and the direct EWeakino searches. Currently allowed pointswith Br ( h → (cid:101) χ (cid:101) χ ) < .
24% are shown in black colour and therefore, are outsidethe projected Higgs to invisible measurement capability of the CEPC. The pointswhich can be probed at the CEPC are illustrated with a colour palette representingthe variation in Br ( h → (cid:101) χ (cid:101) χ ). Fig. 4 (right panel) shows that a large fraction ofpoints which are outside the projected reach of Xenon-nT can be probed at the CEPCthrough measurements of the invisible branching fraction of the Higgs. Furthermore,all the points illustrated in Fig. 4 fall outside the current limits as well as the projectedreach (at 90% CL) of the SuperCDMS experiment [38, 132] which aims at directlydetecting the low mass WIMPs ( (cid:46)
10 GeV). For m (cid:101) χ ∼ σ SI (cid:38) − cm − while its projected sensitivityreaches up to σ SI ∼ − cm − . The current upper limits and the future projectionsfrom SuperCDMS have not been illustrated in Fig. 4 since they fall outside the rangeof the y -axis. Fig. 5. M vs µ for those allowed parameter space points which are within the projectedexclusion reach of direct EWeakino searches in the W Z mediated (left panel) and
W h mediated (right panel) 3 l +E / T channel at the HL-LHC. The colour palette shows the variationof signal significance in the respective channels (from Ref. [131]). The projected capability of the HL-LHC to probe the allowed parameter spacevia direct EWeakino searches in the
W Z and
W h mediated 3 l + E / T channels isshown in the left and right panels of Fig. 5 (from [131]), respectively. The analysisin [131] utilises the projection contours derived in [127]. Direct EWeakino searchesin the W Z mediated channel are able to probe M up to ∼
700 GeV with discoveryreach over the entire scanned range of µ . Similarly, the discovery region extends upto µ ∼
650 GeV for all values of M . Note that the W Z mediated channel displaysa stronger reach in the M > µ while the W h mediated channel shows greater The CEPC is projected to be capable of probing the Higgs to invisible branching fractionas small as ∼ .
24% [133].0 Will be inserted by the editor sensitivity in the µ > M region, thus both channels are complementary as clearlyseen in Fig. 5. In the µ (cid:46)
700 GeV region, as one further move towards smaller µ values, the amount of higgsino admixture in (cid:101) χ and (cid:101) χ ± increases. This increase in thehiggsino admixture leads to an increase in Br ( (cid:101) χ → Z (cid:101) χ ) while causing a relativedecrease in Br ( (cid:101) χ → h (cid:101) χ ). This results in a smaller signal yield in the W h mediated 3 l + E / T channel, thereby, falling outside its projected exclusion reach. Thestudy in [127] shows that the direct EWeakino searches at the HE-LHC would be ableto probe µ ( M ) up to ∼ M ( µ ) withdiscovery reach. Fig. 6.
SI DM-nucleon scattering cross-section vs m (cid:101) χ for all points allowed by the colliderconstraints and with Ωh > . ξ and represents those currently allowed parameterspace points which fall outside the projected discovery reach of direct EWeakino searchesat the HL-LHC (left panel) and the HE-LHC (right panel). The underlying blue colouredpoints result in a signal significance of > σ in the W Z and/or
W h mediated 3 l + E / T search channels at the HL-LHC (left panel) and the HE-LHC (right panel) (from Ref. [131]).The reach of various DD experiments is shown by lines labelled accordingly. Before concluding this section, let us take a look at the complementarity be-tween future DD experiments and the direct EWeakino searches at the future LHCin Fig. 6 (from Ref. [131]). The grey points in the left and right panels of Fig. 6are excluded by the current constraints. The blue points in the left and right panelsfall within the projected discovery reach of direct EWeakino searches in the 3 l + E / T final state at the HL-LHC and the HE-LHC, respectively. The currently allowed pa-rameter space points which also fall outside the projected discovery reach of directEWeakino searches at the HL-LHC (left panel) and the HE-LHC (right panel) areillustrated through an overlapping colour palette showing variation of ξ . Note thatthe blue coloured region extend underneath the coloured points. This implies that theHL-LHC and the HE-LHC will be able to probe even such points which fall below theprojected sensitivity of Xenon-nT over the entire LSP mass range via direct EWeakinosearches. This result is particularly important for the m (cid:101) χ (cid:46)
