Higgs and $Z$ Assisted Stop Searches at Hadron Colliders

Current searches for the light top squark (stop) mostly focus on the decay channels of $\tilde{t} \rightarrow t \chi_1^0$ or $\tilde{t} \rightarrow b \chi_1^\pm \rightarrow bW \chi_1^0$, leading to $t\bar{t}/bbWW+\met$ 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 $\tilde t_1 \to t \chi_2^0/\chi_3^0$, with the neutralinos subsequent decaying to a $Z$ boson or a Higgs boson: $\chi_2^0/\chi^0_3 \to \chi_1^0 h/Z$. Pair production of light stops at the LHC leads to final states of $t \bar t hh\met$, $t \bar t hZ\met$ or $t \bar t ZZ\met$. We consider three signal regions: one charged lepton (1$\ell$), two opposite sign charged leptons (2 OS $\ell$) and at least three charged leptons ($ \ge 3 \ell$). We found that the 1$\ell$ signal region of channel $t \bar t hZ\met$ has the best reach sensitivity for light stop searches. For 14 TeV LHC with 300 ${\rm fb}^{-1}$ integrated luminosity, a stop mass up to 900 GeV can be discovered at 5$\sigma$ significance, or up to 1050 GeV can be excluded at 95\% C.L. Combining all three decay channels for $1 \ell$ signal region extends the reach for about 100$-$150 GeV. We also studied the stop reach at the 100 TeV $pp$ collider with 3 ${\rm ab}^{-1}$ luminosity, with discovery and exclusion reach being 6 TeV and 7 TeV, respectively.


I. 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  mixing betweent 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 neu-tralinos and charginos, which significantly weakens the current search limits [21,22]. 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 ℓ signal region with exact one lepton (e or µ), 2 OS ℓ signal region with exact two opposite-sign (OS) leptons, and ≥ 3ℓ signal region with at least three leptons.
The rest of the paper is organized as follows. In Section II, 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 III, 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 IV, we perform a detailed collider analysis of stop search sensitivity in the three signal regions at the √ s = 14 TeV LHC. In Section V, we extend our analyses to the future √ s = 100 TeV pp machine. In Section VI, we conclude.

II. 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 of the stop sector is [23,24] 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 :  [25,26]: In the minimal mixing case withÃ t = 0, a large M SU SY around 5∼10 TeV is needed to guarantee a SM-like Higgs mass ∼ 125 GeV. In the maximal mixing case withÃ t = √ 6M SU SY , a relatively small M SU SY ∼ 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 [27,28]. 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 I, 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 branching fraction witht 1 → tχ 0 3 .
Decay channel Branching fraction are dominant, with branching fractions close to 50% each, given the large SU(2) L 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 coupling, 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 ), and reversed for negative µ value [29]. Therefore, changing the sign of µ has negligible impact on the collider analysis. Given the degeneracy of χ 0 2 and χ 0 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 coupling, whileb 1 → tχ ± 1 becomes dominant with branching fraction as high as 98%. Therefore the sbottom signal will not contaminate the stop signal.
At the LHC, thet 1t * 1 pair production leads to interesting final states of tthh E T , tthZ E T and ttZZ E T . The branching fractions are shown in Fig. 1  3, 150 and 300 GeV, with µ = 150 GeV + M 1 . When M 1 is small, χ 0 2,3 decay more to Zχ 0 1 , consequently leading to a suppressed channel tthh E T , as shown in the left panel of Fig. 1.
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][15][16][17].

