Complex decay chains of top and bottom squarks

Current searches for the top squark mostly focus on the decay channels of t˜1→tχ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\tilde{t}}_1\to t{\chi}_1^0 $$\end{document} or t˜1→bχ1±→bWχ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\tilde{t}}_1\to b{\chi}_1^{\pm}\to bW{\chi}_1^0 $$\end{document}, leading to tt/bbWW + final states for top squark pair production at the LHC. In supersymmetric scenarios with light gauginos other than the neutralino lightest supersymmetric particle (LSP), different decay modes of the top squark could be dominant, which significantly weaken the current top squark search limits at the LHC. Additionally, new decay modes offer alternative discovery channels for top squark searches. In this paper, we study the top squark and bottom squark decay in the Bino-like LSP case with light Wino or Higgsino next-to-LSPs (NLSPs), and identify cases in which additional decay modes become dominant. We also perform a collider analysis for top squark pair production with mixed top squark decay final states of t˜1→tχ20→thχ10,t˜1→bχ1±→bWχ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\tilde{t}}_1\to t{\chi}_2^0\to th{\chi}_1^0,{\tilde{t}}_1\to b{\chi}_1^{\pm}\to bW{\chi}_1^0 $$\end{document}, leading to the bbbbjjℓ + collider signature. The branching fraction for such decay varies between 25% and 50% for a top squark mass larger than 500 GeV with M2 = M1 + 150 GeV. At the 14 TeV LHC with 300 fb−1 integrated luminosity, the top squark can be excluded up to about 1040 GeV at the 95% C.L., or be discovered up to 940 GeV at 5σ significance.


Introduction
The discovery of a 125 GeV Higgs at the Large Hadron Collider (LHC) [1,2] motivates the consideration of new physics beyond the Standard Model (SM). In the SM, the Higgs receives unstable quadratically divergent radiative corrections to its mass from the top quark loop. An unnatural cancellation is needed to recover the light physical Higgs mass, which is the so called "Hierarchy problem" [3]. Supersymmetry (SUSY) provides a solution to the naturalness problem by introducing superpartners to the SM particles, with interactions following the SUSY relations. The quadratic divergence from the superpartners cancels that of the SM particles, with the remnant contributions being only logarithmically divergent. Given the large top Yukawa coupling, the top and top squark (referred to as stop) sectors of the Minimal Supersymmetric Standard Model (MSSM) provide the largest radiative corrections to the Higgs mass. Stop masses can not be too heavy in order to avoid excessive fine tuning of the Higgs mass. A TeV scale stop typically leads to fine tuning of about 1% [4]. Given the tight connection between the stop and Higgs sectors, it is important to fully explore the discovery potential of the stop at the LHC.
Most of the current searches for the light stop focus on the decayt 1 → tχ 0 1 ort 1 → bχ ± 1 → bW χ 0 1 , with χ 0 1 being the stable lightest supersymmetric particle (LSP) appearing as missing energy ( E T ) at colliders. For stop pair production at the LHC, such processes lead to tt+ E T or bbW W + E T final states. However, due to the large SM backgrounds from tt, searches for the stop can be very challenging. The current limits from ATLAS and CMS experiments exclude stops with masses up to about 645 GeV for a light neutralino LSP [5][6][7][8][9][10]. For small mass spitting between the stop and the LSP,t 1 → cχ 0 1 andt 1 → bf f χ 0 1 has JHEP07(2015)075 been studied [11,12], with limits for stop masses around 240 to 270 GeV. Searches for the second stop witht 2 →t 1 Z/h have also been performed, which provide stop mass limits around 540 to 600 GeV [13][14][15]. Stop decay with a gravitino LSP has also been studied in refs. [13,16]. Similarly, the current bottom squark (referred to as sbottom) searches mostly focus onb 1 → bχ 0 1 , with bb + E T being the dominant search channel. Given data collected at the LHC 7/8 TeV, sbottoms with masses up to 700 GeV are excluded [11,17,18]. Searches based on sbottom decay ofb 1 → bχ 0 2 → bZ/hχ 0 1 exclude sbottom masses between 340 and 600 GeV [19,20].b 1 → tχ ± 1 → tW χ 0 1 decay has also been studied in multi-lepton final states [20-23], which excludes sbottom masses around 440-590 GeV. The left-handed sbottom mass is related to the left-handed stop mass since they are controlled by the same soft SUSY breaking mass parameter. In this paper, we also study the left-handed sbottom decay patterns, as well as its collider signatures.
