Electroweakino searches at the HL-LHC in the baryon number violating MSSM

The projected reach of direct electroweakino searches at the HL-LHC ($\sqrt{s}=14~{\rm TeV}, ~3000~{\rm fb^{-1}}$ LHC) in the framework of simplified models with R-parity violating (RPV) operators: $\lambda_{112}^{\prime \prime}u^{c}d^{c}s^{c}$ and $\lambda_{113}^{\prime\prime}u^{c}d^{c}b^{c}$, is studied. Four different analysis channels are chosen: $Wh$ mediated $1l+2b+jets+\rm E{\!\!\!/}_T$, $Wh$ mediated $1l+2\gamma+jets+\rm E{\!\!\!/}_T$, $WZ$ mediated $3l+jets+\rm E{\!\!\!/}_T$ and $WZ$ mediated $3l+2b+jets+\rm E{\!\!\!/}_T$ and the projected exclusion/discovery reach of direct wino searches in these channels is analyzed by performing a detailed cut based collider analysis. The projected exclusion contour reaches up to $600-700~{\rm GeV}$ for a massless bino-like $\chi_{1}^{0}$ from searches in the $Wh$ mediated $1l+2b+jets+\rm E{\!\!\!/}_T$, $Wh$ mediated $1l+2\gamma +jets+\rm E{\!\!\!/}_T$ and $WZ$ mediated $3l+jets+\rm E{\!\!\!/}_T$ channels, while the $WZ$ mediated $3l+2b+jets+\rm E{\!\!\!/}_T$ search channel is found to have a projected exclusion reach up to $600~{\rm GeV}$ for $150~{\rm GeV}<M_{\chi_{1}^{0}}<250~{\rm GeV}$. The baryon number violating simplified scenario considered in this work is found to furnish a weaker projected reach (typically by a factor of $\sim 1/2$) than the R-parity conserving (RPC) case. The projected reach at the HL-LHC in these four channels is also recasted for realistic benchmark scenarios.


I. INTRODUCTION
Supersymmetry (SUSY) [1][2][3][4] has been among the most attractive frameworks for formulating physics beyond the Standard Model. Numerous studies have reported the plausibility of SUSY in resolving various inadequacies within the Standard Model (SM) of particle physics [5][6][7][8] viz the Hierarchy problem [9,10], gauge coupling unification [11][12][13][14], existence of a viable Dark Matter (DM) candidate [15][16][17], naturalness of Higgs mass [18,19]. In adherence to the experimental observations, SUSY has to be broken, and solution to the Hierarchy problem implores the SUSY breaking scale to be ∼ O(TeV), thus, bringing the SUSY particles within the potential reach of current and future LHC. The minimal supersymmetric extension of the Standard Model (MSSM) (see [20][21][22][23][24] for a detailed review) has been among the prominent class of nominees considered to address the shortcomings within the SM and in the pursuit of new physics phenomenology. A legion of studies have focused on investigating the current status and future prospects of the MSSM parameter space in light of the LHC Run-I and Run-II results . Since the advent of the LHC, the ATLAS and CMS collaborations have performed a multitude of searches to probe the sparticles using the LHC Run-I and Run-II dataset, however, they are yet to observe a clear signature of physics beyond the SM. Robust lower bounds have been derived on the masses of strongly interacting sparticles. Searches by the ATLAS and CMS collaboration using the LHC √ s = 13 TeV data collected at ∼ 137 fb −1 of integrated luminosity (L) have excluded gluinos (g) up to ∼ 2.2 TeV and ∼ 2.3 TeV, respectively, for a LSP (lightest SUSY particle) neutralino (χ 0 1 ) with mass up to ∼ 600 GeV [50][51][52] at 95% C.L., however, within the framework of a simplified SUSY scenario. Using the same respective datasets and within a simplified scenario with some specific decay modes and mass hierarchy, ATLAS and CMS have also excluded the stops (t) and sbottoms (b) up to ∼ 1.2 TeV for a M χ 0 1 ∼ 400 GeV at 95% C.L. [52][53][54]. On the other hand, the electroweakly interacting sparticles viz electroweakinos and sleptons, are rather feebly constrained [55][56][57][58][59][60][61] The MSSM is endowed with an exact symmetry related to the baryon number (B), lepton number (L) and the spin of the particle (S), referred to as R-parity (R p ) 2 . R-parity conservation (RPC) entails pair production of SUSY particles at colliders and also ensures that the lightest SUSY particle, typically the χ 0 1 , is stable and a viable non-baryonic DM candidate. The presence of a stable LSP DM candidate results in missing transverse energy (E / T ) signatures at the colliders, making the RPC scenarios extensively attractive to be analyzed at the LHC. Consequently, a myriad of studies have addressed the phenomenological implications of R-parity conserved scenarios and a non-exhaustive list of such studies can be found in [69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86].
Although the R-parity conserved scenarios display a tempting landscape for collider and astrophysical searches, it must be noted that R-parity conservation is not fundamentally necessary to obtain a viable SUSY framework. Ensuring the stability of the proton was the prime intent behind introducing R-parity conservation (relevant discussions can be found in [87,88]). However, several studies have also explored the possibility to stabilize the proton without conserving R-parity [89][90][91][92]. Another strong incentive to consider RPC scenarios is the possibility of a viable DM candidate with a correct DM relic density as discussed previously. In the presence of R-parity violation (RPV) (see [93,94] for reviews), the LSP would undergo decay and would no longer remain a viable DM candidate. However, results from [95][96][97] indicate that axinos and gravitinos could generate a correct relic abundance in RPV scenarios.
