Higgs and Z assisted stop searches at hadron colliders

Current searches for the light top squark (stop) mostly focus on the decay channels of t˜→tχ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde{t}\to t{\chi}_1^0 $$\end{document} or t˜→bχ1±→bWχ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde{t}\to b{\chi}_1^{\pm}\to bW{\chi}_1^0 $$\end{document}, leading to final states for stop pair productions at the LHC. However, in supersymmetric scenarios with light neutralinos and charginos other than the neutralino lightest supersymmetric particle (LSP), more than one decay mode of the stop could be dominant. While those new decay modes could significantly weaken the current stop search limits at the LHC, they also offer alternative discovery channels for stop searches. In this paper, we studied the scenario with light Higgsino next-to-LSPs (NLSPs) and Bino LSP. The light stop decays primarily via t˜1→tχ20/χ30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\tilde{t}}_1\to t{\chi}_2^0/{\chi}_3^0 $$\end{document}, with the neutralinos subsequent decaying to a Z boson or a Higgs boson: χ20/χ30 → χ10h/Z. Pair production of light stops at the LHC leads to final states of or . We consider three signal regions: one charged lepton (1ℓ), two opposite sign charged leptons (2 OS ℓ) and at least three charged leptons (≥3ℓ). We found that the 1ℓ signal region of channel has the best reach sensitivity for light stop searches. For 14 TeV LHC with 300 fb−1 integrated luminosity, a stop mass up to 900 GeV can be discovered at 5σ significance, or up to 1050 GeV can be excluded at 95% C.L. Combining all three decay channels for 1ℓ signal region extends the reach for about 100−150 GeV. We also studied the stop reach at the 100 TeV pp collider with 3 ab−1 luminosity, with discovery and exclusion reach being 6 TeV and 7 TeV, respectively.


Introduction
The milestone discovery of a light Standard Model (SM)-like Higgs boson at the Large Hadron Collider (LHC) [1,2] calls for the new physics beyond the SM to solve the "Hierarchy problem" [3]. Among various new physics beyond the Standard Model, Supersymmetry (SUSY) remains to be one of the most attractive candidates because of the elegant solution to the "Hierarchy problem" and the accommodation of the light SM-like Higgs. In the supersymmetric models, the third generation scalar tops (stop) might be the most relevant ones given the large top Yukawa coupling to the Higgs sector. Searching for the heavy top partners is one of the primary goals of the LHC to solve the puzzle of electroweak symmetry breaking and the stabilization of the weak scale. The masses for stops are constrained to be less than about a few TeV to avoid extra fine-tuning to the light Higgs mass. There are two scalar tops in the Minimal Supersymmetric Standard Model (MSSM):t L andt R , which are the superpartners of the left-and right-handed top quarks, respectively. To provide large enough loop corrections to the tree-level Higgs mass (m tree h ≤ m Z ), a large left-right mixing termÃ t in the stop mass matrix oft L andt R is typically needed, leading to two mass eigenstates,t 1 andt 2 , with relatively large mass splittings. One of the stops can be as light as a few hundred GeV, leaving the LHC an ideal place to search for those relatively light stops.
The current light stop searches considered a 100% decay branching fraction of stops decaying into particular search channels for simplicity. However, in realistic MSSM, there are typically more than one decay modes open, depending on the mass spectrum of neutralinos and charginos, which significantly weakens the current search limits [21][22][23][24][25]. The scenario we consider in this work is Higgsino-like Next-to-LSPs (NLSPs) and a Bino-like LSP with mass hierarchy M 1 < µ < M 3SQ M 2 . The lighter stop dominantly decays viã t 1 → tχ 0 2 /χ 0 3 given the large SU(2) L gauge coupling and large top Yukawa coupling of a mostly left-handedt 1 , with neutralinos subsequent decaying to a gauge boson or a Higgs boson χ 0 2 /χ 0 3 → χ 0 1 h/Z, leading to tthh E T , ttZZ E T or tthZ E T final states for the stop pair production at the LHC. Given the relatively clean final states containing at least one lepton at the LHC, our search regions are characterized by the charged leptons: 1 signal region with exact one lepton (e or µ), 2 OS signal region with exact two opposite-sign (OS) leptons, and ≥ 3 signal region with at least three leptons.
The rest of the paper is organized as follows. In section 2, we briefly review the stop sector in the MSSM, introduce the mass and mixing parameters, and explore the stop decay in different scenarios. In section 3, we summarize the current LHC search limits on stop search by both ATLAS and CMS collaborations, and validate our simulation with the CMS study oft 2 [19], which has the same final states as our process. We also recast the CMS results in mt 1 vs. m χ 0 1 plane. In section 4, we perform a detailed collider analysis of stop search sensitivity in the three signal regions at the √ s = 14 TeV LHC. In section 5, we extend our analyses to the future √ s = 100 TeV pp machine. In section 6, we conclude.