10 GeV region wherethe DD experiments start losing sensitivity. ill be inserted by the editor 21 (cid:101) χ DM in NMSSM
The NMSSM allows the possibility of much lighter neutralinos with m (cid:101) χ ∼ Ω (cid:101) χ h ≤ Ω maxobs h ). By virtue of the chargino mass constraint as discussedin Section 2.4, the (cid:101) χ has to be either bino-dominated or singlino-dominated in the m (cid:101) χ ≤ . (cid:101) χ has to undergo co-annihilation or annihilation via resonance.The work in [127] focuses on the second possibility and considers the parameter spacewith M fixed at 2 TeV in order to study beyond-the-MSSM-like region of parameterspace, thus, allowing the possibility of an exclusively singlino-like LSP with smalladmixtures from higgsinos and winos. The added advantage of a singlino-like (cid:101) χ isthat it can couple with a singlet-like pseudoscalar or scalar Higgs state even in theabsence of any higgsino admixture with the coupling being proportional to ∼ κN where N refers to the singlino component in (cid:101) χ . The Z and the Higgs boson provideresonance enhancements in the Z and h funnel regions. However, at LSP massesbelow ∼ m Z /
2, efficient annihilation can be realised only in the presence of lightsinglet-like (singlet fraction (cid:38) m A ,h ∼ m (cid:101) χ as shown in [127]. Keepingthese correlations in mind, the following region of parameter space is considered inreference [127]: 0 . < λ < . , − < κ < . , < tan β < < µ < , . < M <
10 TeV2 TeV < A λ < . , −
150 GeV < A κ <
100 GeV (13) M = 2 TeV ,
70 GeV < M < , A t = 2 TeV , A b, ˜ τ = 0The third generation squark mass parameters were fixed at 2 TeV while the firstand second generation quark and slepton masses, and the third generation sleptonmasses were fixed at 3 TeV.In the low DM mass region, m (cid:101) χ (cid:46)
10 GeV , the enhancement in the (cid:101) χ - (cid:101) χ annihilation cross-section is realised by the virtue of h /A having very narrowwidths ( Γ/m h /A ∼ − - 10 − ) along with very small couplings due to their singletnature. This results in a strong velocity dependence of the (cid:101) χ (cid:101) χ annihilation cross-section. In the early universe, the thermal energy of the DM will lead to the requiredenhancement in the annihilation cross-section leading to Ω (cid:101) χ h ≤ .
122 and at times ξ closer to 1. However, this enhancement will be absent at lower galactic velocities,thus allowing the parameter space points to escape the indirect detection constraintsfrom FermiLAT [134]. There can be exceptions when m (cid:101) χ is very near m h /A / v ∼ − c ) and only the tail of the resonance contributesat the higher velocities in the early universe ( v ∼ . c ). Within this Breit Wignerenhancement scenario, the DM annihilation cross-section in the galaxy can be largeror comparable with its early universe counterpart (see for example [135, 114]). Thework in reference [127] observed a few parameter space points which fall within thisfine-tuned category and they were excluded by the current constraints from Fermi-LAT [134].The allowed parameter space points from [127] (Eqn. 14) are illustrated in the ξσ SI vs m (cid:101) χ plane in the left panel of Fig. 7 with the colour palette showing the m (cid:101) χ has been restricted to values larger than 1 GeV.2 Will be inserted by the editor Fig. 7. ξσ SI vs m (cid:101) χ for the currently allowed parameter space points. Left panel (modifiedfrom Ref. [127]) : The colour palette shows the variation of ξ . Right panel (modified fromRef. [127]) : Black points have Br ( h → invisible ) < . Br ( h → invisible ). The reach of various DD experiments is shownby lines labelled accordingly. variation of ξ . The complementarity between the ξσ SI and the Higgs to invisiblebranching ratio is also highlighted in the right panel of Fig. 7 (taken from Ref. [127])where the black points have Br ( h → invisible ) < . Br ( h → invisible ) for the allowed points with Br ( h → invisible ) > . h : h → (cid:101) χ (cid:101) χ , A A → (cid:101) χ , h h → (cid:101) χ and (cid:101) χ (cid:101) χ → ( (cid:101) χ → A /h (cid:101) χ ) (cid:101) χ → (cid:101) χ . Note that the CEPC will be able to probe a small fraction of currently allowedpoints in the m (cid:101) χ (cid:46)
10 GeV region where the projected sensitivity of Xenon-nT falls.The CEPC will also be able to probe the coloured points which fall below Xenon-nT’sfuture reach in the m (cid:101) χ ≥