Furthermore, the presence of R-parity violation has also been shown to ease the amount of fine-tuning required to obtain a ∼ 125 GeV Higgs boson in SUSY [98] by weakening the bounds on gluino [99][100][101][102][103] and stop masses [104,105]. Another critical consequence of RPV terms is the successful explanation of the observed pattern of neutrino masses and mixing [106][107][108][109][110][111][112]. Within RPV scenarios, lepton number violating couplings can initiate lepton flavor violating processes (viz the scattering of unoscillated ν µ into τ ) even in the absence of neutrino oscillation [113]. The R-parity framework has also been studied in light of offering a plausible explanation for the (g−2) µ discrepancy [114]. In addition, the E / T dependent collider search strategies, which are a trademark of RPC scenarios, would be rendered ineffective in the presence of R-parity violating terms, and the collider bounds are expected to alter. Thus, the introduction of RPV terms would result in characteristically distinct final states, a study of which would be extremely relevant in the context of collider searches at the LHC [115,116]. Overall, the discussion until now motivates the impulse of probing the sector of RPV MSSM.
The most general, gauge invariant and renormalizable R-parity violating terms [20,117] which could be added to the MSSM superpotential (W M SSM ) are the following (the notation of [118] has been followed): where, L and Q represents the left handed lepton and quark superfields, respectively, while, e, u and d corresponds to the right handed lepton, up-type quark and down-type quark superfields, respectively. λ, λ and λ are the dimensionless Yukawa couplings while is the three dimensional Levi-Civita symbol.
Here, i, j, k are the generation indices, α, β, γ are the flavor indices and c represents charge conjugation.
The first and second terms in Equation 1.1 violate the lepton number by 1 unit, while the third term in Equation 1.1 violates the baryon number by 1 unit.
The collider implications of the lepton number violating RPV couplings: λ 12k L 1 · L 2 e c k (k ∈ 1, 2) and λ i33 L i · L 3 e c 3 (i ∈ 1, 2) have been studied by the ATLAS collaboration through an interpretation in simplified scenarios with wino-like NLSP pair production (pp → χ 0 2 /χ ± 1 + χ ± 1 ) and higgsino-like NLSP pair production (pp → χ 0 1 /χ 0 2 /χ ± 1 + χ ± 1 ) in the W Z and W h mediated 4l (l = electrons (e) and muons (µ)) final state [119] using the LHC Run-II data collected at L = 36.1 fb −1 . Results from [119] exclude a wino-like χ ± 1 , χ 0 2 up to ∼ 1.46 TeV (∼ 980 GeV) for a bino-like χ 0 1 with mass M χ 0 1 ∼ 500 GeV (M χ 0 1 ∈ [400 − 700] GeV) in the presence of λ 12k L 1 · L 2 e c k (λ i33 L i · L 3 e c 3 ) type RPV coupling. The ATLAS collaboration has also probed direct wino production in the context of RPC scenarios and has excluded winos up to ∼ 350 GeV for a M χ 0 1 ∼ 50 GeV (at 95% C.L.) from searches in the tri-lepton (l = e, µ) + E / T final state [60] using LHC Run-II data (∼ 139 fb −1 ). Similarly, direct wino searches by CMS in three or more charged l final states in a wino-like RPC scenario, using the LHC Run-II 36 fb −1 dataset, has excluded winos up to ∼ 650 GeV (W Z topology) and ∼ 480 GeV (W h topology) [58]. Thus, the 1 2 λ ijk L i ·L j e c k type RPV scenarios imply a more stringent exclusion on the electroweakino sector compared to the RPC scenarios due to harder leptons in the final state. In [120] as well, ATLAS has analyzed the four or more lepton final state in the context of RPV simplified scenario containing λ ijk L i · L j e c k type couplings using the √ s = 8 TeV LHC data collected at ∼ 20.3 fb −1 integrated luminosity. Results from [120] exclude a wino-like chargino below ∼ 750 GeV, gluino below ∼ 1350 GeV and left-handed (righthanded) sleptons below ∼ 490 GeV (410 GeV), for M χ 0 1 = 300 GeV at 95% C.L., within a simplified RPV scenario where the bino-like LSP χ 0 1 can decay only into electrons and muons. If the tau-rich decays are also included, the corresponding exclusion limits get weaker: wino-like chargino ( 450 GeV), gluino ( 950 GeV), left-handed sleptons ( 300 GeV) and right-handed sleptons ( 240 GeV). The CMS collaboration also analyzed the √ s = 8 TeV LHC data (19.5 fb −1 ) and excluded stops up to 1100 GeV and 950 GeV [121] at 95% C.L. in simplified scenarios containing λ 122 and λ 233 type RPV couplings, respectively, for a bino-like χ 0 1 with mass ∼ 400 GeV. The RPV scenario with 1 2 λ 233 L 2 ·Q 3 d c 3 type coupling has also been investigated in [121] and has excluded stops with mass between ∼ 550 GeV and ∼ 700 GeV for a bino-like χ 0 1 with mass ∼ 500 GeV at 95% C.L.. Gluino searches in multi-jet final state [122] and the jets plus two same-sign lepton or three lepton final state [123] by the ATLAS collaboration using the LHC √ s = 8 TeV data (∼ 20 fb −1 ) within λ ijk αβγ u c α i d c β j d c γ k type RPV simplified scenario has excluded gluinos up to 1100 GeV and 1050 GeV, respectively, for M χ 0 1 ∼ 400 GeV, at 95% C.L. CMS has also searched for the gluinos in multi-jet [124] and same-sign di-lepton plus jets final state [125] using LHC √ s = 8 TeV data (∼ 19.5 fb −1 ) within the framework of λ ijk αβγ u c α i d c β j d c γ k type RPV simplified scenarios, and have excluded gluinos below 650 GeV and 900 GeV, respectively, at 95% C.L.. The phenomenology of λ ijk u c i d c j d c k type of RPV operators has also been analyzed in [99,126] and the distinct collider signatures emerging in consequence to λ u c i d c j d c k type of RPV coupling has been analyzed in [104,127,128]. At this point, it would be essential to take a look at the analogous exclusion limits in the RPC framework. Searches by the ATLAS and CMS collaborations within RPC scenarios (using the LHC √ s = 8 TeV, ∼ 20 fb −1 dataset) have excluded gluinos up to ∼ 1400 GeV [129] and ∼ 1300 GeV [130], respectively, for a bino-like χ 0 1 with mass ∼ 400 GeV at 95% C.L. Using the same dataset, ATLAS and CMS also set lower limits on the mass of squarks ( 900 [129]) and stops ( 760 [131]), respectively, at 95% C.L.. It is worthwhile to note that the RPC scenario and the RPV scenario discussed till now imply a comparable exclusion limit on the masses of gluinos and squarks. However, the electroweakino sector of λ ijk αβγ u c α i d c β j d c γ k type RPV models still remain to be explored, and that is precisely the goal of this work.