MSSM stop sector
We work in the framework of the MSSM and focus primarily on the third generation squark sector, with relatively light Higgsino-like NLSPs (a small |µ|) and a Bino-like LSP (a small M 1 ). Other SUSY particles including the Winos, gluinos, sleptons, and the first and second generation squarks are assumed to be heavy and decoupled to be 2 TeV. We also decouple the non-SM heavy Higgses by setting m A to be 2 TeV. The gauge eigenstates of the third generation squarks are (t L ,b L ),t R andb R , with (t L ,b L ) forming a SU(2) L doublet with a soft SUSY breaking mass M 3SQ ,t R andb R being SU(2) L singlets with soft breaking masses M 3SU , and M 3SD , respectively. The mass matrix JHEP05(2018)135 of the stop sector is [26,27] where the ∆ũ L and ∆ũ R terms come from the D-term contribution in the MSSM, which are to the order of m 2 Z . The off-diagonal left-right mixing termÃ t is given by: with A t representing the trilinear coupling, tan β = H 0 u / H 0 d being the ratio of the vacuum expectation values of two Higgs fields H 0 u and H 0 d in the MSSM. The stop mass matrix can be diagonalized with mixing angle θ t : resulting in two mass eigenstatest 1 andt 2 , with convention mt Given the large top Yukawa coupling, the stop sector provides the dominant contribution to the radiative corrections of the SM-like Higgs mass in the MSSM. For M 3SQ = M 3SU = M SUSY , the correction to the SM-like Higgs mass squared is [28,29]: In the minimal mixing case withÃ t = 0, a large M SUSY around 5∼10 TeV is needed to guarantee a SM-like Higgs mass ∼ 125 GeV. In the maximal mixing case withÃ t = √ 6M SUSY , a relatively small M SUSY ∼ TeV can be accommodated given the additional contribution from theÃ t term. In the general MSSM where M 2 3SQ = M 2 3SU , the light stop t 1 as light as 200 GeV is still consistent with a SM-like Higgs mass around 125 GeV. A large mass splitting between the stop mass eigenstates, however, is typically needed, resulting in mt 2 500 GeV in general [30,31]. In the scenario of Higgsino-like NLSPs and a Bino-like LSP, the two neutralinos χ 0 2 , χ 0 3 and charginos χ ± 1 are nearly degenerate, leading to almost undistinguishable collider signals. To illustrate the MSSM mass parameters and the corresponding mass spectrum, we showed one benchmark point in table 1, which consists of a mostly left-handed stop, three almost degenerate Higgsino-like NLSPs (χ 0 2 , χ 0 3 and χ ± 1 ), and a Bino-like LSP (χ 0 1 ). A t is chosen such that the SM-like Higgs mass is in the range of 125 ∼ 126 GeV. Even thoughÃ t is large, the mixing betweent L andt R is still small because of the large mass difference between those two components. If there is a significant left-right mixing, then thẽ t 1 → tχ 0 2 channel is highly suppressed, while thet 1 → χ ± 1 b channel will have a comparable BR witht 1 → tχ 0 3 . For this benchmark point, the decay branching fractions are shown in table 2.t 1 → tχ 0 2,3 are dominant, with branching fractions close to 50% each, given the large SU(2) L JHEP05(2018)135 150 300 2000 2890  650  2000  10  145 308 311 305 620 125   Table 1. Mass parameters and mass spectrum of SUSY particles for one benchmark point. All masses are in units of GeV.
Decay channel Branching fractioñ Decay channel Branching fraction gauge coupling and large top Yukawa coupling of a mostly left-handedt 1 . The decay channels oft 1 → tχ 0 1 andt 1 → bχ + 1 are highly suppressed due to the relatively small U(1) Y gauge coupling and bottom Yukawa couplings, with branching fractions of only 3 − 4%, leading to large relaxation of the current search limits. Neutralinos χ 0 2 /χ 0 3 subsequently decay to a Higgs boson or a Z boson. In the case of positive µ, the χ 0 2 (χ 0 3 ) dominantly decays to Zχ 0 1 (hχ 0 1 ), due to the different composition of χ 0 2.3 as 1 , as well as the closeness of M 1 and µ. Flipping the sign of µ leads to the reversal of the branching fractions into h and Z modes [32]. Therefore, changing the sign of µ has negligible impact on the collider analysis. Given the degeneracy of χ 0 2 and χ 0 3 , and close to 50% branching fraction each fort 1 → tχ 0 2,3 , the stop dominantly decays to thχ 0 1 and tZχ 0 1 , with branching fractions of about 45%, respectively. The left-handed sbottom decay modes ofb 1 → bχ 0 2 /χ 0 3 are highly suppressed due to the small bottom Yukawa couplings, whileb 1 → tχ ± 1 becomes dominant with branching fraction as high as 98%. Therefore the sbottom signal will not contaminate the stop signal.
The current searches for the stop mainly focus on the decay channelt 1 → tχ 0 1 and t 1 → bχ ± 1 → bW ( * ) χ 0 1 , assuming a 100% decay branching fraction into these two channels. Hadronic, semileptonic, and dileptonic channels have been analyzed, with the semileptonic channel typically providing the best limit. The upper limits on the stop mass are about 1120 GeV, depending on the assumption of the decay branching fractions, and masses of the neutralinos and charginos.
In addition to the above two searching channels, the ATLAS and CMS groups also used two different analysis strategies to optimize the search sensitivity of direct stop searches for the decay channels oft 1 → cχ 0 1 andt 1 → bf f χ 0 1 , in particular, for small mass splitting between stop and χ 0 1 . The upper limit on the stop mass is much weaker, about 580 GeV at 95% C.L [4, 14-17].