10 GeV region. Furthermore, CEPC will also have reach inthe region below the coherent neutrino scattering floor which will be forever outsidethe projected reach of any future DD experiment. In Fig. 7, the solid (dashed) red lineillustrates the current limit (projected sensitivity) from SuperCDMS [38] ([132]) at90% CL. This brings out another complementarity between the DD experiments andthe e + e − collider experiments. In the small m (cid:101) χ region ( (cid:46) ξσ SI (cid:38) × − cm − and are thus within the projected sensitivity of Super-CDMS even if Xenon-nT experiment has no sensitivity there. Reference [125] hasalso investigated the prospects of Higgs to invisible decay in the allowed region ofsemi-constrained NMSSM where the gaugino and sfermion mass unification is stillmaintained. They impose a more stringent constraint on Ω (cid:101) χ h than in reference [127]and demand further that the (cid:101) χ gives the observed relic abundance. This much moreconstrained analysis too, yields allowed points, where (cid:101) χ pair annihilation is mediatedthrough h /A in the region m (cid:101) χ (cid:46)
12 GeV. They find that Br ( h → invisible ) is (cid:46)
2% for such points, whereas for allowed points in the Z and h funnel region themaximum value of Br ( h → invisible ) is 1% and 0 . h and A also offers additional possibilities to probe thecurrently allowed parameter space via the direct searches for the light Higgs bosonsat the future colliders. This has been investigated for the HL/HE-LHC in refer- ill be inserted by the editor 23 ence [127]. After translating the projection limits from the direct searches in the h → A A /h h → b µ channel onto the allowed parameter space, the resultsindicate that the discovery potential of the HL-LHC as well as the HE-LHC is notvery strong. Compared to the projected capability of the HE-LHC, an improvementof more than 2 orders of magnitude would be required in order to cover the entireallowed parameter space in the m A /h (cid:38)
15 GeV region. Note that the projectedsensitivity of light Higgs boson searches at the future lepton colliders are projected tobe stronger than that of the HL-LHC by around 1-2 orders of magnitude [136, 137]. Inthat case, the discovery potential of the future lepton colliders would be even strongerthan the HE-LHC.
Fig. 8. M vs µ for the currently allowed parameter space points. The pale blue and greenpoints are within the projected exclusion and discovery reach of direct EWeakino searchesin the W Z (left panel) and
W h (right panel) mediated 3 l + E / T channel at the HL-LHC.The blue points are outside the projected excluded reach of the HL-LHC in the respectivesearch channels (from Ref. [127]). The projected reach of direct EWeakino searches in the
W Z and
W h mediated3 l + E / T channel at the HL-LHC and the HE-LHC has also been analysed in refer-ence [127] and their translation results are illustrated in Fig. 8. The points shownin Fig. 8 correspond to the currently allowed parameter region. The pale blue pointsand the green points fall within the projected exclusion and discovery reach of di-rect EWeakino searches in the W Z (left panel) and
W h (right panel) mediated3 l + E / T channel at the HL-LHC. The dark blue points have S σ <
2, thus, fallingoutside the projected reach of the HL-LHC. At large values of M and µ , the pro-duction cross-section becomes small while the signal efficiency is large. Similarly, inthe small M /µ region, the production cross-sections are larger but the signal effi-ciency becomes smaller. This interplay between the production rate and the signalefficiency determines the signal significance of a parameter space point. In Fig. 8 (leftpanel), dark blue points are observed in the ( µ ∼
700 GeV , M ∼
500 GeV) and( µ ∼ −
400 GeV , M ∼
150 GeV) regions. In both these regions, the M is smaller than µ , and therefore, (cid:101) χ is dominantly wino in nature. Note that thedominant neutralino-chargino pair production mode is (cid:101) χ (cid:101) χ ± . Due to small higgsinoadmixture in (cid:101) χ , the branching fraction of (cid:101) χ into the Z (cid:101) χ final state is suppressedand (cid:101) χ dominantly decays into h (cid:101) χ if kinematically allowed. As a result, the signalyield of these points in the W Z mediated channel is smaller and thereby, falls outsideits projected reach. Both these regions are however within the projected discoveryreach of the HL-LHC via direct searches in the