Our aim is to study the collider constraints on electroweakinos in RPV simplified scenarios with λ 112 u c d c s c and λ 113 u c d c b c type of RPV couplings in context of searches at the future HL-LHC ( √ s = 14 TeV, L = 3000 fb −1 ). Here, we have assumed the χ 0 1 to undergo prompt decay. Naively speaking, a λ ijk u c i d c j d c k type of RPV scenario, where the LSP would decay into a multijet final state: χ 0 1 → j u j d j d (j u = u, c, t and j d = d, s, b), would be expected to be amply sensitive to search strategies which considers large jet multiplicity in the final state. However, if the jets produced from the decay of χ 0 1 are highly collimated, then they would evade identification as isolated jets, thereby, altering the reach of collider search strategies. Within simplified RPC scenarios, direct wino searches in the W h mediated 1l + 2b + E / T and W Z mediated 3l + E / T (l = e, µ) final states [132] furnishes robust bounds on the mass of winos as a function of M χ 0 1 . In this work, we analyze these collider searches in the context of λ 112 u c d c s c type RPV simplified scenarios 3 (in Section II A and Section II C, respectively) and contrast them with the results for RPC scenarios in [132]. Additionally, we also explore the future reach of direct wino searches in the W h mediated 1l + 2γ + jets + E / T final state (Section II B) and W Z mediated 3l + 2b + jets + E / T final state (Section II D), respectively characterized by λ 112 u c d c s c and λ 113 u c d c b c type of RPV operators. We have considered final states containing leptons/photons in addition to the multiple jets since they are easier to trigger and offer a cleaner signature. A few benchmark scenarios and their collider implications are discussed in Section III. We conclude in Section IV.

II. COLLIDER ANALYSIS
A simplified SUSY scenario [133] with mass degenerate wino like χ 0 2 , χ ± 1 , and a bino like χ 0 1 is considered in this analysis. We consider the direct production of wino-like χ 0 2 χ ± 1 pair due to its higher production cross-section compared to wino-type neutralino pair (χ 0 2 χ 0 2 ) or chargino pair (χ ± 1 χ ∓ 1 ). Furthermore, the wino production cross-section is also roughly ∼ 2 times larger than the higgsino production rates. Correspondingly, the other SUSY particles namely sleptons, squarks, heavy Higgses and the heavier electroweakinos (χ 0 3 , χ 0 4 , χ ± 2 ) have been fixed at a higher mass in order to decouple their effects on our study.
Direct wino pair production is considered (pp → χ 0 2 χ ± 1 ) and a detailed collider analysis is performed in multifarious final states originating from the cascade decay of the aforesaid χ 0 2 χ ± 1 pair. As stated in Section I, our aim is to study the collider ramifications of the baryon number violating RPV operator in simplified MSSM. To reiterate the structure of this paper, we study the implications of λ 112 u c d c s c type RPV term in Section II A, II B and II C and λ 113 u c d c b c type RPV term in Section II D. In light of these terms, the χ 0 1 decays into a uds final state in the initial three cases while the χ 0 1 decays into a udb final state in the latter case, resulting in final states with large jet multiplicity. The Feynman diagrams of the signal processes considered in Section II A, II B, II C and II D have been illustrated in Figure 1   In the present work, the signal events have been generated using Pythia-6.4.28 [134,135], while the MadGraph aMC@NLO [136] framework has been used to generate the background events at leading order (LO) parton level in SM. Subsequent showering and hadronization has been performed through Pythia-6.4.28. The background events have been generated by matching up to 3 jets (the 3 jet matched sample of a background process bkg will be represented as bkg+jets) except for the W/Z +jets background process for which the 4 jet matched sample is used. The fast detector response has been simulated using Delphes-3.4.1 [137]. The default ATLAS configuration card which comes along with Delphes-3. ).
In the following subsections, we present a detailed discussion of the collider search strategy employed to maximize the signal significance in the corresponding search channels and present our results on the projected reach of direct wino searches in these respective search channels at the HL-LHC.