There are other theoretical studies in the literature on the stop searches at the LHC, mostly focusing on the light stop decaying to light generation quarks [24][25][26][27][28] with little missing energy, which mimics the W W signal at the LHC [29][30][31][32][33] or multi-b jets final states from a light stop [34]. For the sbottom, in a parameter space with highly degenerate sbottom and LSP masses, a strategy has been proposed to search for sbottom based on boosting bottoms through an energetic initial radiation jet [35].
The current stop and sbottom search limits, however, could be significantly weakened when other decay modes open, which could occur in many regions of MSSM parameter space. On the other hand, the opening of new channels offers alternative discovery potential for stops and sbottoms at the LHC. It is thus important to analyze all possible stop and sbottom decay patterns to fully explore the discovery potential at the 14 TeV LHC.
Even under the usual assumption of a Bino-like LSP, the existence of other light neutralino states, for example, Wino-like or Higgsino-like next-to-LSPs (NLSPs) could lead to new decay channels for the stop. For instance,t 1 could decay to tχ 0 2,3 , with χ 0 2,3 further decaying to Zχ 0 1 , hχ 0 1 . Given the relatively large SU(2) L coupling and top Yukawa coupling, compared to the U(1) Y coupling relevant for the Bino-like LSP, decays to tχ 0 2,3 could even be dominant despite the phase space suppression. In this paper, we study the stop and sbottom decay branching fractions for the Wino-or Higgsino-like NLSP case, considering the minimal mixing and the maximal mixing scenarios in the stop sector, and outline the main search channels for the stops and bottoms at the LHC.
Given the discovery of the SM-like Higgs boson at the LHC, we can now use final states with a Higgs boson to search for new physics beyond the SM. To demonstrate the 14 TeV LHC reach with those complex stop decay channels, we performed a sample collider analysis with a Higgs in the final state: pp →t 1t * 1 with mixed stop decay final states of t 1 → tχ 0 2 → thχ 0 1 ,t 1 → bχ ± 1 → bW χ 0 1 , leading to the bbbbjj + E T collider signature with the assumption of the branching fraction of h → bb being the SM value of 57.7%. The branching fraction for such decay could vary between 25% and 50% for a stop mass larger than 500 GeV with M 2 = M 1 + 150 GeV. By designing selection cuts to identify the signal while suppressing SM backgrounds, we obtained the 95% C.L. exclusion limit as well as the 5σ discovery reach in mt 1 versus m χ 0 1 plane at the 14 TeV LHC with 300 fb −1

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integrated luminosity. Note that other Higgs decay channels: h → W W, ZZ, γγ, τ τ are not considered in our current analyses, which could lead to interesting multi-lepton final states or extremely clean (although suppressed) γγ signatures. Final states with χ 0 2 → Zχ 0 1 are left for future studies.
The rest of the paper is organized as the following. In section 2, we present the third generation squark sector in the MSSM and discuss its connection to the Higgs sector. In section 3, we discuss the stop and sbottom decays for various scenarios, as well as the collider signatures for stop/sbottom pair production. In section 4, we summarize the current and future LHC stop and sbottom search results from both ATLAS and CMS. In section 5, we investigate the 14 TeV reach of the stop via final states with a Higgs. In section 6, we conclude.

MSSM stop sector
In this study, we work in the MSSM and focus primarily on the third generation squark sector. We decouple other SUSY particles: the gluino, sleptons, and the first and second generation squarks. We also decouple the non-SM Higgs particles by setting M A large. The remaining SUSY particles in the model are the third generation squarks, the neutralinos and charginos.
