Probing mild-tempered neutralino dark matter through top-squark production at the LHC

The lightest neutralino, assumed to be the lightest supersymmetric particle, is proposed to be a dark matter (DM) candidate for the mass $\cal{O}$(100) GeV. Constraints from various direct dark matter detection experiments and Planck measurements exclude a substantial region of parameter space of the minimal supersymmetric standard model (MSSM). However, a"mild-tempered"neutralino with dominant bino composition and a little admixture of Higgsino is found to be a viable candidate for DM. Within the MSSM framework, we revisit the allowed region of parameter space that is consistent with all existing constraints. Regions of parameters that are not sensitive to direct detection experiments, known as"blind spots,"are also revisited. Complimentary to the direct detection of DM particles, a mild-tempered neutralino scenario is explored at the LHC with the center of mass energy $\rm \sqrt{s}$=13 TeV through the top-squark pair production, and its subsequent decays with the standard-model-like Higgs boson in the final state. Our considered channel is found to be very sensitive also to the blind spot scenario. Detectable signal sensitivities are achieved using the cut-based method for the high luminosity options $\rm 300$ and $\rm 3000 ~fb^{-1}$, which are further improved by applying the multi-variate analysis technique.


Introduction
The quest for a signature of beyond standard model (SM) physics is a very high priority agenda in high energy physics experiments and it has been going on for a long time in several laboratories. In particular, at the LHC experiments, looking for new physics signals is the major thrust area. Unfortunately, no single direct evidence of new physics signals has been observed at this point. As a consequence, the absence of experimental confirmation leads to stringent constraints to various BSM models [1]. On the other hand, the well-confirmed existence of dark matter (DM) by various cosmological and astrophysical experiments serves as one of the strong motivations to propose the existence of BSM physics [2,3]. Among several probable candidates of DM, the weakly interacting massive particle (WIMP) turns out to be the most suitable one for thermal DM, with a correct relic density measured by the PLANCK experiment which predicts [4], Ωh 2 = 0.12 ± 0.001. (1.1) Enormous efforts have been in place for a long time to look for DM candidates via direct and indirect searches in various experiments [5][6][7][8][9][10]. However, null results, in particular, from some of the direct detection (DD) experiments have resulted in strong constraints on DMnucleon scattering cross sections in terms of DM (WIMP) masses [11][12][13][14][15][16][17][18][19][20]. The DM-nucleon scattering cross section can be classified into two categories, namely, spin-independent (SI) and spin-dependent (SD), depending on the structure of the coupling. Note that, in general, the SI DM-nucleon scattering cross section is smaller than that of the SD case, and it is more sensitive to DD experiments [21][22][23]. For instance, the most stringent bounds come from XENON1T experiment, where the DM-nucleon scattering cross section corresponding to the DM of the mass range ∼20-100 GeV is strongly restricted, σ SI < ∼ 10 −46 cm 2 [13]. The other experiments such as LUX [11], PANDA [12], PICO-60 [17], Darkside [14] etc. also constrain the DM-nucleon cross section for a wide range of masses of DM candidates from few GeV to TeV.
The minimal supersymmetric standard model (MSSM) with R-parity conservation offers the lightest neutralino, assumed to be the lightest supersymmetric particle (LSP) as the potential DM (WIMP) candidate of the mass ∼ 100 GeV [24][25][26][27]. Comprehensive searches of neutralino DM are carried out at the LHC which lead to various constraints in the absence of any signal [28][29][30]. In MSSM, the physical neutralino state is constituted through the linear superposition of electroweak (EW) gauginos (bino( B), wino( W)) and Higgsinos(H 0 u ,H 0 d ). This composition is mainly determined by relative values of two EW gaugino mass parameters, M 1 and M 2 , corresponding to U(1) and SU(2) gauge transformations respectively. In addition, the other two parameters, namely Higgsino mass parameter(µ) and tan β, the ratio of two vacuum expectation values of two neutral Higgs bosons also play an important role in determining the physical masses and composition of neutralino states. A neutralino state with pure Higgsino or wino composition of the mass ∼ O(100) GeV is found not to be a favorable DM candidate because of its under-abundance of relic density [31]. However, for large masses O(TeV), those can serve as a DM candidate [31][32][33][34][35]. Similarly, a neutralino with pure bino composition also does not satisfy the right relic density measurement (see Eq. 1.1). Hence, in order to propose LSP as a viable DM candidate, the "tempered neutralino" scenario is proposed to be the best bet [31], where the neutralino is no longer a pure state, but has admixtures of more than one composition. A well-tempered bino-Higgsino [36][37][38][39] or bino-wino [40][41][42] neutralino is found to be the most suitable DM candidate for the mass ∼100 GeV to achieve the right relic density. The Higgsino component is indispensable to bring down the relic density to the required value (Eq. 1.1) via resonant Z or Higgs-mediated annihilation, where the Higgs can be the SM-like Higgs boson as well as heavier Higgs boson states, in the limit of large sfermion masses. It is to be noted that, the neutralino-nucleon SI scattering cross section is enhanced with the increase of Higgsino composition in the neutralino state. Therefore, the strong experimental limits on the SI scattering cross section