$\mathcal{O}$(1) GeV dark matter in SUSY and a very light pseudoscalar at the LHC

We analyze the prospects of the detection of a $\mathcal{O}(1)$ GeV neutralino dark matter, $\widetilde{\chi}^0_{1}$, in the Next-to-Minimal Supersymmetric Standard Model at the 14 TeV LHC. We perform dedicated scans of the relevant parameter space of the model and find a large number of points where the thermal relic abundance due to such a dark matter is consistent with the PLANCK measurement. We note that this dark matter is highly singlino-dominated and is always accompanied by a pseudoscalar, $A_1$, with a mass around twice its own, which is responsible for its resonant annihilation. For two benchmark points from our scan, we then carry out a detector-level signal-to-background analysis of the pair production of a heavier higgsino neutralino and a chargino. The higgsino thus produced decays into the dark matter and either the $Z$ boson or the $A_1$. For the $Z$-associated production of $\widetilde{\chi}^0_{1}$, we investigate the scope of the trilepton search channel. For the $A_1$-associated production mode, in order to identify the two collimated muons coming from the decay of the $A_1$, we employ an unconventional method of clustering them together into one jet-like object. Using this method, for certain parameter space configurations, a much larger sensitivity can be obtained at the 14 TeV LHC for the $A_1\widetilde{\chi}^0_{1}$ channel compared to the $Z\widetilde{\chi}^0_{1}$ channel, with an integrated luminosity of 300 fb$^{-1}$.

1 , in the Next-to-Minimal Supersymmetric Standard Model at the 14 TeV LHC. We perform dedicated scans of the relevant parameter space of the model and find a large number of points where the thermal relic abundance due to such a dark matter is consistent with the PLANCK measurement. We note that this dark matter is highly singlino-dominated and is always accompanied by a pseudoscalar, A 1 , with a mass around twice its own, which is responsible for its resonant annihilation. For two benchmark points from our scan, we then carry out a detector-level signalto-background analysis of the pair production of a heavier higgsino neutralino and a chargino. The higgsino thus produced decays into the dark matter and either the Z boson or the A 1 . For the Z-associated production of χ 0 1 , we investigate the scope of the trilepton search channel. For the A 1 -associated production mode, in order to identify the two collimated muons coming from the decay of the A 1 we employ an unconventional method of clustering them together into one jet-like object. Using this method, for certain parameter space configurations, a much larger sensitivity can be obtained at the 14 TeV LHC for the A 1 χ 0 1 channel compared to the Z χ 0 1 channel, with an integrated luminosity of 300 fb −1 .
1 Introduction 1 30 GeV, it is thus generally impossible to obtain sufficient Ω DM in the MSSM due to the absence of a mediator with the correct mass.
The Next-to-Minimal Supersymmetric Standard Model (NMSSM) [7,8,9,10] contains a gauge singlet Higgs superfield, S, in addition to the two doublet superfields, H d and H u , of the MSSM. This results in two additional neutral mass eigenstates in the Higgs sector besides the three similar to the MSSM ones. Thus in total there are seven Higgs bosons in the NMSSM, CP-even H 1,2,3 , CP-odd A 1,2 and a charged pair, H ± . Naturally, the two new Higgs bosons are dominated by the scalar component of S, which implies that their couplings to the fermions and gauge bosons of the Standard Model (SM) are typically much smaller than those of the doublet-like Higgs bosons. Their masses are thus generally very weakly constrained by the Higgs boson data from the Large Electron Positron (LEP) collider, the Tevatron or the LHC, and can be as low as a GeV or so. Similarly, the neutralino sector of the NMSSM also contains five mass eignestates, one more than in the MSSM. The fifth neutralino is dominated by the fermion component of S, commonly referred to as the singlino.