B. 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 H T , as demonstrated in Table I in Ref. [19]. The signal regions included in their analysis are: one charged lepton (1ℓ), two opposite-sign charged leptons (2 OS ℓ), two same-sign charged leptons (2 SS ℓ) and at least three charged leptons (≥ 3ℓ). The at least three leptons signal region is further split into two signal regions: on-Z, when there is a pair of same flavor, opposite-sign charge leptons that has an invariant mass within 15 GeV of the nominal Z boson mass; and off-Z, where no such lepton pair exists or the invariant mass lies outside the Z mass window. The background predictions and observed data yields for signal regions are listed in Table II, III, IV in Ref. [19].
We first reproduce the CMS exclusion limits fort 2 as a validation of our analyses.
Event samples are generated using Madgraph 5 [30], processed through Pythia 6 [31] for the fragmentation and hadronization and then through Delphes 3 [32] for the detector simulation. The root package TLimit [33] is used to calculate the 95% confidence level upper limits. Fig. 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.    our simulations (solid lines) for the LHCt 2 pair production, is assumed for the left panel and BR(t 2 →t 1 Z) = 100% is assumed for the right panel. Results [19] from the 8 TeV 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 Since the CMSt 2 search channel has the same final states as ourt 1 study:t 1t * 1 pair production witht 1 → tχ 0 2,3 → th/Zχ 0 1 , we recast the CMSt 2 search limits at 8 TeV LHC 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 Fig. 3 for ttZZ E T (including 3ℓ "on-Z") and tthZ E T (including 1ℓ, 2 OS ℓ, 3ℓ "off-Z" and 3ℓ "on-Z") channels. Because the reach of the 2 SS ℓ 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 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 The benchmark point shown in Table I 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.
• M 1 is scanned from 3 GeV to 750 GeV, in the step size of 25 GeV.
is kinematically open. Event samples including signals and all the SM backgrounds are generated for 14 TeV LHC, using Madgraph 5 [30], processed through Pythia 6 [31] for the fragmentation and hadronization, and then through Delphes 3 [32] with the Snowmass combined LHC No-Pile-up detector card [34] 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 [35][36][37][38][39][40][41][42]. 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.

A. 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 (1ℓ), (2) two opposite-sign charged leptons (2OS ℓ), (3) at least three charged leptons (≥ 3ℓ). "on-Z" region and "off-Z" region are further defined for the ≥ 3ℓ case, with m ℓℓ 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 ℓ < 2.5 and p ℓ 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 [43][44][45], the lower bound on the transverse mass resulting from two missing energies.
• m ℓℓ , the invariant mass of two OS leptons which survive the basic selection cuts.
• 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 IV.
Exact one lepton with p  the benchmark point listed in Table. I. As expected, the signal process has larger m T and In Fig. 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 left) 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. IV, 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 Process σ (fb) Basic     For the 2 OS ℓ signal region, the 5σ discovery reach (red curve) and 95% C.L. exclusion limit (black curve) are shown in Fig. 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 Process σ (fb) Basic  are very similar to that of 10% case since the error is mostly statistically dominated.
The bottom panel of Fig. 6 shows the reach of 2 OS ℓ 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 ℓ 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 ℓℓ − m Z | < 5 GeV, m T 2 > 80 GeV, N j ≥ 5 and N bj ≥ 2.

D. Results of ≥ 3ℓ 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 VII 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 VII, the ttZ is the dominant background, followed by the tth process. The tt and ttbb processes are highly suppressed.
The 95% C.L. upper limits (black curve) and 5σ discovery reach (red curve) for the "on-Z" signal region are shown in Fig. 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 ≥ 3ℓ "on-Z" signal region are shown in the bottom panel of Fig. 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: GeV, |m ℓℓ − m Z | < 5 GeV , N j ≥ 7 and N bj ≥ 1.

E. Results of combined channels
For each signal region, the combined reach of all three channels are shown in previous sections. Here we discuss the reach of each individual channel, combining all the signal regions. In Fig. 8, we show the 5σ discovery reach (red curve) and 95% C.L. exclusion limit 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 3SQ from 1000 to 8000 GeV in a step of 250 GeV, corresponding to mt 1 from 1009 GeV to 8001 GeV.
• M 1 is scanned from 5 GeV to 5000 GeV, in the step of 250 GeV.
• We further require mt 1 > m χ 0 2 /m χ 0 3 + m t such thatt 1 → tχ 0 2 /χ 0 3 is kinematically open. 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. [46], 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 [34] 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 [47] 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 [37,48]. 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 [49] 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.
• N j to be at least 4, 5, 6, 7; N bj to be at least 2, 3 ,4 ,5. 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 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 Fig. 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.  In Fig. 10, the 95% C.L. upper limits (black curve) and 5σ discovery reach (red curve) based on ≥ 1ℓ 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 * , tthZ E T (top right), 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 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.

VI. 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 ℓ, 2 OS ℓ and ≥ 3ℓ. 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 Fig. 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.