restrict the composition of neutralino, in particular, the Higgsino content [43,44]. Hence a bino dominated neutralino with a little mixture of Higgsino component, referred to as "mild-tempered neutralino", is expected to be the viable DM candidate for the mass O(100) GeV or little less [45], and consistent with all existing constraints. In this regard, it is to be noted that few studies exist in the literature based on the extended supersymmetric (SUSY) model, which present very light DM candidates (m χ < ∼ 50 GeV) [46][47][48][49][50], satisfying all current constraints. It is worth pointing out here, that there exists a region of MSSM parameter space where the DM-nucleon SI scattering cross section almost vanishes because of the interplay among various amplitudes. Consequently, direct detection rate of DM becomes insensitive corresponding to that region of parameter space, which is known as the "blind spot"(BS) [51][52][53][54][55]. As the DD experiments fail to probe this BS scenario, it is worth finding a complementary way for DM searches at the LHC.
In this current study, we focus on the mild-tempered scenario, i.e. bino-Higgsino neutralino with a larger bino component, and of the mass O(100) GeV, and then identify the corresponding region of parameter space consistent with all measurements. The existence of a relatively lighter LSP of the mass range considered in this study is still not absolutely ruled out by any SUSY searches at the LHC. Hence, our study will presumably give some idea about its detectability at the LHC with its high luminosity options. With this aim, the characteristic signature corresponding to this mild-tempered neutralino including the BS scenario are discussed for the LHC experiment. We consider the top-squark pair production and then its cascade decay to SM-like Higgs boson and an LSP, the DM candidate. Although m t 1 < ∼ 1.1 TeV are ruled out from searches at the LHC in the context of various simplified models, for low BR( t 1 → χ 0 1 + t) ∼ 10%, m t 1 < 1 TeV are found to be still allowed using statistical analysis. It is be noted that the top-squarks of lower mass range which are within the reach of current LHC energy, are also motivated in the context of "naturalness" scenario [56][57][58][59][60][61]. A detailed investigation is carried out performing simulation to explore the feasibility of finding the signal at the LHC for higher luminosity options, such as L = 300 fb −1 and 3000 fb −1 .
The paper is organized as follows. In section 2, the MSSM model set up providing mildtempered neutralino and BS scenario is discussed, and then corresponding allowed region of parameters are identified. In section 3, signal and background simulations are presented and followed by results. Finally, we summarize in section 4.

Mild-tempered neutralino scenario in the MSSM
In this section, we discuss the MSSM model setup and then delineate the region of parameter space interesting to our scenario which presents a DM candidate of mass ∼ O(100) GeV consistent with the existing data from Planck experiment (Eq. 1.1) and direct searches as mentioned above.
In the gauge eigenstate basis ( B, W 3 , H 0 d , H 0 u ), the neutralino mass matrix can be written as, Here, M 1 (g 1 ) and M 2 (g 2 ) present the (U(1)) B and (SU(2)) W 3 gaugino mass(coupling) parameters respectively, whereas µ is defined to be the Higgsino mass parameter. The two VEVs corresponding to two neutral components of the two Higgs doublets H 0 u and H 0 d are v u and v d respectively and constrained to be v 2 u + v 2 d = v 2 . As practice, we assume tan β = vu v d , and s β ≡ sinβ, c β ≡ cosβ. The symmetric matrix M N can be diagonalized by a unitary matrix N 4×4 to obtain the masses of four neutralino statesχ 0 i (i = 1, 2, 3, 4) as, and the corresponding physical neutralino states are given by, Similarly, in the basis (i W − , H − u ) and (i W + , H + d ) the chargino mass matrix is given by: which is diagonalized by two unitary matrices U and V. For M 2 >> µ, the lighter chargino ( χ ± 1 ) state becomes Higgsino-like. For our considered scenario, the dominant DM annihilation process occurs through the s-channel mediated by CP-even(h, H) and CP-odd(A) Higgs bosons or Z, in the limit of relatively heavier slepton masses. The cross section of the annihilation process primarily depends on the (φ, Z)-χ 0 1 -χ 0 1 couplings, which are of the following form, where α is the mixing angle of the CP-even Higgs sector. Clearly, the combined effect of bino(N 11 ) and Higgsino components(N 13 , N 14 ) in χ 0 1 determine the annihilation rate. In addition, a neutralino with a moderate to large amount of Higgsino content may dominantly co-annihilate with Higgsino-like(large V 12 ) and nearly mass degenerate lighter chargino χ ± 1 , along with other subdominant contributions, which may enhance the annihilation crosssection through the following coupling, Hence, in combination of all processes, whichever are viable, the cross section for annihilation process corresponding to a Higgsino-like LSP goes up leading to an under-abundance of relic density. Hence one can conclude that an LSP with a suitable combination of bino and Higgsino composition appears to be a viable DM candidate around the mass O(100) GeV. In the case of wino-Higgsino dominated LSP, various possible annihilation and co-annihilation processes can occur, which are mediated by SM gauge bosons, and lead to the under-abundant scenario. In order to achieve the right relic density prediction, in this case, one needs to lift the mass(∼ M 2 ) of the LSP to TeV level and suppress annihilation cross section [31,32]. This type of scenario appears naturally in anomaly mediated SUSY breaking model [62][63][64]. Hence, a SUSY DM model disfavors the possibility of Higgsino/wino dominated scenario with DM mass ∼ O(100) GeV.