In the NMSSM, the role of the H obs can be played by either one of H 1 and H 2 [11,12,13,14,15] or even by a combination/superposition of these two when both of them lie near 125 GeV [16,17,18]. Evidently, when H obs is the H 1 , only A 1 can be lighter than it. Conversely, when H obs is the H 2 , there exist the possibilities of either H 1 alone or both H 1 and A 1 being lighter than it. Such light H 1 or A 1 can act as mediators for the annihilation of χ 0 1 as light as a GeV or so in order for it to generate the correct Ω DM -a scenario precluded in the MSSM. In fact, a light NMSSM χ 0 1 can also explain the galactic centre γ-ray excess [19,20] observed by the Fermi Large Area Telesope in the presence of a light A 1 [21,22,23,24]. 1 If the χ 0 1 is even lighter, it has been shown [25,26] to explain the CDMS-II event excess near 10 GeV [27]. However, further experimental evidence is necessary to confirm whether any of these events are indeed caused by the annihilation of the DM and the jury is still out on its correct mass. While the direct-detection experiments such as DAMA/LIBRA [28], CoGeNT [29,30] CRESST-II [31], XENON100 [32] and LUX [33] can cover a wide range of the DM mass, it is extremely unlikely for them to reach below ∼ 2 GeV.
The Run-II of LHC can prove very crucial in this regard, owing to its potential to probe a very light DM, produced in association with the Z boson or the A 1 in the decays of the heavier neutralinos. In some recent studies [34,35,36,37,38] it has been shown that significant regions of the NMSSM parameter space can be covered by the Z-associated production of χ 0 1 at the LHC Run-II, with the Z decaying into two leptons. The χ 0 2,3 → A 1 + χ 0 1 channel has also shown some promise [39] even for the 8 TeV LHC, with the mass of A 1 lying above the τ + τ − production threshold. These search channels can be complemented by those where the light A 1 is not accompanied by the DM. As long as the relic abundance is satisfied for a given SUSY point with a very light DM, observation of the corresponding A 1 , which would be a likely mediator for its annihilation, could serve as a pointer. Such channels include, most importantly, the decays of H obs into A 1 + A 1 or A 1 + Z [40]. At the Run-I of LHC, light pseudoscalars decaying in the µ + µ − channel have already been probed, when they are produced either singly in pp collisions [41] or in pairs from the decays of a 125 GeV Higgs boson [42]. These searches thus strongly constrain the parameter space of the NMSSM. Prospects for the observability of A 1 at the 14 TeV LHC have been analyzed in detail recently in [43,44,45], with the measurement of the mass of H obs providing an additional handle in the kinematic selection of events. The channels investigated in all these analyses, however, show sufficient sensitivity only for A 1 heavier than 5 GeV.
In this study we focus on the production of a very light, O(1) GeV, χ 0 1 via decays of the heavier, higgsino-like, neutralinos of the NMSSM. We perform detailed scans of the NMSSM parameter space to highlight its regions where such a χ 0 1 , consistent with the observed relic abundance of the universe, can be obtained in the presence of a SM-like H 2 . We discuss some important characteristics of these parameter regions and of the χ 0 1 . We note, in particular, that the χ 0 1 is always accompanied by a pseudoscalar with a mass nearly twice its own. We then carry out comprehensive detector-level analyses of the Z-as well as A 1 -associated productions of χ 0 1 . For the A 1 + χ 0 1 production channel, we adopt an unconventional method for reconstructing the pair of highly collinear muons that result from the subsequent decay of the A 1 . We find that by using our signal reconstruction method the A 1 + χ 0 1 channel can have a better signal strength at the 14 TeV LHC compared to the Z + χ 0 1 channel for certain specific parameter configurations. Therefore, the A 1 + χ 0 1 channel can serve as a crucial probe of new physics, complementing well the Z + χ 0 1 channel for very a low-mass singlino-dominated DM.
This article is organized as follows. In section 2, we will briefly discuss the NMSSM and its singlet sector. In section 3 we will present some details of our findings from the numerical scans of the NMSSM parameter space. In section 4 we will explain our signal-to-background analyses and in section 5 we will show their results. We will present our conclusions in section 6.