W h mediated 3 l + E / T channel.The work in reference [127] shows that the direct EWeakino searches in the 3 l + E / T channel at the HL-LHC will be able to probe almost the entirety of the currently allowed parameter space with discovery reach while the same search at the HE-LHCwill be able to probe the entire parameter space with much greater signal significance. We have reviewed here the status of light ( ≤ m h / ) LSP in Supersymmetry. Cos-mological considerations allow the cold dark matter particle mass to be as low asO(GeV). For the cMSSM, a light thermal DM candidate is all but ruled out. Twopossibilities of a light thermal DM in SUSY that are still viable in variants or exten-sion of the MSSM are: a light neutralino (cid:101) χ or a light (cid:101) ν R .In the pMSSM where the gaugino unification condition is modified or disregarded,there still exist regions of the M – µ parameter plane, corresponding to m (cid:101) χ (cid:39) m h / . h funnel region, where the (cid:101) χ can be thermal DMand can account for, quite often, at least a substantial fraction, of the observed relicdensity in the Universe. These regions in the pMSSM parameter space are consistentwith the current constraints from direct sparticle and BSM Higgs searches at theLHC, as well as from the measurements of mass and couplings of h and currentresults from the direct/indirect Dark Matter detection experiments. The currentlyallowed points in the parameter space are clustered around ξ ∼ ξ ∼ − .The future DD experiment Xenon-nT will be able to probe the allowed h funnelregion completely. Further confirmations can come from accurate measurements ofthe invisible width of the Higgs in future e + e − experiments. The HL-LHC (HE-LHC)will be able to cover partially (almost completely) the allowed region of parameterspace through the searches for EWeakinos through their direct production.In the pMSSM analysis if one considers, in addition, the region of parameterspace where the relic is overabundant and assume that with a non thermal cosmologythe (cid:101) χ may be responsible for the observed relic, one sees that the LHC EWeakinosearches and the measurements of the invisible Higgs decays should be able to coverthis situation too. In this case one observes interesting complementarity between theDD experiments, the invisible width measurement of h at the future e + e − collidersand the HL/HE-LHC EWeakino searches. In particular, the current LHC searches forheavier EWeakinos, rule out regions where the LSP lies in the mass range (cid:46)
15 GeVand which are below the current Xenon-1T sensitivity. In the future, the HL/HE-LHC EWeakinos searches as well as precise h invisible width measurements willfurther probe the regions at small (cid:101) χ masses, which are beyond the reach of currentDD experiments.In the NMSSM, there exist four possible funnel regions, corresponding to the h , A , h and Z exchange contributing to the annihilation, where again the (cid:101) χ can be a good thermal DM candidate over a wide rangle of (cid:101) χ masses all the waydown to ∼ m (cid:101) χ correspond to very light A , h . Future DD experiments (Xenon-nT) andmeasurements of invisible Higgs decays at a future e + e − collider will be able tocover a significant fraction of the currently allowed parameter space. Here again theinvisible Higgs measurements at the future e + e − colliders will be able to cover theregion outside Xenon-nT’s future reach over the entire m (cid:101) χ range. Moreover, the HL-LHC and HE-LHC will be able to cover almost the entire region of the currentlyallowed parameter space via the direct searches of EWeakinos in the 3 l + E / T channelwith discovery reach.Finally light sneutrinos provide an alternate DM candidate. A (cid:101) ν L with massgreater than 55 GeV is viable only if another DM particle is responsible for theobserved relic. However, it is consistent with the current LHC DM searches only for ill be inserted by the editor 25 compressed spectra. In extensions of the SUSY models which also contain a (cid:101) ν R , thecase of a pure (cid:101) ν R , with mass ∼
30 – 40 GeV, as thermal DM, has been shown tobe viable in presence of a quasi-stable (cid:101) τ and is consistent with LHC constraints. Inextensions of NMSSM, it is possible to realise a pure (cid:101) ν R LSP, which is light, can bethermal relic and is consistent with the current constraints. All these scenarios willgive rise to very distinctive phenomenology and can be tested at the HL-LHC.
Acknowledgements :
The work of RMG is supported by the Department of Science and Technology,India under Grant No. SR/S2/JCB-64/2007.
Author contribution:
All authors have contributed equally.