A. Searches in
The signal process considered in this subsection is illustrated in Figure 1(a). The χ ± 1 and χ 0 2 are assumed to decay into W χ 0 1 and hχ 0 1 , respectively, with a branching ratio of 100%, while, the SM branching values for h → bb (∼ 57% [140]) and W → l ν (∼ 31.7% [140], l = e, µ, τ ) have been considered. The cascade decay process culminates in two χ 0 1 along with other SM particles. The RPV operator: λ 112 u c d c s c implies χ 0 1 → uds, resulting in multiple light quark jets in the final state. The cascade decay chain eventually results in W h mediated 1l + 2b + jets + E / T final state.
An event is required to have exactly one isolated lepton (l = e, µ), at least two light jets (N j ≥ 2), and exactly two b jets in the final state. The electron (muon) is considered to be isolated if Σp others T /p l T is ≤ 0.12 for electrons and ≤ 0.25 for muons, where, Σp others T is the scalar sum of transverse momenta of charged particles with p T ≥ 0.5 GeV (excluding the lepton under consideration) within a cone of radius ∆R = 0.5 centred around the direction of lepton momentum and p l T is the transverse momentum of the lepton. Here, ∆R is defined as: ∆R = ∆η 2 + ∆φ 2 , where, ∆η and ∆φ are the differences in pseudorapidity and the azimuthal angle, respectively, between the lepton under consideration and the charged particle. The isolated electron (muon) is required to have p T > 30 GeV, while the lighter jets and the b jets are required to have p T > 20 GeV. In addition, the final state leptons and quarks must lie within a pseudorapidity range of ≤ |2.5|.
The most dominant source of background is tt + jets. Contributions to the background also arise from W Z + jets, W W + jets and ZZ + jets when W, Z undergoes decay via leptonic decay modes.
Additional contributions arise from W h + jets and Zh + jets when the h decays to bb while the W/Z decays leptonically. Contributions from W bb + jets, W cc + jets (here, the c jet get mistagged as a b jet) and W + jets are also considered. Here, we have considered the NLO cross-section for tt + jets, where the NLO cross-section has been computed by multiplying the NLO k factor (k = 1. where, L is the integrated luminosity (L = 3000 fb −1 for HL-LHC) and Ef f. represents the efficiency of the signal region 5 . distribution for the signal benchmark points and the tt + jets background has been shown in Figure 2(a) 6 .
The distributions for BP1-A, BP1-B and BP1-C in Figure 2 have been illustrated as red, blue and purple solid colors while the tt + jets background has been shown in brown color.
The tt + jets background also undergoes a considerable reduction upon the application of a lower bound on the contransverse mass (M CT ) [141,142], where M CT is defined as, Here, p T bi and E bi T are transverse momentum and energy of the i-th b-jet. The normalized M CT distribution for the signal benchmark points and the tt + jets background has been shown in Figure 2 The invariant mass of the first three p T ordered light jets, M j 1 j 2 j 3 , and the scalar sum of their transverse momenta, H T , are also utilized in performing the cut based analysis. The larger mass difference (∆M ) between (χ 0 2 , χ ± 1 ) and χ 0 1 in BP1-C results in the χ 0 1 being produced with a relatively larger boost, thereby, producing more collimated light jets from the decay of χ 0 1 . As a result, the kinematic variables constructed by using the momenta of the leading light jets (H T and M j 1 j 2 j 3 ) peak at a higher value for signal scenarios with large mass difference between the NLSP and the LSP (viz BP1-C) as compared to the cases where the χ 0 2 and χ 0 1 are closer in mass to each other (viz BP1-B and BP1-A). In addition, the ∆R between the two final state b jets, ∆R b 1 b 2 , and the difference between the azimuthal angles of the final state lepton and the E / T , ∆φ ,E / T , are also used in constructing the optimized signal regions. The three benchmark points, BP1-A, BP1-B and BP1-C, feature an on-shell h produced from the decay of χ 0 2 → χ 0 1 h. For the case of BP1-C, the relatively larger ∆M between χ 0 2 and χ 0 1 results in a h with relatively larger boost as compared to the case of BP1-A and BP1-B. Thereby, the bb pair in the final state of BP1-C is more collimated. As a result, ∆R b 1 b 2 in BP1-C peaks at a smaller value a relatively lower value (at ∆R b 1 b 2 ∼ 1.1) than for BP1-A. Furthermore, the bb pair which originates from the tt + jets background is generated from two different mother particles, and therefore, are widely separated in the azimuthal angle. Consequently, ∆R b 1 b 2 for the tt + jets background peaks at further where the red, blue and purple solid lines represents BP1-A, BP1-B and BP1-C, respectively, while the brown colored region represents the tt + jets background. Additionally, we also consider the azimuthal It is to be noted that the top quark dominantly decays into a bW pair and effectively contributes to the background when one of the W boson undergoes leptonic decay while the other W decays hadronically.