As pointed out earlier, the composition of the LSP DM candidate is also constrained by direct detection experiments [11-13, 16, 17], where DM candidate scattering off a heavy nucleus mediated by Higgs/gauge bosons or squarks. The effects due to heavier squarks (O(1) TeV) are very much suppressed. Hence the main contribution to SI(SD) cross section occurs through Higgs(Z) boson exchange via t-channel diagram [21,22]. The dominant contribution comes from the diagram mediated by the CP-even lightest Higgs boson, whereas contributions due to other heavier Higgs bosons are suppressed. Interestingly, this suppression can be compensated by enhanced couplings of heavier Higgs bosons with the quarks for a certain range of parameters, in particular, for higher values of tan β, which we will discuss later.
The SI scattering cross section is also sensitive to couplings g h χ 0 . The presence of a larger Higgsino component in χ 0 1 enhances the SI DM-nucleon scattering cross section mediated mainly by the CP even lightest Higgs boson, which is tightly constrained by the existing limits on DM-nucleon scattering cross section from the XENON1T experiment [13]. On the other hand, the composition of the χ 0 1 state is also constrained by relic density. Hence, the bino-Higgsino content of a mild-tempered neutralino state is severely restricted by the combined effect of relic density measurements and DM-nucleon cross section limits. This feature of mild-tempered neutralino is reflected in Fig. 1(left), where the variation of relic density with the relative size of bino and Higgsino composition of the LSP is presented in . It is to be noted that this figure is subject to the condition µ > 0 to avoid effects from "blind spots," which occur for µ < 0 when M 1 is assumed to be positive. It will be discussed in detail later. In Fig. 1(right), we present the ranges of µ and M 1 allowed by relic density, limits from DD experiments along with some other constraints as described in section 2.1. These figures are obtained by performing a numerical scan of parameters (Eq.2.18), which will be discussed later.  content, makes under-abundance of relic density. In this case, along with DM annihilation (Eq. 2.6), the co-annihilation process(Eq. 2.11) also takes place resulting in a larger DM annihilation cross section. Towards the rightmost region of Fig. 1(left), due to the absence of sufficient Higgsino-components in the LSP, the DM-nucleon scattering cross section goes down because of the couplings(Eq. 2.7) and becomes consistent with DD limits. This region is presented(yellow) in Fig. 1(left) at the higher values of ratio N 2 11 /(N 2 13 +N 2 14 ). Hence, it can be concluded that the bino dominated LSP with little admixtures (∼ 1%) of Higgsino component is the most favoured option in a decoupled scenario (M 2 is very large). We referred to this as a scenario of "mild-tempered" neutralino in the previous section. In this scenario, relatively higher values µ are found to be allowed with light to moderate values of M 1 . It is clearly seen in Fig. 1(right) that, for µ > 0, the Higgsino fraction in the LSP is tiny. However, for µ < 0, there exist parameter spaces with a comparatively higher amount of Higgsino components that are still allowed. It occurs mainly due to the effect of "blind spots", which is discussed next.