2
The singlet sector of the NMSSM The scale-invariant superpotential of the NMSSM (see, e.g., [46,47] for reviews) is written as where λ and κ are dimensionless Yukawa couplings. The above superpotential observes a discrete Z 3 symmetry, which forbids the µ H u H d term present in the MSSM superpotential and at the same time breaks the dangerous Peccei-Quinn (PQ) symmetry [48]. Here, an effective µ-term is generated upon spontaneous symmetry breaking, when S develops a vacuum expectation value (VEV), s ≡ S , so that µ eff = λs. The soft SUSY-breaking terms in the scalar Higgs sector are then given by Through the minimization conditions of the complete tree-level Higgs potential, the soft masses m Hu , m H d and m S can be traded for the VEVs v u , v d and s of the corresponding Higgs fields. The neutral scalar and pseudoscalar Higgs mass matrices are obtained from the Higgs potential evaluated at the vacuum. Diagonalization of these matrices yields the mass expressions for the five neutral Higgs bosons. The tree-level masses of the two lightest CP-even Higgs bosons, which are of our interest here, can be approximated, for moderate-to-large tan β (≡ v u /v d ) and EW-scale dimensionful parameters, by [49] where v ≡ v 2 u + v 2 d ≃ 174 GeV. Thus there is a strong correlation between the masses of H 1 and H 2 , implying that requiring one of these to lie near 125 GeV constrains the other also. Similarly, the tree-level mass of the singlet-like pseudoscalar can be given, assuming negligible singlet-doublet mixing, by the approximate expression The neutralino mass matrix in the NMSSM is written as with m W being the mass of the W boson and θ W being the weak mixing angle. This symmetric mass matrix can be diagonalized by a unitary matrix N to obtain the five neutralino states, χ 0 1−5 , ordered by their masses, implying that χ 0 1 . This mass eigenstate is given by the linear combination We define the gaugino fraction in χ 0 1 as Z g = |N 11 | 2 + |N 12 | 2 , the higgsino fraction as Z h = |N 13 | 2 + |N 14 | 2 and the singlino fraction as Z s = |N 15 | 2 . The composition of χ 0 1 thus depends on the values of the various model parameters appearing in the above mass matrix.
In the MSSM, the fifth row and column, corresponding to the singlino and containing the terms proportional to λ do not exist. There, the smaller the µ compared to the min[M 1 , M 2 ], the larger the higgsino fraction in χ 0 1 . Since the mass of the higgsino-like chargino, which is the lighter χ ± 1 in this case, is also proportional to µ, the value of this parameter is bounded from below to around 100 GeV by the non-observation of a chargino at the large electron positron (LEP) collider. On the other hand, in order to avoid excessive fine-tuning of the model parameters for obtaining the correct Higgs boson mass, µ ought not to be too large. However, a purely higgsino LSP does not give the correct thermal relic density for masses below ∼ 1 TeV, as the annihilation cross section becomes too large. As noted in the Introduction, the only way for the χ 0 1 in the MSSM to give good relic abundance with a mass O(10) GeV is to have a sizable bino component [6,50].
In the NMSSM, the presence of the singlino leads to some additional possibilities in the context of DM phenomenology. In the limit µ eff ≪ min[M 1 , M 2 ], the term [M χ 0 ] 55 = 2κs = 2 κµ eff λ , in eq. (5) implies that the LSP is singlino-dominated for 2κ/λ < 1. The singlino fraction in χ 0 1 can be increased by reducing κ. One could alternatively increase λ, while keeping µ eff fixed, to reduce the size of the [M χ 0 ] 55 term, but this also enlarges the sizes of the off-diagonal mixing terms.
Eq. (4) shows that the mass of A 1 also scales with κs. Thus a light singlino-like χ 0 1 can be naturally accompanied by a light A 1 . Note that the strong correlation, eq. (3), between the H 2 mass, which is required to be around 125 GeV, and the H 1 mass generally prevents the latter from taking very low values, although it also scales mainly with κs. Importantly though, even if H 1 has a mass close to 2 χ 0 1 , the χ 0 1 annihilation via s-channel H 1 is p-wave suppressed, which would make it extremely difficult to generate the correct thermal relic abundance. We therefore focus only on a light A 1 here, which can result in the singlino-like χ 0 1 yielding the correct relic density even with its mass around a GeV.