Recasting CMS search results
Both ATLAS and CMS groups performed the search for the heavier stop (t 2 ) [18, 19] with cascade decays oft 2 →t 1 h and/ort 2 →t 1 Z witht 1 further decaying viat 1 → tχ 0 1 assuming mass relation mt 1 − m χ 0 1 = m t , leading to the finals states of tthh E T , tthZ E T and ttZZ E T for the pair production oft 2 at the LHC. The analysis of the CMS group is based on the multiplicities of the leptons, jets, b-jets, missing energy E T , transverse mass m T and 3ℓ on-Z Figure 2. The comparison of 95% C.L. upper limits between CMS results ("+" symbol lines) and our simulations (solid lines) for the LHCt 2 pair production,  We first reproduce the CMS exclusion limits fort 2 as a validation of our analyses. Event samples are generated using Madgraph 5 [33], processed through Pythia 6 [34] for the fragmentation and hadronization and then through Delphes 3 [35] for the detector simulation. The root package TLimit [36] is used to calculate the 95% confidence level upper limits. Figure 2 shows the comparison of the 95% C.L. upper limits between CMS results ("+" symbol lines) [19] and our simulations (solid lines) in the plane of mt 2 vs. mt 1 fort 2 →t 1 h (left) andt 2 →t 1 Z (right) assuming a 100% branching fraction. Our simulations match the CMS results quite well except for the edge region. The discrepancy between the CMS results and our simulations are mostly due to the different detector simulations of the signal process and systematics estimation.
Combining both h-and Z-channel, the 95% C.L. upper limits in the plane of mt 2 vs mt 1 for BR(t 2 →t 1 Z) =100% (purple), 50% (black) and 0% (red) are shown in the left panel of figure 3, for the comparison between the CMS results and our simulations. The decay channel oft 2 →t 1 h is only considered when the Higgs boson production is kinematically open.
Since the CMSt 2 search channel has the same final states as ourt 1 study:t 1t *  Figure 3. The comparison of 95% C.L. upper limits between CMS results ("+" symbol lines) and our simulations (solid lines) for the LHCt 2 pair production, with combinedt 2 →t 1 h/Z and to that of the lighter stop in the scenario of Higgsino-NLSP and Bino-LSP. We use exactly the same event selections as the CMSt 2 search to obtain our simulated signal event yields after cuts and we use the backgrounds estimations and observed data yields in ref.
[19] to get the lighter stop search limits. The recasted results in the plane of mt 1 vs. m χ 0 1 are shown in the right panel of figure 3 for ttZZ E T (including 3 "on-Z") and tthZ E T (including 1 , 2 OS , 3 "off-Z" and 3 "on-Z") channels. Because the reach of the 2 SS signal region is very low, it is not considered in this analysis. There is also no excluding reach for the channel of tthh E T due to its low branching fraction as shown in figure 1. The light stop mass up to 480 GeV is excluded at 95% C.L. for a small mass LSP ∼ 25 GeV via the tthZ E T channel. For the ttZZ E T channel, the light stop mass up to 530 GeV is excluded at 95% C.L. for a massless LSP.