References
1. P. A. Zyla et al.,
PTEP , 2020:083C01, 2020.2. M. Drees, R. Godbole, and P. Roy,
Theory and phenomenology of sparticles: Anaccount of four-dimensional N=1 supersymmetry in high energy physics . 2004.3. H. Baer and X. Tata,
Weak scale supersymmetry: From superfields to scatteringevents . Cambridge University Press, 5 2006.4. K. L. Chan, U. Chattopadhyay, and P. Nath,
Phys. Rev. , D58:096004, 1998.arXiv: hep-ph/9710473.5. H. Baer, V. Barger, P. Huang, A. Mustafayev, and X. Tata,
Phys. Rev. Lett. ,109:161802, Oct 2012. arXiv: 1207.3343.6. Planck Collaboration, N. Aghanim et al., arXiv: 1807.06209.7. J. Silk et al.,
Particle Dark Matter: Observations, Models and Searches . Cam-bridge Univ. Press, Cambridge, 2010.8. G. Bertone and D. Hooper,
Rev. Mod. Phys. , 90(4):045002, 2018. arXiv:1605.04909.9. E. W. Kolb and M. S. Turner,
The Early Universe , volume 69. 1990.10. G. Jungman, M. Kamionkowski, and K. Griest,
Phys. Rept. , 267:195–373, 1996.arXiv: hep-ph/9506380.11. K. Griest and M. Kamionkowski,
Phys. Rept. , 333:167–182, 2000.12. P. S. B. Dev, A. Mazumdar, and S. Qutub,
Front. in Phys. , 2:26, 2014. arXiv:1311.5297.13. C. Boehm, X. Chu, J. Kuo, and J. Pradler, arXiv: 2010:02954.14. M. I. Gresham and K. M. Zurek,
Phys. Rev. D , 89(1):016017, 2014. arXiv:1311.2082.15. CRESST Collaboration, A. H. Abdelhameed et al.,
Phys. Rev. D ,100(10):102002, 2019. arXiv: 1904.00498.16. CRESST Collaboration, A. H. Abdelhameed et al.,
Eur. Phys. J. C , 79(7):630,2019. arXiv: 1902.07587.17. G. Bertone and T. M. P. Tait,
Nature , 562(7725):51–56, 2018. arXiv: 1810.01668.18. G. B´elanger, F. Boudjema, A. Pukhov, and A. Semenov,
Comput. Phys. Com-mun. , 149:103–120, 2002. arXiv: hep-ph/0112278.19. G. B´elanger, F. Boudjema, A. Pukhov, and A. Semenov,
Comput. Phys. Com-mun. , 174:577–604, 2006. arXiv: hep-ph/0405253.
20. G. B´elanger, F. Boudjema, A. Pukhov, and A. Semenov,
Comput. Phys. Com-mun. , 192:322–329, 2015. arXiv: 1407.6129.21. G. B´elanger, F. Boudjema, A. Goudelis, A. Pukhov, and B. Zaldivar,
Comput.Phys. Commun. , 231:173–186, 2018. arXiv: 1801.03509.22. L. J. Hall, K. Jedamzik, J. March-Russell, and S. M. West,
JHEP , 03:080, 2010.arXiv: 0911.1120.23. J. McDonald,
Phys. Rev. Lett. , 88:091304, 2002. arXiv: hep-ph/0106249.24. G. B. Gelmini and P. Gondolo,
Phys. Rev. D , 74:023510, 2006. arXiv: hep-ph/0602230.25. G. Gelmini, A. Soldatenko, and C. E. Yaguna,
Phys. Rev. D , 74:083514, 2006.arXiv: hep-ph/0605016.26. D. Hooper,
Phys. Rev. D , 88:083519, 2013. arXiv: 1307.0826.27. M. W. Goodman and E. Witten,
Phys. Rev. D , 31:3059, 1985.28. F. S. Queiroz, pages 427–436. ARISF, 2016. arXiv: 1605.08788.29. G. Duda, A. Kemper, and P. Gondolo,
JCAP , 04:012, 2007. arXiv: hep-ph/0608035.30. XENON Collaboration, E. Aprile et al.,
Phys. Rev. Lett. , 121(11):111302, 2018.arXiv: 1805.12562.31. LUX Collaboration, D.S. Akerib et al.,
Phys. Rev. Lett. , 118(2):021303, 2017.arXiv: 1608.07648.32. CoGeNT Collaboration, C.E. Aalseth et al.,
Phys. Rev. Lett. , 106:131301, 2011.arXiv: 1002.4703.33. G. Angloher, M. Bauer, I. Bavykina, A. Bento, and C. Bucci,
Eur. Phys. J. C ,72:1971, 2012. arXiv: 1109.0702.34. CDMS-II Collaboration, Z. Ahmed et al.,
Science , 327:1619–1621, 2010. arXiv:0912.3592.35. CDMS Collaboration, R. Agnese et al.,
Phys. Rev. Lett. , 111(25):251301, 2013.arXiv: 1304.4279.36. DAMA and LIBRA Collaborations, R. Bernabei et al.,
Eur. Phys. J. C , 67:39–49, 2010. arXiv: 1002.1028.37. DAMA-LIBRA Collaborations, R. Bernabei et al.,
Eur. Phys. J. C , 74(3):2827,2014. arXiv: 1403.4733.38. SuperCDMS Collaboration, R. Agnese et al.,
Phys. Rev. Lett. , 112(24):241302,2014. arXiv: 1402.7137.39. C. Boehm, T. A. Ensslin, and J. Silk,
J. Phys. G , 30:279–286, 2004. arXiv:astro-ph/0208458.40. C. Boehm, M. J. Dolan, and C. McCabe,