As noted in the Introduction, the light χ 0 1 can be produced in the decays of the heavier neutralinos. In particular, the χ 0 2 and χ 0 3 as well as χ ± 1 in this scenario with a light singlino-like DM are predominantly higgsinos [39]. Their main production channel is pp → χ 0 2,3 + χ ± 1 , which is followed by the decays χ 0 where / E T implies missing transverse energy. The complete processes are shown in Fig. 1(a) and (b). The Z + χ 0 1 decay channel of χ 0 2,3 is by far the dominant one, while χ 0 2,3 → A 1 + χ 0 1 is generally suppressed. The Z + W + / E T production, which results in trileptonic final states, is therefore the preferred search channel for the higgsinos, also since it has minimal dependence on m χ 0 1 . Dedicated searches carried out by both the CMS and ATLAS collaborations [51,52,53] have either already put strong constraints on significant regions of the NMSSM parameter space or are likely to cover large portions of it, where χ 0 1 can be as light around a GeV, at the LHC Run-II. It is, however, important to note that, for sufficiently large values of the parameter λ, the branching ratio (BR) for the χ 0 2,3 → A 1 + χ 0 1 decay channel, while still subdominant, can become sizable. For A 1 masses of interest here, i.e., below the τ + τ − threshold, the decay mode with the largest BR is A 1 → cc. The main leptonic decay channel, A 1 → µ + µ − , is highly subdominant, with its BR never exceeding 9%, as we shall see below. This value is still twice that of the BR(Z → µ + µ − ) (≃ 0.034). But one challenge that arises in this context is the reconstruction of the very light A 1 from two highly collinear muons it decays into and the isolation of this signal from the background. As long as this complication can be overcome, the two observations above imply that the A 1 + χ 0 1 search channel can possibly complement the Z χ 0 1 channel for certain specific NMSSM parameter space points. In the following sections we will analyze such parameter combinations and also  introduce our method for reconstructing the very light A 1 from two collinear muons. We should point out here that while in principle the same method can alternatively be used to probe these A 1 in the decays of the heavy CP-even Higgses, our requirement of the presence of / E T in the final state, as an indication of light DM, renders these channels irrelevant here.

Parameter space scan and constraints
Due to the presence of the additional singlet superfield, the NMSSM contains several new parameters besides the 150 or so of the MSSM at the electroweak (EW) scale. However, assuming the sfermion mass matrices and the scalar trilinear coupling matrices to be diagonal reduces the parameter space of the model considerably. In this study, since our main focus is the the higgsino-singlino sector, we further assume the following universality conditions. 3 and M E 1,2,3 are the soft masses of the sfermions, M 1,2,3 those of the gauginos and A t,b,τ the trilinear Higgs-sfermion couplings. Along with M 0 , M 1/2 and A 0 , the model then contains λ, κ, µ eff , tan β, A λ and A κ as the only free parameters, which are input at the SUSY-breaking scale, M SUSY = √ mt 1 mt 2 , with mt 1,2 being the physical masses of the two stops.
We performed a scan of the above mentioned nine parameters using the nested sampling package MultiNest-v2.18 [54], which was interfaced with NMSSMTools-v4.5.0 [55,56,57,58] for calculation of the SUSY mass spectrum and BRs for each model point sampled. The scanned ranges of the parameters are given in table 1 and were chosen, based loosely on the findings of [39], to maximally yield points with m χ 0 1 2 GeV as well as H 2 having a mass near the one measured for H obs at the LHC. H 2 was additionally required to have SM-like signal rates. This rate, obtained from NMSSMTools as an output, is defined, for a given decay channel X, as Parameter Scanned range where h SM is the SM Higgs boson with the same mass as m H 2 . NMSSMTools takes into account the exclusion limits on A 1 from the LEP data as well as the 4µ searches at the CMS [42]. It also ensures that the LEP limit on χ ± 1 mass and the perturbativity constraints on the various Higgs boson couplings are satisfied and that χ 0 1 is the lightest supersymmetric particle. Each scanned point was required to meet the following constraints.
The b-physics observables above were calculated using the package SuperIso-v3.4 [59] and the relic density using the MicrOMEGAs-v4.1.5 [60] package. The allowed range of Ω χ 0 1 assumes a ±10% theoretical error around the central value of 0.119 measured by the PLANCK telescope [4]. Similarly an error of ±3 GeV is allowed in the theoretical estimation of the H 2 mass, given the H obs mass measurement of 125 GeV at the LHC. Consistency with the LEP and LHC exclusion limits on the non-SM-like Higgs bosons, including A 1 , was further ensured by testing each point that passed the above constraints with the program HiggsBounds-v4.2.0 [61,62,63,64].