Collider analyses at √ s = 1TeV
In MSSM with more than one neutralino/chargino lighter than the stop, typically more than one decay mode for stop are present, some of which even dominate the most commonly studied channels oft 1 → tχ 0 1 /bχ + 1 . Those extra stop decay modes weaken the current search limits usingt 1 → tχ 0 1 /bχ + 1 . Furthermore, the new decay channels offer alternative discovery potential for the stops. In our analyses, we work in the scenario of a Bino LSP with Higgsino NLSPs lighter thant 1 , assuming the mass hierarchy of M 1 < µ < M 3SQ M 2 . The benchmark point shown in table 1 is only for the illustration purpose. In the following analyses, we perform a broad scan over the mass parameter space: • M 3SQ from 400 to 1250 GeV with a step size of 25 GeV, corresponding to mt 1 varying from 350 GeV to about 1260 GeV.
• We further require mt Event samples including signals and all the SM backgrounds are generated for 14 TeV LHC, using Madgraph 5 [33], processed through Pythia 6 [34] for the fragmentation and hadronization, and then through Delphes 3 [35] with the Snowmass combined LHC No-Pileup detector card [37] for the detector simulation. Both the SM backgrounds and the stop pair production signal are normalized to the predicted cross sections, calculated including higher-order QCD corrections [38][39][40][41][42][43][44][45]. For the event generation, the top quark mass m t is set to be 175 GeV, and the Higgs mass m h is set to be 125 GeV.

Event selection
For the stop pair productiont 1t * 1 at the LHC, both stops decay via tχ 0 2 /χ 0 3 with neutralinos subsequent decaying to a Z boson or a Higgs boson, leading to final states of tthh E T , ttZZ E T and tthZ E T . Similar to the CMSt 2 searches, we divide the signal regions into three primary categories: (1) one charged lepton (1 ), (2) two opposite-sign charged leptons (2OS ), (3) at least three charged leptons (≥ 3 ). "on-Z" region and "off-Z" regions are further defined for the ≥ 3 case, with m window of m Z ± 15 GeV. The signal region of two same-sign leptons is not considered in this analysis because the cross section of this signal region is quite small, which results in limited reach of this signal region.
The jets are reconstructed using anti-k t algorithm with cone radius of 0.5. All jets are required to meet the basic selection cuts of p j T > 30 GeV and η j < 2.5. All leptons (e or µ) are required to meet the basic selection cuts of η < 2.5 and p T > 10 GeV. In addition to the selection cuts mentioned above, we also apply some advanced cuts which are defined below: • E T , the magnitude of the missing transpose momentum p miss T .
• H T , the scalar sum of the p T of all the jets which meet the basic selection cuts: • m T , the invariant mass of the lepton and the missing transpose momentum: • M T 2 [46][47][48], the lower bound on the transverse mass resulting from two missing energies.
• m , the invariant mass of two OS leptons which survive the basic selection cuts.
Basic cuts Leading three jets p T > 40 Leading two jets p T > 40 - Exact one lepton with p T > 25 Exact two leptons with p T > 25   • N j , the number of all the jets which meet the basic selection cuts.
• N b , the number of all the b jets which meet the basic selection cuts.
We summarize the cuts we used in table 4.