JCAP , 08:041, 2013. arXiv: 1303.6270.41. Fermi-LAT Collaboration, M. Ackermann et al.,
Astrophys. J. , 840(1):43, 2017.arXiv: 1704.03910.42. L. Goodenough and D. Hooper, arXiv: 0910.2998.43. D. Hooper and L. Goodenough,
Phys. Lett. B , 697:412–428, 2011. arXiv:1010.2752.44. D. Hooper and T. Linden,
Phys. Rev. D , 84:123005, 2011. aeXiv: 1110.0006.45. T. Daylan, D. P. Finkbeiner, D. Hooper, T. Linden, S. K. N. Portillo, N. L. Rodd,and T. R. Slatyer,
Phys. Dark Univ. , 12:1–23, 2016.46. CMS Collaboration, A. Sirunyan et al.,
JHEP , 07:014, 2017. arXiv: 1703.01651.47. ATLAS Collaboration, M. Aaboud et al.,
JHEP , 01:126, 2018. arXiv:1711.03301.48. CMS Collaboration, A. M. Sirunyan et al.,
Eur. Phys. J. C , 79(3):280, 2019.arXiv: 1811.06562.49. ATLAS Collaboration, M. Aaboud et al.,
Phys. Rev. Lett. , 119(18):181804, 2017.arXiv: 1707.01302.50. J. F. Gunion,
Phys.Rev.Lett. , 72:199–202, 1994. arXiv: hep-ph/9309216. ill be inserted by the editor 27
51. D. Choudhury and D. P. Roy,
Phys.Lett. , B322:368–373, 1994. arXiv: hep-ph/9312347.52. O. J. P. Eboli and D. Zeppenfeld,
Phys.Lett. , B495:147–154, 2000. arXiv: hep-ph/0009158.53. R.M. Godbole, M. Guchait, K. Mazumdar, S. Moretti, and D. P. Roy,
Phys.Lett. ,B571:184–192, 2003. arXiv: hep-ph/0304137.54. ATLAS collaboration, ATLAS-CONF-2020-008.55. ALEPH Collaboration, D. Decamp et al.,
Phys. Rept.
Phys. Lett.
B544:73-88, 2002.arXiv:hep-ex/0207056.57. DELPHI Collaboration, J. Abdallah et al.,
Eur. Phys. J.
C31: 421-479, 2003.arXiv:hep-ex/0311019.58. L. M. Carpenter, H. B. Gilmer, and J. Kawamura, arXiv: 2007.10360.59. B. Dumont, G. B´elanger, S. Fichet, S. Kraml, and T. Schwetz,
JCAP , 09:013,2012. arXiv: 1206.1521.60. C. Arina, M. E. C. Catalan, S. Kraml, S. Kulkarni, and U. Laa,
JHEP , 05:142,2015. arXiv: 1503.02960.61. S. Banerjee, G. B´elanger, B. Mukhopadhyaya, and P. D. Serpico,
JHEP , 07:095,2016. arXiv: 1603.08834.62. S. Banerjee, G. B´elanger, A. Ghosh, and B. Mukhopadhyaya,
JHEP , 09:143,2018. arXiv: 1806.04488.63. D. G. Cerde˜no, C. Munoz, and O. Seto,
Phys. Rev. D , 79:023510, 2009. arXiv:0807.3029.64. D. G. Cerde˜no, M. Peir´o, and S. Robles,
JCAP , 08:005, 2014. arXiv: 1404.2572.65. D. G. Cerde˜no, M. Peir´o, and S. Robles,
Phys. Rev. D , 91(12):123530, 2015.arXiv: 1501.01296.66. T. Asaka, K. Ishiwata, and T. Moroi,
Phys. Rev. D , 73:051301, 2006. arXiv:hep-ph/0512118.67. ATLAS and CMS Collaborations, Georges Aad et al.,
Phys. Rev. Lett. ,114:191803, 2015. arXiv: 1503.07589.68. ATLAS and CMS Collaborations, G. Aad et al.,
Journal of High Energy Physics ,2016(8), Aug 2016. arXiv: 1606.02266.69. S. Banerjee, P. S. B. Dev, S. Mondal, B. Mukhopadhyaya, and S. Roy,
JHEP ,10:221, 2013. arXiv: 1306.2143.70. L. Roszkowski, E. M. Sessolo, and S. Trojanowski,
Rept. Prog. Phys. ,81(6):066201, 2018. arXiv: 1707.06277.71. M. Chakraborti, U. Chattopadhyay, and S. Poddar,
JHEP , 09:064, 2017. arXiv:1702.03954.72. G. B´elanger, F. Boudjema, F. Donato, R. Godbole, and S. Rosire-Lees,
Nucl.Phys. B , 581:3–33, 2000. arXiv: hep-ph/0002039.73. G. B´elanger, F. Boudjema, A. Cottrant, R. M. Godbole, and A. Semenov,
Phys.Lett. B , 519:93–102, 2001. arXiv: hep-ph/0106275.74. D. Hooper and T. Plehn,
Phys. Lett. B , 562:18–27, 2003. arXiv: hep-ph/0212226.75. G. B´elanger, F. Boudjema, A. Cottrant, A. Pukhov, and S. Rosier-Lees,
JHEP ,03:012, 2004. arXiv: hep-ph/0310037.76. H. K. Dreiner, S. Heinemeyer, O. Kittel, U. Langenfeld, and A. M. Weber,
Eur.Phys. J. C , 62:547–572, 2009. arXiv: 0901.3485.77. E. Kuflik, A. Pierce, and K. M. Zurek,
Phys. Rev. D , 81:111701, 2010. arXiv:1003.0682.78. A. V. Belikov, J. F. Gunion, D. Hooper, and T. M. P. Tait,
Phys. Lett. B ,705:82–86, 2011. arXiv: 1009.0549.79. D. A. Vasquez, G. B´elanger, C. Boehm, A. Pukhov, and J. Silk,
Phys. Rev. D ,82:115027, 2010. arXiv: 1009.4380.