One obtains two solutions for the z-component of momentum of the neutrino ( / p ν z ) produced from the leptonically decaying W : Signal and background yields plane. The projection contours have been derived from searches in the 1l + 2b + jets + E / T final state resulting from the cascade decay of directly produced wino-like χ 0 2 χ ± 1 pair within a simplified model scenario containing λ 112 u c d c s c type RPV term. The solid black line represents the current observed limit at 95% C.L. from direct wino searches in the W H mediated 1l + 2b + E / T final state, in a RPC simplified scenario, derived by ATLAS using the LHC Run-II dataset collected at L ∼ 139 fb −1 [61]. The light green colored region corresponds to the projected exclusion reach (at 95% C.L.) of HL-LHC, derived by ATLAS, in direct wino searches in the W H mediated 1l + 2b + E / T final state within a simplified RPC scenario [132]. The brown dashed line represents the condition for on-shell Higgs production (M χ 0 The optimized selection cuts corresponding to SR1-A, SR1-B and SR1-C have been shown in Table I. The signal yields for BP1-A, BP1-B and BP1-C, along with the corresponding background yields obtained after successive application of selection cuts listed in SR1-A, SR1-B and SR1-C, respectively, have also been shown in Table I. It should be noted that the signal significances 7 tabulated in Table I  as well as the projected reach of direct wino production at the HL-LHC in the analogous channel for the RPC scenario: W h mediated 1l + 2b + E / T final state in [61] and [132], respectively. The current observed limit (at 95% C.L.) reaches up to M χ 0 2 ,χ ± 1 ∼ 720 GeV for M χ 0 1 = 100 GeV. The projected exclusion and discovery contour of ATLAS reaches up to M χ 0 2 ,χ ± 1 ∼ 1300 GeV and ∼ 600 GeV for a bino like χ 0 1 with mass up to 100 GeV at 95% C.L.. The ATLAS exclusion contour has been shown in light green color in Figure 3. Thus, the projected reach of direct wino searches interpreted in a RPC simplified scenario can get significantly weakened in the presence of λ 112 u c d c s c type RPV coupling. In the next three subsections, we further study the collider implications of RPV couplings in different final states.
In the current subsection, we consider the process: , which culminates in 1l+2γ +jets+E / T final state (Figure 1(b)). Here, Br(χ ± 1 → W χ 0 1 ) and Br(χ 0 2 → hχ 0 1 ), have been assumed to be 100%. The small branching rate of h → γγ is a significant drawback for this channel, however, a large photon detection efficiency, sharp di-photon invariant mass peak and a smaller background makes it a promising one. Unlike the W h mediated 1l + 2b + jets + E / T channel (discussed in Section II A), no HL-LHC projection study has been performed for the analogous RPC scenario channel The event selection criteria requires the presence of exactly one isolated lepton (l = e, µ), two photons, and at least two light jets (N j > 2) in the final state. The lepton isolation criteria specified in Section II A is implemented here as well. The final state lepton, jets and photons satisfy the criteria : |η l, jet, γ | < 2.5 and p l, jet, γ T > 30, 30, 20 GeV respectively. In addition, we demand that no pair of final state particles must be within ∆R < 0.5 of each other. Furthermore, a b-jet veto is applied.    Here The normalized distributions of the dominant background processes: tth + jets and W h + jets, are also shown as brown and green colored regions, respectively. In analogy with the analysis in Section II A, the normalized distributions of M j 1 j 2 j 3 and H T for BP2-C is relatively wider and falls smoothly when compared to the analogous distributions for BP2-A and BP2-B. This feature is due to the larger mass splitting between χ 0 2 (χ ± 1 ) and χ 0 1 . The list of selection cuts for these three signal regions along with the cut flow for the three benchmark points have been tabulated in Table II. The total background yield corresponding to the three signal regions, the corresponding signal yields for BP2-A, BP2-B and BP2-C and the signal significances obtained from the cut-based analysis have also been tabulated in Table II C. Searches in the W Z mediated 3l + jets(N j ≥ 2) + E / T channel A study by the ATLAS collaboration, which probed the future reach of directly produced winos in the W Z mediated 3l + E / T final state at the HL-LHC [132], shows a projected exclusion reach up to M χ ± 1 ,χ 0 2 ∼ 1150 GeV for a bino like M χ 0 1 ∼ 100 GeV at 95% C.L. The future reach of direct wino searches at HL-LHC in the W h mediated 3l + E / T channel has also been studied by ATLAS in [144]. The projected reach excludes winos upto ∼ 650 GeV for M χ 0 1 ∼ 0 GeV at 95% C.L.. One of the main reasons behind the weaker reach of W h mediated 3l + E / T channel compared to the W Z mediated process is the longer cascade decay chain in the former case. This results in a smaller event yield even if one assumes a similar signal region efficiency. In the current subsection, we focus only on the analogous W Z mediated final state reinterpreted in λ 112 type RPV simplified scenario.
In the presence of a λ 112 type RPV coupling, the χ 0 1 would decay into χ 0 1 → uds resulting in W Z mediated 3l + jets + E / T final state and the projected exclusions are expected to alter. In the present subsection, we explore this facet and study the projected future reach of W Z mediated 3l + jets + E / T final state at the HL-LHC within the framework of a simplified λ 112 type RPV scenario. The Feynman diagram of the signal process under consideration is illustrated in Figure 1 (c). The decay chain proceed  as follows: The SM value for Br(Z → ll) (∼ 6.72% [140]) has been assumed here.
An event is required to have exactly three isolated leptons with p T > 30 GeV and at least two light jets with p T > 20 GeV in the final state. Among the three final state leptons, two are required to form a same flavor opposite charge (SFOS) lepton pair with invariant mass in the range of |M Z ± 25 GeV|.
In presence of two different SFOS lepton pairs with invariant mass within |M Z ± 25 GeV|, the SFOS pair with invariant mass closest to the Z boson mass is considered to be the correct SFOS pair and their invariant mass is represented as M SF OS ll . The lepton isolation criteria discussed in Section II A is applied here as well.
The important sources of background are W Z + jets, ZZ + jets and V V V + jets (V = W, Z).