Results of one lepton signal region
In this section and the following sections, we focus on the discovery/exclusion reach of the light stop at the 14 TeV LHC with integrated luminosity of 300 fb −1 . In the 1 signal region, the advanced selection cuts of E T , H T , m T , N j and N b are used to cut down the huge SM backgrounds. Table 5 shows the cumulative cut efficiencies after each level of advanced cuts and final cross sections for both signal as well as the SM backgrounds, for the benchmark point listed in table. 1. As expected, the signal process has larger m T and E T than the background processes due to the extra contributions from the LSP. tt, ttbb and ttZ are the dominant backgrounds after strong E T , H T and m T cuts. The irreducible SM backgrounds tthh, tthZ and ttZZ are almost negligible because of the very low production cross sections. In figure 4, the 95% C.L. upper limits (black curve) and 5σ discovery (red curve) reach are shown in the plane of MSSM parameter mt 1 vs m χ 0 1 for the stop pair production pp →t 1t * , tthZ E T (top right) and ttZZ E T (bottom) at the 14 TeV LHC with 300 fb −1 integrated luminosity. µ is fixed to be M 1 + 150 GeV and 10% systematic uncertainties are assumed. All combinations of the values of advanced cuts for E T , H T , m T , N j and N bj , as given in table. 4, are examined. The optimized combination that gives the best significance is used for a particular mass point. The channel tthh E T has no sensitivity in the low χ 0 1 mass region because of the very low branching fraction of the tthh E T channel. In contrary, the channel ttZZ E T has the largest reach in the low χ 0 1 mass region due to its large branching fraction. The tthZ E T has the best reach in the whole mass parameter region because of its comparably large branching fraction. For the channel tthh E T , stop masses up to 750 GeV can be discovered at the 5 σ significance level for m χ 0 1 JHEP05(2018)135   The stop mass can be discovered at 5σ significance up to 1030 GeV, or excluded at 95% C.L. up to 1200 GeV for the 1 signal region.

Results of 2 OS signal region
In the 2 OS signal region, in addition to the advanced cuts of H T , E T , M T 2 , N j and N bj , m are also used for the tthZ E T and ttZZ E T channels. The normalized distributions of M T 2 and m for the signal processes and the SM backgrounds are shown in figure 5. The M T 2 distribution for the signal extends to larger value, while the M T 2 distributions for the SM backgrounds are cut off at m W given that the two leptons of the SM backgrounds mostly come from leptonic W Decay. The m distribution for the signals and SM ttZ has a sharp peak at the Z boson mass, while the m distributions for the other SM backgrounds are spread out because the two leptons are not from the Z boson decay. Table 6 illustrates the cumulative cut efficiencies after each level of advanced cut and the final cross sections for the signals and SM backgrounds in the 2 OS signal region for the benchmark point. The dominant background in the 2 OS signal region is ttZ, given its relatively large cross section and similar final states to the signal processes. tt is the second dominant background due to its large cross section. A significance of about 12σ (7.

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Process σ (fb) Basic  For the 2 OS signal region, the 5σ discovery reach (red curve) and 95% C.L. exclusion limit (black curve) are shown in figure 6 for the 14 TeV LHC with 300 fb −1 integrated luminosity, including 10% systematic uncertainties. The channel tthh E T has no reach because of its low branching fraction of the dilepton channel. A stop mass up to 800 GeV (920 GeV) can be discovered at 5σ significance, and excluded up to 900 GeV (980 GeV) at 95% C.L. for the channel tthZ E T (ttZZ E T ). Limits with 20% systematic uncertainties are very similar to that of 10% case since the error is mostly statistically dominated.
The bottom panel of figure 6 shows the reach of 2 OS signal region combining both the tthZ E T and ttZZ E T channels. The stop mass up to 930 GeV can be discovered at 5σ significance, or a stop mass less than about 1060 GeV is excluded at the 95% C.L. for the 2 OS signal region. The specific set of advanced selection cuts used to do the signal combinations are: E T > 150 GeV, H T > 500 GeV, |m − m Z | < 5 GeV, m T 2 > 80 GeV, N j ≥ 5 and N bj ≥ 2.