The blind spot is an interesting scenario where the DM-nucleon scattering cross section is found to be very insensitive for a certain range of relevant parameters in the MSSM, and the corresponding region of parameters is called "blind spot". It may happen for various reasons. For instance, the tree-level scattering cross section may vanish either for a pure gaugino (i.e N 13 , N 14 ∼ 0) or Higgsino (i.e N 11 ∼ 0) neutralino state. Moreover, scattering takes place via one and two loop diagrams mediated by gauge bosons, and an accidental cancellation among various scattering amplitudes for pure Higgsino and gaugino LSP state, lead the total cross sections too small and beyond the sensitivity of DD experiment( σ SI << 10 −46 cm 2 ) [51,65,66]. Finally, BS may also arise at the tree level due to cancellation among various amplitudes. The dominant contribution to DM-nucleon cross section comes from the diagram mediated by the CP even lightest Higgs boson, whereas contributions due to other heavier Higgs bosons are found to be very small for the decoupling scenario(m A >> M Z ). Interestingly, at the tree level, the suppression of contribution mediated by heavier Higgs bosons can be compensated by its enhanced coupling with the (down type) fermions for the range of moderate to higher values of tan β. Additionally, the coupling between heavier Higgs bosons and neutralinos, H-χ 0 1 -χ 0 1 (Eq. 2.8) may receive similar kind of enhancement for a larger value of N 13 , the down type of Higgsino content in the LSP. Consequently, the amplitudes mediated by heavier Higgs bosons turn out to be comparable or at the same level of the CP even SM-like Higgs boson exchange diagram. Depending on the relative signs of µ and M 1 , the interference between these two diagrams, may become destructive or constructive [53]. Incidentally, for a certain range and combination of related parameters, these two contributions almost cancel each other leading to the scattering cross section insensitive [53]. A detailed analytical study shows that the combination of parameters corresponding to the BS for moderate to larger values of tan β follow the relation among µ, m A , tanβ, and m χ 0 1 (∼ M 1 ), as [53], Corresponding to this parameter space, naturally a larger Higgsino component ∼ O(10%) can be accessible without violating DD bounds in contrast to the requirement of ∼ O(1%) or less for a mild-tempered neutralino case. The above condition for BS connects the gaugino mass parameter with the Higgs sector.  Note that a substantial region of tan β and m A plane is excluded from the Higgs searches in the channel, h, A → τ τ [67,68]. This m A -tan β exclusion can be traded to obtain constraints on µ/m χ 0 1 , by using Eq. 2.13 in the m A -tan β plane. In Fig. 2, following Eq. 2.13 the contour plots of µ [53]. The region above the red and blue lines are excluded due to the non observation of any signal events in the h, A → τ τ searches by ATLAS [67](L = 139.5 fb −1 ) and CMS [68](L = 35.9 fb −1 ) experiments respectively. Depending on the value of m A , the BS condition, i.e. the ratio µ M 1 may vary from -1.5 to -3.5. It implies that the lightest neutralino state is bino like whereas the second and third heavier states are Higgsino like in the limit of large M 2 , which is exactly the scenario that we try to explore at the LHC experiment.
As explained before, the main focus of this study is to explore the feasibility of finding mild-tempered neutralino scenario at the LHC. The added advantage of our proposed channel is its sensitiveness to the region of parameters corresponding to the BS scenario, which can also be probed at the LHC. As we know, the content of bino and Higgsino in the LSP depends on the splitting between µ and M 1 . Therefore, mild-tempered scenario appears with the condition |µ| − M 1 > ∼ 100 GeV, which provides also an LSP of mass O(100) GeV. The scenario with little Higgsino admixture along with the dominant bino composition in χ 0 1 presumably predicts Higgsino-dominated χ 0 2,3 and χ ± 1 states that are degenerate in mass ∼ µ, for a decoupled wino state (i.e large M 2 ). In such cases, heavier states χ 0 2,3 prefer to decay to a Z boson and an LSP, and χ ± 1 decays to a W and an LSP. The coupling involved in χ 0 2,3 decays is Z-χ 0 2,3 -χ 0 1 ∝ N 13 N 23 − N 14 N 24 , and since χ 0 1 is primarily bino dominated (i.e N 13 , N 14 very tiny), it is suppressed. Thus χ 0 2,3 preferably decay as, and a larger Higgsino composition in χ 0 2,3 state(Eq. 2.7) makes its rate higher. This decay channel of χ 0 2,3 is found to be the characteristic feature for the mild-tempered neutralino scenario. Hence testing of this scenario can be performed by studying χ 0 2,3 and χ ± 1 production at the LHC [69,70] and their subsequent decays. Earlier, this channel is thought to be a "spoiler" mode corresponding to trilepton signal in pp→ χ 0 2 χ ± 1 → + − χ 0 1 χ 0 1 production [71,72]. In this study, instead of considering the χ 0 2 χ ± 1 production via electroweak interaction, we consider the production of χ 0 2 through lighter top-squark production via strong interaction, where t 1 dominantly decays to Higgsino-like χ 0 2,3 and χ ± 1 [70,73]. The decay t 1 → t + χ 0 2,3 , is governed by the interactions, where, Here θt is the mixing angle in the top-squark sector. Evidently, the m t dependent term becomes dominant for Higgsino(N i4 )-like neutralino states leading higher branching ratio (BR) for t 1 → χ 0 2,3 + t. Due to large enough splitting between µ and M 1 , it is natural to have m χ 0 2,3 − m χ 0 1 > 125 GeV, resulting in the χ 0 2,3 → h + χ 0 1 decay to be dominant. Hence the mild-tempered neutralino DM can be indirectly produced from the decay of Higgsino-like χ 0 2,3 producing those in the lighter top-squark( t 1 ) production. It is be noted that, this type of scenario can also be probed through the associated production, such as pp → χ 0 2,3 χ ± 1 and with the three lepton final states along with missing energy [74][75][76]. However, we observe that for the same set of parameters, the rates corresponding to signal final states are higher for top-squark pair production via strong interaction than the case of electroweak associated production.