In Fig. 2(a) we show the ranges of the A 1 and χ 0 1 masses obtained for the good points from our scan. The heat map corresponds to the χ 0 1 relic density. One can see a strong correlation between m χ 0 1 and m A 1 , with the former almost always being half of the latter in order for the resonant annihilation of χ 0 1 via A 1 . The tiny χ 0 1 masses are a result of vanishing κ as seen in Fig. 2(b), implying an almost PQ-symmetric model. The heat map in the figure shows the distribution of the singlino fraction in χ 0 1 which increases as κ decreases and is always larger than 0.88. A large singlino component implies a small higgsino fraction, which is necessary to prevent an under abundance of χ 0 1 due to too much annihilation. Fig. 3(a) illustrates that A 1 is restricted to a lower mass, needed for satisfying the relic density constraint, by adjusting A κ to a narrow range of low negative values. This is in agreement with eq. (4), along with the fact that λ, illustrated by the heat map in the figure, also generally tends to be small. In Fig. 3(b) the distributions of the parameters A λ and µ eff are shown against the H 1 mass range obtained in the scan. We see that when both A λ and tan β are small m H 1 is low, while its maximum value, ∼ 45 GeV, is obtained for the largest allowed values of A λ , with tan β 10. Fig. 4(a) shows that the mass of χ 0 2 is almost equal to the parameter µ eff as long the parameter M 1/2 , given by the color map, approaches its maximum allowed value. As the splitting between M 1/2 and µ eff decreases, the gaugino-higgsino mixing increases, which results in somewhat lowering m χ 0 2 relative to µ eff . Fig. 4(b) similarly shows that, since χ 0 3 and χ ± 1 are higgsino-like as well, their masses are also proportional to µ eff . Moreover, χ ± 1 is always almost mass-degenerate with χ 0 2 , while χ 0 3 is generally heavier than both of them, but only slightly so. 2 Fig. 5(a) illustrates that the BR( χ 0 2 → A 1 χ 0 1 ) increases with λ, shown by the heat map. This is because, for vanishing singlet-doublet mixing in the pseudoscalar mass matrix as well as singlino-higgsino mixing in the neutralino mass matrix, the coupling between A 1 , χ 0 1 and χ 0 2 , given by eq. (A.14) of [46], can be approximated by the simple relation Still, the BR( χ 0 2 → A 1 χ 0 1 ) exceeds 10% only for a few points, reaching as high as about 30% for a couple of them. On the other hand, the BR( χ 0 2 → Z χ 0 1 ), given on the x-axis, drops quite sharply with increasing λ and can reach as low as about 30%. This is due mainly to the fact that the BR( χ 0 2 → H 2 χ 0 1 ) (not shown here) also rises, much more abruptly than the BR( χ 0 2 → A 1 χ 0 1 , as λ increases. Fig. 5(b) shows that the BR( χ 0 3 → A 1 χ 0 1 ) never exceeds 9% while the BR( χ 0 3 → Z χ 0 1 ) never falls below 50%, implying a relatively weaker dependence on λ. The heat map in the figure shows that the maximum BR(A 1 → µ + µ − ) achievable is 9%. Note that the BR( χ ± 1 → W ± χ 0 1 ) is unity for all the points shown in these figures.
We point out here that we also carried out a test scan of the NMSSM with partial universality at the grand unification (GUT) scale. In this model the unified scalar mass parameter, m 0 , the universal gaugino mass, m 1/2 , the universal Higgs-sfermion trilinear couplings, a 0 , as well as the paramaters a λ and a κ are input at the GUT scale. The EW scale values of the individual soft scalar and gaugino masses and of all the Higgs trilinear couplings are obtained by the running of these parameters using the renormalization group equations. The other Higgs sector parameters, λ, κ, µ eff and tan β are input at M SUSY . But, owing particularly to the GUT scale definition of the parameters a λ and a κ , severe fine-tuning is necessary in this model for the scan to find the right combinations of these parameters at M SUSY that yield both H 2 and A 1 with the desired masses.