80. L. Calibbi, T. Ota, and Y. Takanishi,
JHEP , 07:013, 2011. arXiv: 1104.1134.81. S. Choi, S. Scopel, N. Fornengo, and A. Bottino,
Phys. Rev. D , 85:035009, 2012.arXiv: 1108.2190.82. D. A. Vasquez, G. B´elanger, and C. Boehm,
Phys. Rev. D , 84:095015, 2011.arXiv: 1108.1338.83. D. Feldman, Z. Liu, and P. Nath,
Phys. Rev. D , 81:117701, 2010. arXiv:1003.0437.84. G. B´elanger, S. Biswas, C. Boehm, and B. Mukhopadhyaya,
JHEP , 12:076, 2012.arXiv: 1206.5404.85. C. E. Yaguna,
Phys. Rev. D , 76:075017, 2007. arXiv: 0708.0248.86. D. A. Vasquez, G. B´elanger, R. M. Godbole, and A. Pukhov,
Phys. Rev. D ,85:115013, 2012. arXiv: 1112.2200.87. A. Arbey, M. Battaglia, and F. Mahmoudi,
Eur. Phys. J. C , 72:2169, 2012.arXiv: 1205.2557.88. L. Calibbi, J. M. Lindert, T. Ota, and Y. Takanishi,
JHEP , 10:132, 2013. arXiv:1307.4119.89. A. Arbey, M. Battaglia, and F. Mahmoudi,
Phys. Rev. D , 88:095001, 2013.arXiv: 1308.2153.90. G. B´elanger, G. D. L. Rochelle, B. Dumont, R. M. Godbole, and S. Kraml,
Phys.Lett. B , 726:773–780, 2013. arXiv: 1308.3735.91. K. Hagiwara, S. Mukhopadhyay, and J. Nakamura,
Phys. Rev. D , 89(1):015023,2014. arXiv: 1308.6738.92. C. Boehm, P. S. B. Dev, A. Mazumdar, and E. Pukartas,
JHEP , 06:113, 2013.arXiv: 1303.5386.93. L. Calibbi, J. M. Lindert, T. Ota, and Y. Takanishi,
JHEP , 11:106, 2014. arXiv:1410.5730.94. T. Han, Z. Liu, and S. Su,
JHEP , 08:093, 2014. arXiv: 1406.1181.95. J. Cao, Y. He, L. Shang, W. Su, and Y. Zhang,
JHEP , 03:207, 2016. arXiv:1511.05386.96. K. Hamaguchi and K. Ishikawa,
Phys. Rev. D , 93(5):055009, 2016. arXiv:1510.05378.97. K. Fukushima, C. Kelso, J. Kumar, P. Sandick, and T. Yamamoto,
Phys. Rev.D , 90(9):095007, 2014. arXiv: 1406.4903.98. OPAL Collaboration, G. Abbiendi et al.