Numerical scan
In order to identify the region of parameter space of our interest we perform an illustrative numerical scan of all relevant parameters. This scan is carried out using SUSPECT [77] to calculate the spectrum for a given set of input parameters, and then interfacing with SUSYHIT [78] to obtain respective branching fractions of SUSY particle decays. Also micrOMEGAs [79][80][81][82] is interfaced for the calculation of DM related observables and then checking the constraints.
We have set the ranges of the most relevant parameters, including third generation soft squark masses (M Q 3 , M t R ), in the random scan (every unit is in GeV, wherever applicable): while the other gaugino mass parameter is fixed as, First two generations squark masses are assumed to be, The A-term corresponding to the third generation quark(A t ) plays an important role in determining the lightest CP even SM-like Higgs boson mass, and it is varied in the range, All the slepton masses of the first two generations are fixed to 2 TeV. While performing the scan, each model point is tested with PLANCK [4] data (Eq. 1.1) and limits from direct searches [11][12][13][14][15][16][17][18][19][20]. We focus only on the LSP of the mass range ∼50-500 GeV. The presence of SM-like Higgs boson (h), with mass 125±3 GeV is also ensured. Other absolute constraints from LEP [83], for example, mχ± 1 ≥ 103.5 GeV and m H ± > 78.6 GeV are imposed. In addition, Higgsbounds-5.5.0 [84][85][86][87][88] is used to check the Higgs couplings and related measurements. The exclusion of top-squark-neutralino mass plane predicted by CMS [89][90][91][92] and ATLAS [93][94][95][96] experiments are also examined using the SModelS-1.2.3 package [97,98]. Generally the SMS model with BR( t 1 → χ 0 1 + t) = 100% is used to interpret data. Whereas, in our scenario, BR( t 1 → χ 0 1 +t) ∼ 10% implies much weaker exclusion limits and consequently relatively light top-squarks (m t 1 ∼ 700 GeV) are also found to be allowed. Performing the scan, Fig.1(left) is plotted, where mainly the relic density and DD constraints are relaxed to show the effect of the compositions of χ 0 1 on the relic density and DD measurements. Few representative benchmark points (BP) are chosen (see Table 1), which are consistent with all constraints mentioned above. These BPs are used to obtain the signal sensitivities by performing the simulation of our proposed signal process. These BPs primarily represent two scenarios, namely "mild-tempered neutralino" and "blind spots". But under these broad pictures, they also encompass compressed and non-compressed spectrum corresponding to various choices of mass differences, ∆m 1 = m t 1 − (m t + m χ 0 2,3 ) and ∆m 2 = m χ 0 2,3 − m χ 0 1 . Notice also that for all cases of BPs, m t 1 varies from 600-1700 GeV and for all cases BR( t 1 → χ 0 1 + t) is subdominant, while χ 0 2,3 → χ 0 1 + h is dominant. Performing the simulation of signal and backgrounds, signal sensitivities are presented for all these BPs.