As noted above in Fig. 3(a), A κ at M SUSY is restricted to a narrow range of values, which would imply an even smaller set of its possible values at the GUT scale. Furthermore, the SUSY-preserving parameter κ is also very small due to our requirement of m χ 0 1 ∼ 1.5 GeV, though the approximate PQ symmetry this results in still avoids the cosmological constraints on the PQ axion [65]. Keeping µ eff around the EW scale, κ is typically smaller than 0.01λ. Despite all these limiting conditions, some points with the right masses of χ 0 1 and A 1 were indeed found. However, they did not cover, for example, the wide range of the BR( χ 0 2 → A 1 χ 0 1 ) seen in fig. 5(a), which stretches beyond 0.1. We therefore opted for the 9-parameter EW-scale NMSSM for this study.

4
Very light DM via higgsino decays at the LHC For our signal-to-background analyses, we selected two benchmark points, BP1 and BP2, out of the good points from the NMSSM parameter space scan. BP1 is chosen such that the BR( χ 0 2,3 → Z χ 0 1 ) is sufficiently large, while BP2 has a relatively enhanced BR( χ 0 2,3 → A 1 χ 0 1 ). The parton-level signal and background events for these points were generated with MadGraph aMC@NLO [66] and passed to Pythia 6.4 [67] for hadronization.

The trilepton channel
As noted earlier, the ATLAS and CMS experiments have separately performed searches for trileptons (3ℓ) [51,52,53] resulting from the χ 0 2,3 χ ± 1 pair production. In the ATLAS 3ℓ search [51], which is the one we will consider in the following, six signal regions (SRs) are defined in terms of the invariant mass of two same flavor leptons with opposite sign (SFOS), m SFOS . These regions also depend on the momentum, p T (ℓ 3 ) , of the third lepton, ℓ 3 , that is left after requiring two SFOS leptons to reconstruct m SFOS , / E T and the transverse mass,   Table 2: Selection requirements for the six signal regions defined for the trilepton searches by the ATLAS collaboration. All the dimensionful parameters in rows 2 − 5 are in units of GeV.
far dominant over the ttW/Z one [51]. Among the reducible backgrounds are included top quarks produced singly or in pairs, W W and W or Z bosons produced in association with jets or photons. Among these the tt background is highly dominant. For each BP, the cross section for the signal process was calculated at next-to-leading order (NLO) using Prospino-v2.1 [68]. We then first generated the event files corresponding to √ s = 8 TeV for the signal process and passed these to the public package CheckMATE-v1.2.0 [69] for testing against the current LHC limits from the trilepton searches. In CheckMATE the signal regions given in table 2 have been defined and the corresponding backgrounds from the ATLAS experiment implemented. For testing a model point it therefore calculates the signal efficiency for each region, after ATLAS detector simulation with DELPHES 3 [70]. After confirming that the given BP is not excluded by the available data, we proceeded to the future 3ℓ search at the 14 TeV LHC. We generated the signal event files for √ s = 14 TeV and passed these to CheckMATE again. In this way we obtained the signal efficiencies, after multiplying the NLO cross section with an assumed integrated luminosity, L, of 300 fb −1 (i.e., design luminosity of the LHC) to get the number of signal events in each signal region. As for the backgrounds, we only simulated the three dominant ones, ZZ, ZW ± and tt, for the 14 TeV LHC. We used MadGraph to generate the background events and passed these to CheckMATE to get the cut efficiencies for all the backgrounds in each signal region. After multiplying the NLO cross section [71,72] and the luminosity, we got the number of background events in each signal region.

Collimated muons from A 1
Due to the smallness of the A 1 mass of our interest here, the muons it decays into are highly collinear. In order to isolate such muons, we employ the technique of clustering them together into one object, µ col . This method, similar in concept to the construction of a 'lepton-jet' [73], has recently been shown in [74] to be very effective for probing highly mass-degenerate higgsinos.