Eur. Phys. J. , C35:1–20, 2004. arXiv:hep-ex/0401026.99. R. K. Barman, G. B´elanger, B. Bhattacherjee, R. Godbole, G. Mendiratta, andD. Sengupta,
Phys. Rev. D , 95(9):095018, 2017. arXiv: 1703.03838.100. G. H. Duan, W. Wang, L. Wu, J. M. Yang, and J. Zhao,
Phys. Lett. B , 778:296–302, 2018. arXiv: 1711.03893.101. M. Abdughani, L. Wei, and J. M. Yang,
Eur. Phys. J. C , 78(1):4, 2018. arXiv:1705.09164.102. A. Arbey, M. Boudaud, F. Mahmoudi, and G. Robbins,
JHEP , 11:132, 2017.arXiv: 1707.00426.103. G. Pozzo and Y. Zhang,
Phys. Lett. B , 789:582–591, 2019. arXiv: 1807.01476.104. M. van Beekveld, S. Caron, and R. Ruiz de Austri,
JHEP , 01:147, 2020. arXiv:1906.10706.105. M van Beekveld, W. Beenakker, S. Cohen, R. Peeters, and R. Ruiz de Austri,
Phys. Rev. D , 96(3):035015, 2017. arXiv: 1612.06333.106. U. Ellwanger, C. Hugonie, and A. M. Teixeira,
Phys. Rept. , 496:1–77, 2010.arXiv: 0910.1785.107. S. Baum, K. Freese, N. R. Shah, and B. Shakya,
Phys. Rev. D , 95:115036, Jun2017. arXiv: 1703.07800. ill be inserted by the editor 29
JCAP ,0509:001, 2005. arXiv: hep-ph/0505142.109. F. Mahmoudi, J. Rathsman, O. Stal, and L. Zeune,
Eur. Phys. J. C , 71:1608,2011. arXiv: 1012.4490.110. J. F. Gunion, D. Hooper, and B. McElrath,
Phys. Rev. D , 73:015011, 2006.arXiv: hep-ph/0509024.111. F. Ferrer, L. M. Krauss, and S. Profumo,
Phys. Rev. D , 74:115007, 2006. arXiv:hep-ph/0609257.112. D. Das and U. Ellwanger,
JHEP , 09:085, 2010. arXiv: 1007.1151.113. J. Cao, K. Hikasa, W. Wang, and J. M. Yang
Phys. Lett. B , 703:292–297, 2011.arXiv: 1104.1754.114. D. A. Vasquez, G. B´elanger, and C. Boehm,
Phys. Rev. D , 84:095008, 2011.arXiv: 1107.1614.115. J. Kozaczuk and S. Profumo,
Phys. Rev. D , 89(9):095012, 2014. arXiv:1308.5705.116. U. Ellwanger,
JHEP , 11:108, 2013. arXiv: 1309.1665.117. J. Cao, C. Han, L. Wu, P. Wu, and J. M. Yang,
JHEP , 05:056, 2014. arXiv:1311.0678.118. J. Huang, T. Liu, L. Wang, and F. Yu,
Phys. Rev. D , 90(11):115006, 2014.arXiv: 1407.0038.119. U. Ellwanger and A. M. Teixeira,
PoS , EPS-HEP2015:161, 2015.120. D. Barducci, G. B´elanger, C. Hugonie, and A. Pukhov,
JHEP , 01:050, 2016.arXiv: 1510.00246.121. U. Ellwanger,
JHEP , 02:051, 2017. arXiv: 1612.06574.122. Q. Mou and S. Zhang, arXiv: 1703.00343.123. U. Ellwanger and C. Hugonie,
Eur. Phys. J. C , 78(9):735, 2018. arXiv:1806.09478.124. W. Abdallah, A. Chatterjee, and A. Datta,
JHEP , 09:095, 2019. arXiv:1907.06270.125. K. Wang and J. Zhu,
Phys. Rev. D , 101(9):095028, 2020. arXiv: 2003.01662.126. M. Guchait and A. Roy, arXiv: 2005.05190.127. R. K. Barman, G. B´elanger, B. Bhattacherjee, R. Godbole, D. Sengupta, andX. Tata, arXiv: 2006.07854.128. S. Ma, K. Wang, and J. Zhu, arXiv: 2006.03527.129. XENON Collaboration, E. Aprile et al.,
JCAP , 1604(04):027, 2016. arXiv:1512.07501.130. CMS Collaboration, A.M. Sirunyan et al.,
JHEP , 03:160, 2018. arXiv:1801.03957.131. R. K. Barman, G. B´elanger, and R. Godbole, HL and HE LHC reach for light,thermal and non thermal DM in SUSY. In preparation.132. SuperCDMS Collaboration, R. Agnese et al.,
Phys. Rev. D , 95:082002, 2017.arXiv: 1610.00006.133. CEPC Study Group, M. Dong et al.,
IHEP-CEPC-DR-2018-02, IHEP-EP-2018-01, IHEP-TH-2018-01 . arXiv: 1811.10545134. Fermi-LAT and DES Collaborations, A. Albert et al.,
Astrophys. J. , 834(2):110,2017. arXiv: 1611.03184.135. M. Ibe, H. Murayama, and T. T. Yanagida,
Phys. Rev. D , 79:095009, 2009.arXiv: 0812.0072.136. Z. Liu, L. Wang, and H. Zhang,