Signal and Background
As discussed before, we consider the following process where the lightest neutralino originates from the decay of second and third lightest neutralino( χ 0 2,3 ) produced via top-squark production as shown below, Since in this scenario, the χ 0 2 / χ 0 3 are dominantly Higgsino-like, hence BR( t 1 → t + χ 0 2,3 ) is larger than the BR( t 1 → t + χ 0 1 ). Subsequently, the higher neutralino state (either χ 0 2 or χ 0 3 ) dominantly decays to SM-like Higgs boson and χ 0 1 . Here X ≡ χ 0 1 , χ 0 2,3 leads to a χ 0 1 accompanied by either Z or h in the final state. We focus only on single Higgs boson in the final state. However, we found that the contribution of di-Higgs boson events in the signal is negligible. The bb channel of Higgs boson decay is considered owing to its higher BR and comparatively easy to reconstruct its mass. The pair of lightest neutralinos escape the detector leading to a huge amount of missing energy in the final state. Moreover, there is another pair of b-jets originating from two top quarks. Hence, the final state of the signal event is characterized by, We found that the contribution of di-Higgs production to the signal event is negligible. It is known that QCD is the main source of background corresponding to any pure hadronic final state. Hence, in order to eliminate it, the leptonic decay of one of the top quarks is considered. We require the presence of only one lepton in the final state. The other dominant SM backgrounds are: p p → tt(1 ), tt(2 ), tth, ttZ, ttbb (3.23) where, the combination of two b's coming from the top, h, Z, or gluon splitting mimics the signal b-jets from Higgs decay. The lepton and E / T arise from the semi-leptonic decay of one of the top quarks, while the other top decays hadronically.
It is to be noted that in the signal events, the angular separation between two b-jets depends on the boost of Higgs boson, which is determined by the mass differences, ∆m 1 = m t 1 −(m t +m χ 0 2,3 ) and ∆m 2 = m χ 0 2,3 −m χ 0 1 . Accordingly, we simulate signal events in resolved and non-resolved categories depending on the boost of Higgs boson. In Table 1, BP1-BP5 correspond to the non-resolved category while BP6-BP9 represent the resolved one. For the boosted case, two b-jets likely to appear as a single fat jet, which we refer to as the "Higgs jet(HJ)" now onwards.
The PYTHIA8 [99,100] is used to generate tt(1 ), tt(2 ) events, while the other background processes are generated using Madgraph5-aMC@NLO-2.7.3 [101] interfacing with PYTHIA8, for showering and hadronization. Signal events are generated in Madgraph5-aMC@NLO-2.7.3 using UFO for the MSSM (MSSM-SLHA2), where the parameter card is generated from SLHA file [102], obtained from SUSYHIT, corresponding to each BP. The same SLHA file is used for subsequent showering of signal events in PYTHIA8. Detector effects are taken into account by passing all signal and background events through Delphes-3.4.2 [103] using the CMS detector card 1 .
In the simulation, the following selections are imposed, where objects are selected using Delphes inputs.
(1) Lepton selection : Leptons are selected with p T > 20 GeV and |η| < 2.5. Isolation is ensured using mini-isolation criteria by checking e-flow objects of Delphes as follows [104]: (3) HJ selection: The reconstruction of HJ is performed in two ways depending on the boost of the Higgs boson, i.e., resolved and non-resolved categories, as described below.
• HJ in non-resolved category: At first, fat jets are constructed taking inputs from Delphes, using Fastjet3.3.2 [105] with Cambridge-Aachen [106] algorithm and R=1.0. Minimum p T of the fatjets is set to be 100 GeV. These fat jets are then passed through mass-drop Tagger (MDT) [107,108] with µ =0.667 and y cut > 0.09 to remove contamination due to soft radiation. The subjets of the 'tagged fat jet' are further matched with the b-quarks of the event which are selected within |η| < 2.5 and with a matching cone ∆R < 0.3. When both the subjets are found to be b-like, we call the tagged fatjet as the HJ (J bb ). We also checked the presence of B-hadron in the b-like subjets and found that for about 95% cases, it exists.
• Resolved category: In this case, jets, subject to cuts p j T >20 GeV and |η| <4.0, are constructed from e-flow objects of Delphes, using Fastjet3.3.2 [105], but with the Antik T [109] algorithm with a jet size parameter R=0.5. Using the same technique as above, by matching jets with b-quarks of the event, b-like jets are identified. The pair of b-like jets that construct the invariant mass closest to Higgs boson mass within the range 100 GeV≤ m HJ ≤150 GeV, is identified as HJ, and the resultant four-momentum of the two jets is regarded as the momentum of HJ.
(4) Other jets and b-jets: This selection also differs according to two categories.
• Jets in non-resolved category: Once HJ is constructed, the remaining hadrons are used to construct regular QCD jets through Fastjet3.3.2 with Anti-k T algorithm setting R=0.5.
1 Results are checked with ATLAS card as well, and no appreciable change is observed.
Out of these jets, b-like jets are identified by matching technique with the remaining set of b-quarks in the event, which are not part of J bb .
• Jets in resolved category: The two b-jets, which are found to be related to the HJ, are removed from the list of jets and b-jets, and this new list is used further.