The gauge eigenstates for the superpartners of the top and bottom quarks are (t L ,b L ), t R andb R , with the left-handed states grouped as an SU(2) L doublet and the right-handed states as singlets. The mass matrix for the stop sector is with M 2 3SQ and M 2 3SU representing the soft SUSY breaking masses fort L andt R , m 2 t term coming from the F-term contribution in the SUSY Lagrangian and the ∆ terms coming from the D-term contribution. The off-diagonal termÃ t is given by: for A t representing the trilinear coupling and µ representing the supersymmetric bilinear mass term in the Higgs sector. tan β = H 0 u / H 0 d is the ratio of the vacuum expectation values of H 0 u and H 0 d in the MSSM. The stop mass matrix can be diagonalized with a stop mixing angle θ t :

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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 [36]: In the minimal mixing case withÃ t = 0, a large M SUSY around 5-10 TeV is needed to provide a SM-like Higgs mass of 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 when M 2 3SQ = M 2 3SU , to provide a SM-like Higgs mass of 125 GeV, the light stopt 1 can still be as light as 200 GeV. A large mass splitting between the stop mass eigenstates (and a largeÃ t term), however, is typically needed, resulting in mt 2 500 GeV in general [37,38]. Similarly, the mass matrix for the sbottom is given as: Given the suppression of the off-diagonal terms by the small bottom mass, mixing among the sbottom mass eigenstates is typically small. ForÃ b ∼ TeV, the sbottom mixing angle is about one degree for M 3SQ ∼ M 3SD ∼ TeV.
Since the stop sector provides the dominant contribution to the Higgs mass corrections, we decouple the right-handed sbottom in our analysis. The left-handed sbottom mass, however, is determined by M 3SQ and could be relatively light. Given m bÃb , M 2 3SQ M 2 3SD , the light sbottom mass eigenstate is mostly left-handed:b 1 ∼b L . Although the sbottom corrections to the Higgs mass are small compared to the stop corrections, there can be significant modifications to the Higgs couplings, especially the bottom Yukawa coupling [39].
• Case IB, Bino-like LSP with Higgsino-like NLSPs: The decays of the light stop or sbottom highly depend on the low-lying neutralino/chargino spectrum, as well as the composition of the light stop and sbottom. In each scenario, we consider two limiting cases with different stop left-right mixing. In the minimal mixing case,Ã t = A t −µ cot β = 0, the lightest stop mass eigenstatet 1 is either purelyt L (M 3SQ < M 3SU ) or purelyt R (M 3SQ > M 3SU ). We decouplet 2 for simplicity. In the maximal mixing case with M 3SQ = M 3SU = M SUSY and |Ã t | = √ 6M SUSY , both t 1,2 are a mixture oft L andt R , with mass squared splitting ∆m 2 t ≈ 2 √ 6m t M SUSY . In our analysis below, we useÃ t > 0. Negative values ofÃ t introduce little changes to the numerical results. Since M 3SQ also controls the mass forb L , there is a lightb 1 ∼b L for the light M 3SQ case, assuming small sbottom left-right mixing and a decoupledb R .

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The mass spectra for stops and sbottom are shown in figure 1. In the minimal mixing case (left panel), mt L (mt R ), mb 1 ∼ M 3SQ (M 3SU ), especially for large M 3SQ (M 3SU ). In the maximal mixing case (right panel), the mass difference betweenb 1 andt 1 is typically about 250 GeV while the mass difference betweent 2 andt 1 is about 350 GeV or larger.
We used SUSY-HIT [40] to calculate the supersymmetric particle spectrum and decay branching fractions. In this section, unless otherwise specified, we have set the Bino-like LSP mass parameter M 1 = 150 GeV, the intermediate gaugino mass parameters M 2 , µ = 300 GeV in Cases IA and IB, respectively, and tan β = 10.

Case I: Bino-like LSP with decoupled Wino and Higgsino
The simplest case has a mass spectrum with stop(s), left-handed sbottom, and only the low-lying neutralino being the Bino-like LSP.
In the minimal mixing case with the light stopt 1 as a pure left-or right-handed state, t 1 either directly decays to tχ 0 1 when it is kinematically accessible or through bW * χ 0 1 with 100% branching fraction. Similarly, in the case of small M 3SQ ,b 1 decays directly through bχ 0 1 with 100% branching fraction.