For using this method the signal events generated for BP1 and BP2 were passed to Pythia 6.4 for hadronization and subsequently to DELPHES 3 for jet-clustering via the anti-k T [75] algorithm using FastJet-v3.0.6 [76]. The object µ col is constructed as follows.
1. Require the transverse momentum, p T , larger than 10 GeV for each muon in the signal. In addition, impose the cut m µμ < 5 GeV on the invariant mass of the muon pair.
2. Define I sum as the scalar sum of the transverse momenta of all additional charged tracks, each with p T > 0.5 GeV, within a cone centered along the momentum vector of µ col and satisfying ∆R = 0.4. Impose I sum < 3 GeV.
The main backgrounds, containing two collinear muons along with a third lepton and / E T , include W (→ ℓ ± v)γ * and Z(→ ℓ + ℓ − )γ * , wherein the µ col comes from the photon, and W bb, when one of the b-jets produces the µ col . In case of the Zγ * background, one of the two leptons can escape undetected then fake the signal events. Note that while the tt background mentioned above for the 3ℓ search is also relevant for this signal process, it becomes negligible here owing to the requirement of two final state muons being highly collinear. In order to isolate these backgrounds, we implement the following cuts.
1. Since the A 1 resulting from the higgsino decay is highly boosted, we expect the µ col from its subsequent decay to have a large p T . We therefore require p T (µ col ) > 50 GeV. We also require p T (ℓ 3 ) > 20 GeV.
2. In order to reduce the background a large / E T is required, so we add a cut, / E T > 50 GeV.
3. In the W γ * background the M T distribution has an end point around the W boson mass, which leads us to impose M T > 80 GeV.
4. Our signal would appear as a narrow peak in the m µ col distribution. Hence, we impose a narrow cut width, 5×σ A 1 , around m A 1 , where σ A 1 = 0.26+0.0013m A 1 . This parametrization of σ A 1 follows the mass resolution study of the J/Ψ resonance in [77]. We also remove the J/ψ resonance region (3.0 GeV < m µ col < 3.2 GeV).
To get a sufficient number of Monte Carlo events in the kinematic regime of our interest, we require m µμ > 1.5 GeV and p T (ℓ 3 ) > 10 GeV at the parton level for the W γ * and Zγ * backgrounds. For the W bb background, we additionally require the p T of the b-jet to be larger than 30 GeV.

Results and discussion
In table 3 are recorded some specifics of the two BPs used for the signal-to-background analyses.
The consistency of each of the H 2 signal rates given in the last three rows of the table is to be checked against the experimental quantity µ X ≡ σ(pp→H obs →X) σ(pp→h SM →X) for each corresponding channel X. Note that this comparison assumes that the inclusive pp cross section for H 2 production can be approximated by the dominant gluon-fusion production cross section. Note also that, since the W W and ZZ decays of H 2 are proportional to the same coupling, NMSSMTools provides a unique value of the signal rates for these two channels, which we denote by R V V in the table. The most recent measurements of µ X by the CMS (ATLAS) collaboration(s) [78,79,80,81] read Using each of the two analysis methods described in the previous section we calculated the number of signal events, S, and that of background events, B, for each BP at the LHC with √ s = 14 TeV and L = 300 fb −1 . In table 4 we provide the S and B corresponding to each of the six signal regions in the ATLAS 3ℓ search. The total signal cross sections obtained are 24.3 fb and 3.93 fb for BP1 and BP2, respectively. In the Z-enriched region, ZW ± production dominates the total background. In the Z-depleted region, a comparable contribution is obtained from the tt background. One can notice in the table that for both the BPs, the highest sensitivity is obtained in the signal region SRZc.  Table 3: Properties of the two benchmark points used for the signal-to-background analyses.
In the µ col channel, the cross sections for the signal and background processes are given in table 5 for the BP1, along with the efficiency of the cuts and the effective cross sections and numbers of events after implementing these cuts. One notices that the W bb is by far the largest background. It, however, gets greatly reduced by the cuts, after which W γ * takes over as the most dominant background. The corresponding quantities for the BP2 are listed in table 6. Due to the different masses of the A 1 and χ 0 1 obtained for the two BPs, different sets of cuts need to be implemented for each of them.