Furthermore, to suppress backgrounds, we impose few more selection cuts. For example, the transverse mass between lepton and E / T , defined as, is restricted by M W for all semileptonic tt background events as seen in the m T distribution presented in Fig. 3(left) along with signal events corresponding to two BPs. On the contrary, for signal events, having a large E / T due to neutralinos, which is also not correlated with the lepton coming from tt decay, is expected to have a more wide m T distribution without any peaks (see Fig. 3 (left)). Hence a cut m T ( , E / T ) ≥ 110 GeV turns out to be very effective in eliminating a certain fraction of the background. Another discriminating variable is H T , defined as the scalar sum of p T of all jets except those that constitute HJ. For signal events, larger number of harder jets exist leading to higher H T as seen from the distribution shown in Fig. 3 (right). A cut H T ≥ 500 GeV turns out to be useful to reject background events substantially. In the case of the non-resolved category, the mass distribution of J bb shows a clear peak at ∼125 GeV, which is absent in most of the backgrounds, and very small for tth as shown in Fig. 4. Thus the selection of m J bb > 100 GeV is found to be useful in eliminating significant background events. In the resolved category case, this mass requirement is already imposed while constructing HJ. The presence of HJ with a specific mass requirement is a very important feature of our signal and helps to eliminate almost all the tt backgrounds by enormous amount except tth process where the source of J bb is same as the signal.
Signal events are simulated for 9 BPs which are chosen in such a way that BP1-BP5 represent the non-resolved cases, whereas BP6-BP9 correspond to the resolved category. The BPs labeled as 'BS' in the parenthesis correspond to BS scenario. In Table 2, the crosssection yields for the signal and background processes for the non-resolved categories are presented after imposing selection cuts. The first row presents the LO cross-sections of each processes, computed by Madgraph5-aMC@NLO-2.7.3, at the center of mass energy √ s = 13 TeV, using NNPDF23LO [110] for parton distribution and choosing the dynamic QCD . Higher order effects are taken into account by multiplying respective K-factors(K = σ NLO σ LO ). A K-factor of 1.4 is used for top-squark pair production(for NNPDF31LO) [111] and tt [112,113]. Whereas, for tth, ttZ and ttbb K-factors are considered to be 1.2 [114], 1.35 [115] and 1.8 [116] respectively. As indicated in the table, the m J bb cut is very useful to eliminate backgrounds significantly. In addition, the m T cut also kills backgrounds substantially.  Similarly, cross section yields for the resolved category are presented in Table 3. It is clear that the selection of HJ, in this case, is not as efficient as the non-resolved category, but still having good discriminating power. In general, overall signal acceptance efficiency is 1-2%; while for overall backgrounds, it is found to be 0.0001% for the non-resolved category and 0.007% for the resolved category. The total cross-sections of background events are found to be 0.232 fb for the non-resolved category and 16.2 fb for the resolved cases respectively. Finally, the signal sensitivities ( S √ S+B ) are presented in Table 4 for two high luminosity options L = 300 fb −1 and 3000 fb −1 . It is to be noted that for the non-resolved category, the sensitivities are ∼ 2 − 3σ for L = 300 fb −1 , whereas they are large(∼ 5 − 8σ) for the resolved category, mainly because of the high production cross-sections, due to smaller top-squark masses. The tiny sensitivities for BP3 and BP5 can be attributed to a very low top-squark production cross-section because of its higher masses. Assuming 10% background uncertainty the sensitivity for the BPs in resolved category drops by ∼ 7% and for the non-resolved category, it reduces by about 0.1%. Though we obtain reasonable signal sensitivity in the resolved category, the acceptance efficiencies for backgrounds, in that case, are not appreciably small as in the non-resolved category in the cut-based method. In order to improve further, we carry out multivariate analysis (MVA) based on boosted decision tree (BDT) method within the framework of TMVA [117,118] framework.

Multivariate Analysis
The basic idea of MVA [117][118][119][120][121] is to examine patterns in multidimensional data by considering several variables at once. Several kinematical variables are constructed, keeping in mind the features of signal events, for training purposes. Depending upon the performances of those variables, we use 13 of those for the non-resolved category and 15 for the resolved category to train signal and background samples. The description of those variables are presented in Tables 5 and 6 corresponding to BP5 for non-resolved category and BP7 for the resolved category respectively. The first column of these tables shows the ranking of these variables, which represents the relative importance in discriminating signal and backgrounds. The set of variables are the

Rank
Variable Description ∆R between two b-jets inside Higgs-jet. 4 ∆R(E / T , J bb ) ∆R between E / T and J bb 5 pT ratio of two b-jets inside Higgs-jet. 6 ∆R(E / T , j) ∆R between E / T and leading jet 7 ∆R(b 1 , J bb ) ∆R between leading b-jet (outside J bb ) and J bb 8 Njets Number of outside J bb . 9 HT Scalar sum of p T of all jets outside J bb same for all BPs for a given category, but depending on the kinematics, the ranking of those variables is found to be little different. While doing MVA for each BP, overtraining tests are performed to ensure that there are no significant deviations between the performance of training and testing data. In Fig. 5, the variation of cross section yields for signal and backgrounds and the signal significance ( S √ S+B ) as a function of threshold on MVA output discriminator for luminosity L = 300 fb −1 , is presented corresponding to the BP1 for the non-resolved category and BP6 for the resolved category case. It indicates that a sensitivity above ∼ 5σ can be achieved for luminosity L = 300 fb −1 corresponding to a cut of the classifier > 0.9.