Results of ≥ 3 signal region
For signal region with at least 3 leptons, it is further divided into "off-Z" and "on-Z" signal region. The "off-Z" signal region is applied to the tthh E T channel, while the "on-Z" signal region is applied to the tthZ E T and ttZZ E T channels. The cumulative cut efficiencies after each level of advanced cuts and cross sections for the "on-Z" signal region are shown in table 7 for the benchmark point. We do not list such table for the "off-Z" signal region because the reach is very small for all three channels. As can be seen from table 7, the ttZ is the dominant background, followed by the tth process. The tt and ttbb processes are highly suppressed.

on-Z
Process  Table 7. Cumulative cut efficiencies after each level of advanced seletion cuts and cross sections for the signalt 1t * 1 → tthZ E T and ttZZ E T as well as SM backgrounds in the ≥ 3 "on-Z" signal region at the 14 TeV LHC. The tthh has no reach sensitivity because of the extremely low branching fraction of three leptons channel. The tt and ttbb processes are also not listed since they are highly suppressed after all the cuts. The 95% C.L. upper limits (black curve) and 5σ discovery reach (red curve) for the "on-Z" signal region are shown in figure 7. 10% systematic uncertainties are assumed. tthh E T channel has almost no reach, therefore not shown in the plot. A stop mass up to 780 GeV (850 GeV) for the channel tthZ E T (ttZZ E T ) can be discovered at the 5σ significance, and up to about 860 GeV (960 GeV) for 95% C.L. exclusion. Limits with 20% systematic uncertainties are very similar to that of 10% case. The reach for the "off-Z" signal region is much smaller than that of "on-Z" signal region.
The combined reaches of tthZ E T and ttZZ E T channels for the ≥ 3 "on-Z" signal region are shown in the bottom panel of figure 7. The 5σ reach of a stop mass is about 880 GeV, and the 95% C.L. exclusion limit can reach up to 1000 GeV. The specific set of advanced selection cuts used to do the signal combinations are: E T > 200 GeV, H T > 500 GeV, |m − m Z | < 5 GeV , N j ≥ 7 and N bj ≥ 1. regions. In figure 8, we show the 5σ discovery reach (red curve) and 95% C.L. exclusion limit (black curve) for combination of three signal regions of tthh E T (top left panel), tthZ E T channel (top right panel) and ttZZ E T channel (bottom middle panel). Since both the 2 OS and ≥ 3 have no reach for tthh E T channel, the combined reach for tthh E T is simply the 1 reach as in the top left panel of figure 4. For both tthZ E T and ttZZ E T channel, 1 signal region gives the best sensitivity. The 5σ reach can discover a stop with mass up to 950 GeV, and the 95% exclusion limits can reach up to 1100 GeV for the channel tthZ E T . The corresponding limit for the channel ttZZ E T is a little weaker due to the smaller branching fraction. In dashed lines, we also show the reach of tthh E T and ttZZ E T channel assuming a 100% decay branching fraction.