We quantify the strengths of the two analyses in terms of S/B for comparing them against each other. This quantity is listed in   hand, S/B for the BP2 in the µ col analysis is considerably larger than the S/B obtained for the BP1 in each of the two analyses. This is due, evidently, to the sizable BR( χ 0 2 → A 1 χ 0 1 ) as well as BR(A 1 → µ + µ − ), as noted in table 3. In addition, the cut efficiency for the signal is much higher while that for the W γ * background is much lower in the case of the BP1.
For a more realistic analysis of the prospects of a signal process though, the statistical and systematic uncertainties in it also need to be taken into account. Hence, for each BP we have also provided in table 7 the statistical significance, given by the approximate formula, where the systematic uncertainty is given by the fraction ε of the background. From the ATLAS 3ℓ search [51], we note that the systematic uncertainty is 21% for the SRZc signal region, where the highest sensitivity is achieved, as seen above. We expect this number not to vary considerably at the 14 TeV LHC and hence use ε = 0.21 in our estimation of Z for the 3ℓ channel. For the W + µ col + / E T channel, since there is no experimental analysis available, the systematic uncertainty has to be estimated roughly. There are two major sources of this uncertainty: the reconstruction of the µ col , in which case it is around 5% [42], and that of the ℓ 3 , where it is less than 2% [82]. As a conservative estimate, which also allows a direct comparison between the 3ℓ channel and this channel, we set ε = 0.21 here also. This results in Z = 27 σ in this channel for the BP2, as seen in table 7, which is much higher than the estimated Z for the same point in the 3ℓ channel.
There is, however, a caveat here. As noted from table 6, B for the BP2 is much smaller than S, resulting in a large S/B. In such a case, the approximate expression for Z, which assumes S ≪ B, is in principle not valid [83]. While, for a consistent treatment of the systematic uncertainties between the two search channels, we retain this approximate expression for the µ col channel also, we emphasize that the given S/B values be considered a much more accurate estimate of the

Conclusions
In this article we have discussed an O(1) GeV neutralino DM in the NMSSM and its detectability at the LHC. Despite being very light, such a singlino-like DM can generate thermal relic abundance of the universe consistent with the PLANCK measurement, owing to the presence also of a singletlike pseudoscalar, A 1 , with a mass around twice the DM mass. A very light DM giving the correct relic abundance is impossible to obtain in the MSSM, and thus its detection will provide a clear indication of physics beyond minimal SUSY. We have noted that the current direct and indirect detection facilities have very poor detection prospects for such a light DM with and hence its dedicated searches at the LHC can prove very crucial. We have therefore studied in depth the prospects for its observation at the 14 TeV LHC. By performing a through scan of the NMSSM parameter space, chosen taking into account the analytical structure of the neutralino mass matrix, we found a variety of its configurations where an O(1) GeV DM can be obtained. We then carried out detector-level analyses of two of the main production modes of such a DM. In both these modes, the DM is produced in the decays of a higgsino-like heavier neutralino, χ 0 2,3 , which itself is produced in pair with the lightest chargino. The χ 0 2,3 then decays into either Z + DM or A 1 + DM. The former channel, combined with the chargino decay, results in a trilepton+ / E T final state, for which dedicated searches are already being performed by the CMS and ATLAS collaborations. In the latter channel the final state comprises of a pair of muons and a third lepton along with the DM.
In the χ 0 2,3 → DM + A 1 channel, the two muons that the very light A 1 decays into are highly collinear. Therefore, this channel can not be probed using the usual muon identification criteria. For this reason, we have adopted the technique of grouping the two muons together into a single jet-like object by applying certain unconventional rigorous cuts. By implementing this method on two benchmark points from our scan, we have found that this channel can have a signal strength comparable to that of the trilepton channel at the 14 TeV LHC with L = 300 fb −1 . In fact, for one of the two points, wherein the BR( χ 0 2,3 → DM + A 1 ) is significant and the BR(A 1 → µ + µ − ) is maximal, the obtained S/B for this cannel is much larger than that for the trilepton channel. We thus emphasize that dedicated searches in this channel may prove very crucial for the discovery of a very light SUSY DM within a few years of the current LHC run.