Evidently, the achievable signal significance for all the BPs are presented in Table 7 for two luminosity options. Clearly, the signal sensitivities are found to be well above 5σ at L= 300 fb −1 , except for BP3 and BP5, where the production cross-section is too low due to a heavier top-squark mass.

Summary
In the MSSM framework, the lightest neutralino, an LSP of the mass ∼ O(100) GeV, is found to be one of the best suitable DM candidates. However, the constraints from direct DM detection experiments and measurement of the relic density restrict the composition of the physical neutralino states. It is observed that, instead of a pure state, neutralino DM in MSSM is "mild-tempered" where it is bino-dominated with a presence of little Higgsino, providing the best DM solution at this mass range. In this scenario, the DM annihilation process takes place via Higgs and gauge bosons where Higgsino content along with dominant bino helps to provide the right relic density. It is to be noted that, eventually the Higgsino composition in the LSP is strongly restricted by the limits of SI DM-nucleon scattering cross section measurements in the direct DM detection experiments, primarily by XENON1T. Considering this DM solution, a numerical scan is performed to identify the range of sensitive parameters, in particular, µ and M 1 in the limit of a very large M 2 value. It is found that, with |µ| − M 1 > M Z , the most preferred ranges are M 1 ∼ 50 − 600 GeV and µ ∼ 400 − 1000 GeV. Moreover, there is a region of parameter space that is blind to the SI scattering cross section due to the interplay of parameters and cancellation among various amplitudes mediated by the lighter and heavier Higgs bosons. Consequently, in such cases, the Higgsino content in the lightest neutralino is not severely constrained. In mild-tempered DM scenario, χ 0 1 is accompanied with Higgsino-like χ 0 2,3 and χ ± 1 having masses around µ. It is indeed the case even for the region of parameters corresponding to the BS scenario. Due to the gaugino-Higgsino-Higgs type of coupling, χ 0 2,3 → h + χ 0 1 decay rate gets enhanced, leading to an interesting phenomenology at the LHC corresponding to our considered scenario.
We focus on the top-squark pair production to explore the mild-tempered neutralino scenario at the LHC. As BR( t 1 → χ 0 1 + t) is very small, χ 0 1 is indirectly produced through the production of χ 0 2,3 . The presence of SM-Higgs boson in the final state adds an extra advantage to probe this channel. Interestingly, this channel also provides an opportunity to probe the BS scenario. The signal is characterized by one HJ consisting of b-like jets or subjets, large E / T , one lepton, plus at least one extra b-like jet. The HJ tagging turns out to be very efficient to separate out the signal from the debris of backgrounds. The presence of HJ adds robustness to this signal.
Signal significances are presented for few illustrative BPs including BS scenario. We observe that for top-squarks of the mass range 600-1700 GeV, for most of the BPs, a reasonable signal sensitivity(∼ 3−5σ) can be achieved corresponding to L = 300 fb −1 luminosity option, which goes up roughly by a factor of three for L= 3000 fb −1 . Furthermore, we demonstrate that the sensitivities can be increased by employing MVA technique. Remarkably, we notice that, for the above luminosity options, and in particular for the resolved category case, the improvement is significant, by a factor of ∼3-4. The signal is detectable even for L = 300 fb −1 option except for BP3 and BP5 for which top-squark masses are ∼ 1.5 TeV. For the center of mass energy √ s = 14 TeV, which is the energy option for RUN3 experiment at the LHC, our projected sensitivities are expected to increase by 15-20% depending on the top-squark masses. A 10% uncertainty in background estimation reduces sensitivity by about 7% and 0.1% for resolved and non-resolved category respectively. Our analysis shows that both the "mild-tempered" neutralino providing a DM candidate in the framework of MSSM and also the BS scenario where the direct search is not sensitive, can be detected at the LHC with a reasonable sensitivity for projected luminosity options.