In the maximal mixing case,t 1 ,t 2 , andb 1 appear in the spectrum, with a typical mass order mt 1 < mb 1 < mt 2 with relatively large mass splittings of 150 GeV or larger. While JHEP07(2015)075  Case I: left panel shows σ × BR of final states fort 1 pair production in both the minimal and maximal mixing scenarios, as well asb 1 pair production in the minimal mixing scenario. The middle and right panel show σ ×BR for various final states ofb 1 andt 2 pair production, respectively, in the maximal mixing scenario. All channels include E T in the final states. All the cross sections are for the 14 TeV LHC stop and sbottom pair production, calculated including NLO + NLL corrections [41][42][43]. The choice of neutralino and chargino mass parameters is the same as in figure 2.
the decay oft 1 is straightforward (100% into bW ( * ) χ 0 1 ), the decays ofb 1 andt 2 could have multiple competing channels, as shown in figure 2. Forb 1 , it dominantly decays into Wt 1 while the branching fraction of theb 1 → bχ 0 1 channel is only about a few percent or less.  the σ × BR of final states tt/bbW W + E T fort 1 in the minimal and maximal mixing scenarios, as well as bb + E T forb 1 in the minimal mixing scenario at the 14 TeV LHC.
All the cross sections shown in the plots are for stop and sbottom pair production at 14 TeV including NLO supersymmetric QCD correction as well as resummation of softgluon emission at next-to-leading logarithmic accuracy [41][42][43]. Sincet 1 → t/bW χ 0 1 and b 1 → bχ 0 1 dominate in those channels, σ × BR is the same as the production cross sections for the stop pair and sbottom pair. The middle panel of figure 3 shows the σ × BR forb 1b1 pair production in the maximal mixing scenario. The bb + E T channel is highly suppressed, while bbW W W W + E T becomes dominant. The right panel of figure 3 shows the σ ×BR for t 2t2 pair production in the maximal mixing scenario. The dominant channel is ttZZ + E T , with ttW W Z being the second dominant channel. The cross section, however, is relatively small, less than about 10 fb for mt

Case IA: Bino LSP with Wino NLSP
The low lying neutralino/chargino spectrum in Case IA comprises of a Bino-like LSP, as well as a pair of Wino-like states: χ 0 2 and χ ± 1 with nearly degenerate masses. In the minimal mixing scenario, the decay branching fractions are shown in figure 4 for lefthandedt 1 (left),b 1 (middle), and right-handedt 1 (right). For the left-handedt 1 , decays to bχ ± 1 (∼ 70% for large mt 1 ) and tχ 0 2 (∼ 30% for large mt 1 ) dominate over tχ 0 1 once kinematically accessible, due to the stronger SU(2) L coupling compared to the relatively neutralino/chargino: 1 almost 100%, since its couplings to the Wino-like neutralino/charginos are highly suppressed.
The left, middle and right panels of figure 5 show the σ × BR for pure left-handed t 1t1 ,b 1b1 and pure right-handedt 1t1 pair production, respectively, in the minimal mixing scenario of Case IA. For pure left-handedt 1 , bbW W Z/h + E T is as abundant as the bbW W + E T channel, which could be an important new search channel for the stop. For pure left-handedb 1 , the bb+ E T channel is highly suppressed. New final states of bbW W Z/h and bbW W W W are dominant and comparable in size, with bbZ/hZ/h being subdominant, opening up new channels for sbottom searches. The final state for the pure right-handed t 1 is still bbW W + E T , despite the existence of light Wino NLSPs in the spectrum.
For the maximally mixed scenario, the decay oft 1 ,b 1 andt 2 are shown in the left, middle and right panels of figure 6, respectively. Fort 1 with large mass, the decay to bχ ± 1 , tχ 0 2 still dominates over tχ 0 1 , but the corresponding branching fractions are smaller compared to the pure left-handed case (figure 4) due to the decrease of the coupling to the Wino-like state caused by the right-handed stop component. Forb 1 , while tχ ± 1 and bχ 0 2 modes still dominate over bχ 0 1 mode, the new decay channel of Wt 1 opens up and even dominates over most of the mass range. Its branching fraction varies between 100% to about 40% for mb 1 between 600 GeV to 1500 GeV. Fort 2 , in addition to bχ ± 1 and tχ 0 1,2 (about a few percent to 20%), decays to a light stop/sbottom plus a gauge boson [45] become comparable or even dominant: about 50%-70% for Zt 1 and about 20%-15% for Wb 1 .