Collider analysis at √ s = 100 TeV
To explore the physics potential of the future 100 TeV pp machine, it is critical to explore the complete parameter space of the MSSM. We scan the MSSM stop and neutralino/chargino mass parameter in the following region:
• M 1 is scanned from 5 GeV to 5000 GeV, in the step of 250 GeV.
At the 100 TeV future machine, the decay kinematics will be significantly different from that of the LHC. The decay products such as the top quark from heavy stop are highly boosted as discussed in ref. [49], leading to highly collinear leptons with the high p T jets. So we do not require the separation ∆R(j, l) between jets and leptons to be larger than 0.5 at the Monte Carlo event generation stage. The Delphes 3 Snowmass combined LHC No-Pile-up detector card [37] is modified for the 100 TeV future collider for the detector simulation. We allow up to one additional parton in the final state, and adopt the MLM matching scheme [50] with xqcut = 80 GeV for ttj background. Both the SM backgrounds and the stop pair production signal are normalized to theoretical cross sections, calculated including higher-order QCD corrections [40,51]. At the event generation level, we apply the S T cut (the scalar sum of p T for all partons) as following: S T ≥ 3 TeV for the ttj background and S T ≥ 1 TeV for the ttB background, where B stands for bosons including W , Z and h. We apply the following cuts for both the signal and the SM backgrounds: • All jets reconstructed using anti-k t algorithm [52] with cone radius R = 0.5 are required to have p T > 50 GeV and |η| < 2.5, including at least two jets with p T > 1000 (500) GeV.
• All leptons (e or µ) are required to have p T > 30 GeV and |η| < 2.5, including at least one lepton with p T > 100 (200) GeV contained within a ∆R = 0.5 cone centered around one of the two leading jets.
• The separation ∆Φ(p miss T , j) between the missing transverse momentum and jets with p T > 100 (200) GeV and |η| < 2.5 is required to be larger than 1.0.
The above selection cuts are efficient to suppress the SM backgrounds. For example, after imposing the collinear leptons to the two leading jets requirement on the SM backgrounds, the selected samples mainly contain the boosted heavy quarks. The neutrinos in the form of E T from their decay are highly aligned with the jet momenta. However, the signal E T has extra contribution from the LSP, which is usually not aligned with the jet JHEP05(2018)135 momenta. Therefore it is useful to impose the angle separation ∆Φ(p miss T , j) cut between E T and the jets with p j T > 100 (200) GeV and |η| j < 2.5 to suppress the ttj and ttB backgrounds. The normalized distributions of E T and m T after the above cuts are displayed in figure 9. The E T and m T distributions of the signal are very broad because of the extra contribution from the LSP. Contrarily, the E T and m T distributions of the SM backgrounds are typically bounded around m W . Those two selection cuts are highly efficient to suppress the SM backgrounds. Table 8 shows the cross sections, yields and cumulative cut efficiencies after each level of selection cut for the signals with mt 1 = 4000 GeV and m χ 0 1 = 1000 GeV as well as the SM backgrounds. The ttB (B = W, Z, h) is the dominant background after all cuts. Other SM backgrounds are typically small after strong selection cuts, then they can be neglected. The discovery significance for the channel tthZ E T can reach 7σ for this benchmark point.
In figure 10, the 95% C.L. upper limits (black curve) and 5σ discovery reach (red curve) based on ≥ 1 signal regions are shown in the plane of MSSM parameter space mt 1 vs m χ 0 1 for the stop pair production pp →t 1t * , ttZZ E T (bottom left) and all channels combined (bottom right) at 100 TeV LHC with 3 ab −1 integrated luminosity. µ is fixed to be M 1 + 500 GeV and 10% systematic uncertainties are assumed. The channel tthZ E T has the best reach sensitivity due to its large branching fraction, with discovery reach about 5 TeV and exclusion reach about 6 TeV. Combining all three channels, the discovery (exclusion) reach could be pushed to to about 6 (6.6) TeV. This will greatly improve our understanding of the TeV scale SUSY and the nature of electroweak breaking. For tthh E T and ttZZ E T , we also show the reach assuming a 100% decay branching fraction in dashed lines.  Table 8. The cumulative cut efficiencies, cross sections and yields for the signal with mt 1 = 4000 GeV and m χ 0 1 = 1000 GeV as well as SM backgrounds for 100 TeV pp collider with 3 ab −1 integrated luminosity. The B stands for bosons including W , Z and h.

Summary and conclusion
Most of the current stop searches at the LHC have been performed considering the channels of tt E T , bbW W E T for the stop sector, assuming the stop 100% decaying to either tχ 0 1 or bχ ± 1 . However, in MSSM parameter space with light neutralinos and charginos other than the LSP, these decay channels become subdominant or even highly suppressed, resulting in much relaxed bounds from current LHC searches. In this work, we studied the stop decay behavior in the scenario of a Bino-like LSP (M 1 ) with Higgsino-like NLSPs (µ). The new decay channels oft 1 → tχ 0 2 /χ 0 3 dominate because of the large SU(2) L coupling and top Yukawa coupling. Given the further decays of χ 0 2 /χ 0 3 to a Higgs boson or Z boson, the stop pair production at the LHC leads to tthh E T , tthZ E T and ttZZ E T final states.
In this work, we focused on the stop search sensitivity at the 14 TeV LHC with 300 fb −1 integrated luminosity, in three primary signal regions based on lepton multiplicities: 1 , 2 OS and ≥ 3 . We combined all the three production channels or three signal regions to obtain the best reach. We also explore the reach at the future 100 TeV pp collider with 3000 fb −1 integrated luminosity. The 95% C.L. exclusion and 5 σ discovery reach are summarized in figure 11.
Although we only consider one very interesting scenario of MSSM parameter space, it is important to identify the leading decay channels in various regions of parameter space to fully explore the reach of the LHC for the third generation squarks, which has important implications for the stabilization of the electroweak scale in supersymmetric models. The strategy developed in our analyses can be applied to the study of top partners in other new physics scenarios as well.   Figure 11. The 5 σ discovery reach and 95% exclusion limit of light stop mass for three primary signal regions at the 14 TeV LHC with 300 fb −1 integrated luminosity (left panel) and at least one lepton signal region at the future 100 TeV pp collider with 3000 fb −1 integrated luminosity (right panel).

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Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
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