Potential contribution to background can also arise from W h + jets and Zh + jets processes, however, their contribution is much lesser when compared to the diboson and triboson backgrounds. Consequently, we ignore the contribution from both, W h + jets and Zh + jets.  Table III. The signal and background yields obtained upon the successive application of the selection cuts have also been listed in Table III along with the respective values of signal significance.
The future reach of direct wino searches in the W Z mediated 3l + jets + E / T final state at HL-LHC is studied. In this context, we evaluate the projected exclusion (> 2σ) and projected discovery (> 5σ) contours assuming zero systematic uncertainty in the M χ 0 2 ,χ ± 1 -M χ 0 1 plane (shown in Figure 7). The light blue colored region and the dark blue colored regions in Figure 7 represents the projected  Since BP4-A features lower mass difference between χ 0 2 (χ ± 1 ) and χ 0 1 than BP4-B and BP4-C, the light jets emanating from the decay of less boosted χ 0 1 in BP4-A carry relatively smaller p T as compared to the jets produced from the decay χ 0 1 in the other two benchmark points. This in turn shifts the peak of the H T distribution towards higher values for BP4-B and BP4-C.  Table IV. The cut flow exhibiting the signal and background yields is also presented in Table IV along with signal significance.
We derive the projected exclusion and discovery contour in the context of HL-LHC, which have been illustrated in light blue and dark blue colors, respectively, in Figure 9. GeV. Thus, we observe that a variety of interesting multiparticle final states can be produced from the cascade decay of direct wino production on account of the introduction of R-parity violating operators, many of which display a strong potential to be excluded and even discovered at the HL-LHC. In the present work, we explored the future prospects of two different types of RPV operator: λ 112 u c d c s c (in W h mediated 1l+2b+jets+E / T channel, W h mediated 1l+2γ +jets+E / T channel, W Z mediated 3l+jets+E / T channel) and λ 113 u c d c b c (in W Z mediated 3l + 2b + jets + E / T channel) by performing a detailed cut based analysis involving all relevant background processes. We intend to evaluate the implications from various other types of RPV operators on a multitude of search channels in an ongoing work. A more sophisticated analysis of the underlying final state jets and better understanding of the multiparticle backgrounds might help in further improving the future discovery prospects in these channels. Before concluding this work, we briefly discuss the implications from pure higgsino searches and also analyze the projected sensitivity for a few realistic MSSM benchmark points where the neutralinos and charginos are gaugino-higgsino admixtures.

III. BENCHMARK SCENARIOS
We begin our discussion in this section by considering two benchmark points with higgsino-like χ 0 2 , χ 0 3 , χ ± 1 and bino-like χ = 500 GeV, M χ 0 1 = 200 GeV), for the four signal channels considered in this work. BP-αW and BP-βW fall within the projected exclusion reach of direct wino searches in the W h mediated 1l + 2b + jets + E / T final state (see Figure 3).
However, direct higgsino searches in the same search channel results in a signal significance of ∼ 1.56 and ∼ 0.83 for their pure-higgsino counterparts BP-αH and BP-βH , respectively, thereby, putting both these benchmark points outside the projected exclusion region. BP-αW also falls within the projected discovery reach of direct wino searches in the other three search channels (see Figure 5, 7 and 9). However, direct higgsino searches (for BP-αH ) result in a signal significance of ∼ 2.94, ∼ 2.30 and ∼ 1.76 in W h mediated 1l + 2γ + jets + E / T , W Z mediated 3l + jets + E / T and W Z mediated 3l + 2b + jets + E / T search channels, respectively, and thus, BP-αH falls within (outside) the projected exclusion (discovery) reach of the aforementioned former two channels and even outside the projected exclusion region of the later search channel. BP-βW also falls within the projected discovery reach of direct wino searches in the W h mediated 1l + 2γ + jets + E / T channel, and within the projected exclusion reach in the W Z mediated 3l + jets + E / T tan β Signal significance   and W Z mediated 3l + 2b + jets + E / T . On the contrary, in direct higgsino searches, the signal significance of BP-βH marginally crosses 2σ in the W h mediated 1l + 2γ + jets + E / T channel, while registers a value of ∼ 1.66 and ∼ 1.4 in the W Z mediated 3l + jets + E / T and W Z mediated 3l + 2b + jets + E / T channels, respectively. The direct higgsino searches, thus, imply weaker exclusion reach than the analogous wino counterparts, mainly, due to a smaller production cross-section.