The left, middle and right panels of figure 7 show the σ × BR fort 1t1 ,b 1b1 , and t 2t2 respectively for the maximal mixing scenario of Case IA at the 14 TeV LHC. For JHEP07(2015)075

Case IB: Bino-LSP with Higgsino-NLSP
The low lying neutralino/chargino spectrum in Case IB comprises of a Bino-like LSP, as well a pair of Higgsino-like neutralino states χ 0 2,3 and chargino states χ ± 1 with nearly degenerate masses. Figure 8 shows the branching fractions of left-handedt 1 andb 1 and JHEP07(2015)075  Given the further decays of χ ± 1 → W χ 0 1 , χ 0 2,3 → Zχ 0 1 /hχ 0 1 as discussed in detail in [44], the pair production of stops and sbottoms lead to complicated final states at the collider. The left, middle and right panels of figure 9 show the σ × BR for pure left-handedt 1t1 ,b 1b1 and pure right-handedt 1t1 pair production in the minimal mixing scenarios of Case IB. For pure left-handedt 1 , bbW W Z/hZ/h + E T is the dominant final state with the stop search channel bbW W + E T being highly suppressed. For pure left-handedb 1 , bbW W W W + E T is the dominant channel. The dominant final states for pure right-handedt 1 are bbW W Z/h+ E T as well as bbW W + E T .

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For small mass splitting betweent 1 and χ ± 1 (for example, 10 GeV) with soft b jets, stop masses below 390 GeV are excluded for a massless LSP. When both decay modes t 1 → tχ 0 1 andt 1 → bχ ± 1 are open, the excluded stop masses increase from 530 GeV to 660 GeV for an LSP mass of 100 GeV when BR(t 1 → tχ 0 1 ) is increased from 0% to 100% and m χ ± 1 = 2m χ 0 1 . The limits get weaker with an increased branching ratio to decays other thant 1 → tχ 0 1 andt 1 → bχ ± 1 . Limits from the pure leptonic channels are weaker [7]. Stops with masses between 215 GeV and 530 GeV decaying to an on-shell t-quark and a neutralino are excluded at 95% C. L. for a 1 GeV neutralino. For m b + m W + m χ 0 1 < mt 1 < m t + m χ 0 1 with an off-shell top and a neutralino LSP, the stop masses are excluded between 90 GeV and 170 GeV. For BR(t 1 → bχ ± 1 ) = 100%, the limits on the stop mass depend on both the LSP mass and m χ ±  The interpretation is performed in the region mt 1 − m χ 0 1 ∼ m t , which is hard to probe byt 1 → tχ 0 1 channel given the relative small E T . For BR(t 2 →t 1 Z) = 100%, the second stop mass is excluded up to about 600 GeV for a light LSP mass. For BR(t 2 →t 1 h) = 100%, the second stop mass exclusion limit is about 540 GeV. When JHEP07(2015)075 the decay branching fraction tot 1 Z andt 1 h is 50% each, the exclusion limit is about 580 GeV for a light LSP mass.
Sbottom pair production withb 1 → bχ 0 1 leads to signals with two b jets and large E T . The null results from ATLAS [17] exclude sbottom masses up to 620 GeV for m χ 0 1 <120 GeV. mb 1 − m χ 0 1 is excluded up to 50 GeV for sbottom masses up to 300 GeV. The exclusion limits depend sensitively on the branching fraction ofb 1 → bχ 0 1 . For 60% branching fractions, the sbottom exclusion limit is reduced to 520 GeV. Sbottom searches on direct sbottom pair production withb 1 → tχ ± 1 with 100% decay branching fraction of χ ± 1 → W χ 0 1 have been performed at both ATLAS and CMS [21,22], looking for signals with two same charge leptons or three leptons plus multiple jets. The interpretation was done for fixed m χ 0 1 = 60 GeV as well as varying m χ 0 1 with m χ ± 1 = 2m χ 0 1 . The sbottom mass limit is about 440 GeV in both cases for m χ ± At the 14 TeV LHC, with the dominant decay channel oft 1 → tχ 0 1 , studies using semileptonic channel and fully hadronic channel show that for LSP masses below 200 GeV, a 5σ reach of stop discovery is possible for stop masses up to about 1 TeV with 300 fb −1 integrated luminosity [46]. For the high luminosity option of LHC (HL-LHC) with 3000 fb −1 integrated luminosity, the discovery reach is extended by about 200 GeV. The 95% exclusion limit is about 1.2 TeV (1.45 TeV) with 300 (3000) fb −1 integrated luminosity. For sbottom searches withb 1 → bχ 0 1 , the discovery reach is about 1.1 (1.3) TeV and the exclusion reach is about 1.4 (1.55) TeV with 300 (3000) fb −1 integrated luminosity [47]. CMS analyses using specific full spectrum benchmark points show similar sensitivities [48].

Collider analysis
Given a different neutralino/chargino mass spectrum, many new decay channels for stop and sbottom appear, while the channels oft 1 → tχ 0 1 , bχ ± 1 andb 1 → bχ 0 1 could be highly suppressed. This leads to the relaxation of current collider search limits based on those above mentioned channels. At the same time, those new channels provide new discovery opportunities. To demonstrate the new discovery potential, we pick one particular channel as our benchmark scenario for collider analyses. Studies on other possible mass spectrum and decay channels are left for future study.
In this section, we study the detectability of the light stop in Case IA with a mass hierarchy of M 1 < M 2 < M 3SQ |µ|, M 3SU , resulting in a mass spectrum including a mostly left-handed stop and mostly left-handed sbottom, Wino-like NLSPs, and a Bino-like LSP. In our analyses, we consider the kinematic region of mt 1 −m χ 0 2 > m t and m χ 0 2 −m χ 0 1 > m h such thatt 1 → tχ 0 2 and χ 0 2 → hχ 0 1 are kinematically open. The collider analyses of the current event topology can not be applied for the more compressed scenarios when either M 3SQ is close to M 2 or M 2 is close to M 1 . To illustrate the decay branching fractions, we choose a benchmark point with the specific set of parameters and the corresponding mass spectrum shown in table 1. The value ofÃ t is chosen such that the SM-like Higgs mass is around 125 GeV. Note that even thoughÃ t is set to a large value, the large mass splitting between M 3SQ and M 3SU results in a mostly left-handedt 1 and mostly right-handedt 2 . Therefore, the decay patterns oft 1 andb 1 follow those of the Case IA: purely left-handed stop/sbottom in the minimal mixing scenario.
The decay channels for the light stop of the benchmark point are shown in table 2. While the dominant decay channel ist 1 → bχ + 1 with 71% branching fraction, the subdominant channelt 1 → tχ 0 2 is about 27%, providing an interesting signal where χ 0 2 can either decay to a Higgs or a Z boson. For our choice of parameters with µ > 0, χ 0 2 dominantly decays to hχ 0 1 , as shown in table 2. Flipping the sign of µ could lead to another interesting channel of χ 0 2 → Zχ 0 1 , which is left for future study. For our benchmark point with the reduced branching fraction of BR(t 1 → bχ ± 1 ) = 71%, the current collider search limits on the stop are much more relaxed: less than about JHEP07(2015)075 500 GeV for mt 1 . However, new search channels open up, which play a complementary role for stop searches at the LHC.
In our analysis, we study the stop pair production with mixed stop decay final states oft 1 → tχ 0 2 → thχ 0 1 ,t 1 → bχ ± 1 → bW χ 0 1 . The branching fraction for such decay is about 38% for our benchmark point and varies between 25% and 50% for a stop mass larger than 500 GeV with M 2 = M 1 + 150 GeV. We consider semileptonic decays of the two W s and the Higgs decay to two b-quarks. Since we choose the CP-odd Higgs mass m A to be 2000 GeV, we are in the decoupling region of the Higgs sector with the light CP-even Higgs being SM-like. Given that we are in the Bino-LSP scenario with M 2 = M 1 +150 GeV, additional possible decay modes of h into neutralino/charginos are either highly suppressed or kinematically forbidden. Therefore, the light CP-even Higgs is consistent with the observed signal of a 125 GeV SM-like Higgs boson. In our analyses, we have taken the branching fraction of h → bb to be the SM value of 57.7%. The signal contains four b-jets, two jets, one isolated lepton and large missing energy. The presence of a single lepton helps to reduce QCD multijets backgrounds without significant branching fraction suppression.
The dominant SM backgrounds are bbW W (dominantly from tt) and ttbb. While tth is an irreducible background, the production cross section is typically small. Other backgrounds consist of ttW and ttZ.