In the MSSM, the tree level electroweakino sector is governed by four input parameters: M 1 (bino mass parameter), M 2 (wino mass parameter), µ (higgsino mass parameter) and tan β (ratio of vacuum expectation value of the two Higgs doublets). We first consider the case of BP-βW (M 1 ∼ 200 GeV, M 2 ∼ 500 GeV, µ ∼ 2 TeV) and study the collider implications of varying tan β. In this respect, we the signal yield is computed in each of the 4 signal channels by multiplying the χ ± 1 χ 0 2 pair production cross-section (σ(χ ± 1 χ 0 2 )) with the branching rates of the relevant cascade decay modes, the integrated luminosity (L = 3000 fb −1 ) and the efficiency of the respective signal regions. In the case of W h mediated signal channels (W h mediated 1l + 2b + jets + E / T and W h mediated 1l + 2γ + jets + E / T ), the relevant ino branching modes are: Br(χ 0 2 → hχ 0 1 ) and Br(χ ± 1 → W χ 0 1 ), while the relevant ino decay modes in the later two cases (W Z mediated 3l + jets + E / T and W Z mediated 3l + 2b + jets + E / T ) are: Br(χ 0 2 → Zχ 0 1 ) and Br(χ ± 1 → W χ 0 1 ). The SM branching rates are considered for the successive decay of Z, h and W bosons. Prospino [145,146] is used to compute σ(pp → χ ± 1 χ 0 2 ) at NLO while SUSY-HIT [147] is used to compute the ino branching rates. The corresponding ino pair production cross-section and the ino branching rates are dependent on tan β and have been shown in Table V against their respective tan β values. We have also listed the respective signal significance values in the 12 signal regions (4 different analysis channels × 3 signal regions in each) in Table V. The coupling of the Z boson with a pair of neutralinos (χ 0 i χ 0 j (i, j = 1, 2, 3, 4)) is crucially controlled by the higgsino composition of χ 0 i,j while the hχ 0 i χ 0 j couplings are proportional to the gaugino-higgsino admixture in χ 0 i,j . As stated earlier, the tree level neutralino mixing matrix is governed by M 1 , M 2 , µ and tan β. Thereby, the Zχ 0 i χ 0 j and hχ 0 i χ 0 j couplings are also controlled by the same input parameters at the tree level. In the present case, χ 0 2 is dominantly wino in nature with a small higgsino component (which varies with tan β) in all the 8 benchmark points. This makes χ 0 2 → χ 0 1 h as the most preferable decay mode of χ 0 2 with a branching ratio of ∼ 98.34% for tan β = 5. However, Br(χ 0 2 → χ 0 1 h) decreases up to ∼ 88.22% upon increasing tan β to 40. Correspondingly, Br(χ 0 2 → χ 0 1 Z) increases from ∼ 1.65% at tan β = 5 up to ∼ 11.77% at tan β = 40, thus, registering a nearly ∼ 7 times improvement. The increase in the branching rate of χ 0 2 → χ 0 1 Z is reflected in the signal significance of W Z mediated analysis channels (shown in Table V and bottom panel of Figure 10). The signal significance of SR3-A, SR3-B and SR3-C (the optimized signal regions corresponding to W Z mediated 3l+jets+E / T channel) increases from 0.14, 0.14 and 0.13 (at tan β = 5) to 0.98, 1.01 and 0.94, respectively, at tan β = 40. A similar increase is also evident in the signal significance of SR4-A, SR4-B and SR4-C (signal regions corresponding to the W Z mediated 3l + 2b + jets + E / T channel) which has a value of 0.001, 0.004 and 0.004, respectively, at tan β = 5 while the respective values at tan β = 40 are 0.01, 0.03 and 0.03. Equivalently, the signal significance of the W h mediated signal channels decrease with increasing tan β. In Figure 10, we have illustrated the variation of the signal significance (shown along y-axis) of the 4 analysis channels considered in this work with tan β (shown along x-axis) for BP-βW . For a particular final state, the largest value of signal significance among the respective 3 signal regions has been considered in Figure 10.
We also analyze additional realistic benchmark scenarios where we vary the higgsino and wino admixtures in the neutralinos and charginos, and study the projected reach of HL-LHC in probing them in the W h mediated 1l + 2b + jets + E / T , W h mediated 1l + 2γ + jets + E / T , W Z mediated 3l + jets + E / T and W Z  Cross-section  Cross-section  Cross-section   mass spectrum is shown in Table VI. We have also listed the higgsino and wino composition in Table VI. In the previous case of BP-βW , the amount of higgsino admixture in χ 0 2 was 1% for tan β = 10. Also, χ 0 3 , χ 0 4 and χ ± 2 were much heavier (∼ 2 TeV) and therefore, the contributions to the signal yield from χ 0 2 χ ± 1 , χ 0 3 χ ± 1 , χ 0 4 χ ± 1 , χ 0 3 χ ± 2 and χ 0 4 χ ± 2 production processes could be safely ignored due to their small cross-sections. However, in the present case, when we attempt to introduce a finite amount of higgsino admixture in χ 0 2 while keeping its mass fixed at ∼ 500 GeV, we are forced to reduce the value of µ. Consequently, χ 0 3 , χ 0 4 and χ ± 2 are no more in the ∼ O(1) TeV range. For example, in the case of BP-β 10 W where the χ 0 2 is composed of higgsinos and winos in the proportion of ∼ 10% and ∼ 90%, respectively, we are required to choose µ ∼ 670 GeV. As a result, χ 0 3 , χ 0 4 and χ ± 2 also become admixtures of winos and higgsinos and have a mass of ∼ 672.90 GeV, ∼ 693.11 GeV and ∼ 692.73 GeV, respectively. Correspondingly, it would be imperative to take into account the contributions from the heavier chargino-neutralino pairs as well. In the present scenario, therefore, contributions to the signal yield can potentially arise from: The production cross-section of these charginoneutralino pairs for BP-β 10 W , BP-β 30 W , BP-β 50 W and BP-β 70 W are listed in Table VI. Here, we have used Prospino-2.1 to compute the cross-sections at NLO. The branching ratios of χ 0 i → Z/hχ 0 1 (i = 2, 3, 4) and χ ± j → W χ 0 1 (j = 1, 2) are also shown in Table VI where SUSY-HIT has been used to compute them. The signal significance of these 4 benchmark points is computed for (SR1-A, SR1-B, SR1-C), (SR2-A, SR2-B, SR2-C), (SR3-A, SR3-B, SR3-C) and (SR4-A, SR4-B, SR4-C), corresponding to W h mediated 1l + 2b + jets + E / T , W h mediated 1l + 2γ + jets + E / T , W Z mediated 3l + jets + E / T and W Z mediated 3 + 2b + jets + E / T channels, respectively, and have been listed in Table VI. It can be observed from Table VI that the signal significance of the W Z mediated channels improve with an increase in the amount of higgsino content in χ 0 2 . For example, the signal significance of SR3-A and SR4-A increases from ∼ 0.09 and ∼ 0.03 for BP-β 10 W to ∼ 0.34 and ∼ 0.58 for BP-β 70 W . This increase is mainly an outcome of the combined effect of an increased χ 0 2 /χ 0 3 → Zχ 0 1 branching rate, an increased σ(χ 0 3 χ ± 1 ) and a lowered σ(χ 0 2 χ ± 1 ). Upon combining the highest signal significance values in each of the analysis channels in quadrature, we obtain a combined signal significance of 2.01, 1.98, 2.33 and 2.12 for BP-β 10 W , BP-β 30 W , BP-β 50 W and BP-β 70 W , respectively. Before concluding this section, we would like to note that additional contribution to the signal yield may also arise by considering the cascade decay modes of the heavier charginos and neutralinos. For example, in a generic case, the χ 0 3 can decay into a Z/hχ 0 2 pair and this χ 0 2 can further decay into a Z/hχ 0 1 pair, resulting in an additional Z/h bosons in the final state. A multifarious number of such possibilities are potentially feasible, and are outside the scope of this present work. We intend to explore such scenarios on a case by case basis in a future work. In the last section, we provide a detailed summary and conclusion to our results.

IV. SUMMARY AND CONCLUSIONS
In this work, we studied the sensitivity of the future HL-LHC to direct wino searches in a simplified scenario with λ 112 u c d c s c and λ 113 u c d c b c type RPV operators. The collider implications of λ 112 u c d c s c type RPV coupling on direct wino searches in the W h mediated 1l + 2b + jets(N j 2) + E / T , W h mediated 1l + 2γ + jets(N j 2) + E / T and W Z mediated 3l + jets(N j 2) + E / T has been studied in Section II A, II B and II C, respectively, while Section II D examined the projected reach of direct wino searches in the W Z mediated 3l + 2b + jets(N j 2) + E / T final state, by the virtue of λ 113 u c d c b c type RPV operator.
The direct production of mass degenerate wino type χ ± 1 χ 0 2 was considered which eventually underwent cascade decay into bino type χ 0 1 along with the h, W and/or Z bosons. In the presence of λ u c d c s c (b c ) type RPV operator, the χ 0 1 decays into χ 0 1 → uds (χ 0 1 → udb) resulting in jets in the final state. A detailed collider analysis was performed in the aforesaid channels by taking into account all relevant background samples and by considering a multitude of important kinematic variables. Direct wino searches in the W h mediated 1l+2b+jets+E / T final state in the context of λ u c d c s c type RPV scenario exhibited a projected 2σ exclusion (5σ discovery) reach up to M χ ± 1 ,χ 0 2 ∼ 680 GeV (∼ 450 GeV) for a bino like χ 0 1 with mass up to ∼ 0 GeV. It is to be noted that the respective reinterpretation within a RPC scenario (studied in [132]) furnishes considerably stringent projections, and the respective 95% C.L. projected exclusion contour reaches up to M χ ± 1 ,χ 0 2 up to ∼ 1100 GeV for bino like χ 0 1 with mass M χ 0 1 ∼ 0 GeV. The same simplified RPV scenario was also interpreted in terms of searches in the W h mediated 1l + 2γ + jets + E / T final state, and a relatively stronger potential reach was observed. Here, the projected exclusion and discovery contours had reach up to ∼ 700 GeV and ∼ 600 GeV, respectively.
As discussed previously in Section II C, the future reach of direct wino searches in the W Z mediated 3l+E / T final state within a RPC framework has been studied in [132], and the projected 95% C.L. exclusion contour reaches up to ∼ 1150 GeV for a bino like χ 0 1 with mass up to ∼ 0 GeV. We performed a collider study to derive the projected reach of direct wino searches in the W Z mediated 3l + jets + E / T final state and reinterpreted the projected reach within a λ 112 u c d c s c type RPV scenario. The projected exclusion and discovery contours displayed a considerably weaker reach as compared to the RPC scenario [132].
The projected 2σ exclusion contour reached up to ∼ 660 GeV while the projected 5σ discovery contour reached up to ∼ 490 GeV. Similarly, in Section II D, the projected reach of direct wino searches in the W Z mediated 3l + 2b + jets + E / T final state was reinterpreted to simplified scenario with λ 113 u c d c b c type RPV coupling. The projected exclusion reach of this search channel reaches up to ∼ 600 GeV for M χ 0 1 in between ∼ 150 GeV and ∼ 250 GeV.
A few benchmark scenarios have been explored in Section III. The future reach of direct higgsino production at the HL-LHC in the aforesaid channels was analyzed for BP-αH and BP-βH . It is observed that the direct higgsino searches furnish weaker projection contours compared to the wino counterparts due to a smaller production rate. Furthermore, the sensitivity of the analysis channels to tan β is also studied. The W Z mediated channels displayed an improvement in signal significance with an increase in tan β, will all other MSSM input parameters kept fixed. The implications of a finite wino-higgsino mixing in the heavier ino states on the projected reach of the search channels considered in this work is also analyzed for the case of BP-β 10 W , BP-β 30 W , BP-β 50 W and BP-β 70 W . These benchmark points resulted in a combined signal significance of 2.01, 1.98, 2.33 and 2.12, respectively, thereby, marginally falling within the projected exclusion reach (except for BP-β 30 W ) of HL-LHC.