Event samples are generated using Madgraph MG5 aMC V2 2 1 [49], processed through Pythia 6.420 [50] for fragmentation and hadronization and then through Delphes-3.1.2 [51] with the Snowmass combined LHC detector card [52] for detector simulation. Both the SM backgrounds and the stop pair production signal are normalized to theoretical cross sections, calculated including higher-order QCD corrections [41][42][43][53][54][55][56][57]. For event generation, we have set m t to be 173 GeV, and the Higgs mass m h to be 125 GeV. The renormalization scale and factorization scale are taken to be M 2 + p 2 T for a single heavy particle. For pair production of heavy particles, the geometric mean of M 2 + p 2 T for each particle is used. For the signal process, we scan the parameter range of M 3SQ = 400 . . . 1100 GeV with step size of 25 GeV, and M 1 = 3 . . . 750 GeV with step size of 25 GeV. We fix M 2 to be M 2 = M 1 + 150 GeV.
We apply the following basic event selection cuts: • Events are required to have at least four isolated jets 2 with p j1,j2,j3 All isolated jets satisfying p j T > 25 GeV, |η j | < 2.5 are counted in N j .
• Among the jets, at least two are b-tagged jets. The b-tagging efficiency depends on the p T and η of the jets, which is 0 for p T < 15 GeV or |η| > 2.5, about 70% for |η j | < 1.2 and about 60% for 1.2 < |η j | < 2.5 with p j T 200 GeV. The mistag rate depends on the quark species, as well as p T and η of the jets. It is about 15% for c-quark and a constant 2% for light jets.  from the neutrino, which is typically smaller than that of the signal with additional E T contribution from the LSP. The transverse mass for the signal process extends beyond the SM threshold of the W boson mass. The H T distribution of the signal is maximum at a higher value compared to the SM backgrounds.
In table 3, we present the cumulative cut efficiencies for the signal and dominant SM backgrounds with one set of selection cuts. By utilizing strong E T , H T and m T selection cuts, we significantly reduce the SM backgrounds. The stop signal process typically generates multiple hard jets in our specified decay. The N bj cut further plays an important role in cutting tt, ttW , and ttZ backgrounds. tt is the dominant background given its large cross section. The tails in the tt missing E T and H T distribution are more relevant than those of the rare SM processes of ttZ/W . ttbb is the second dominant background given its relatively large cross section and similar final states to the signal process. tth, ttZ, and ttW can be sufficiently suppressed due to low cross sections. We impose a constraint on the number of signal events, N s ≥ 3 for 300 fb −1 in order to obtain sufficient statistics.
In figure 13, we show the 95% C.L. exclusion limit and 5σ reach in the parameter space of mt 1 versus m χ 0 1 for the 14 TeV LHC with 300 fb −1 luminosity. M 2 is fixed to be M 1 +150 GeV and 10% (30%) systematic uncertainties on SM backgrounds are assumed for solid (dotted) curves. For each mass point of (mt 1 , m χ 0 1 ), given the mass dependence of the production cross section and decay branching fractions, the signal σ×BR for each individual point has been used. All combinations of the cut values for the advanced selection cuts of E T , H T , m T , N j and N bj are examined. The optimized combination that gives the best significance is used for that particular mass point. For the 5σ reach, stop masses up to 740 GeV can be reached for a massless LSP and about 940 GeV with m χ 0 1 = 250 GeV, assuming 10% systematic uncertainties. The 95% C.L. exclusion limits are about 840 GeV for stops with a light χ 0 1 , while the reach is 1040 GeV for m χ 0 1 = 250 GeV. Limits with 30% systematic uncertainties are about 50 GeV worse.
Note that a light left-handed sbottom with mixed decay ofb 1 → bχ 0 2 andb 1 → tχ ± 1 could lead to the same final states. We focused on the stop search sensitivities in the current study. Collider studies for the sbottom search as well as the combined reach in M 3SQ versus m χ 0 1 plane can be found in ref. [58].  Figure 13. The plot shows the 5σ discovery reach (red) and 95% exclusion limits (black) of the stop in the mt 1 −m χ 0 1 plane for 14 TeV LHC with 300 fb −1 of integrated luminosity. M 2 is fixed to be M 1 + 150 GeV and 10% (30%) systematic uncertainties are assumed for solid (dotted) curves. The color coding on the right indicates the signal significance defined simply as S/ √ B to guide the eye. For exclusion and discovery reach, we used the signal significance defined as S/ S + B + ( × B) 2 and S/ B + ( × B) 2 , respectively. Here is the assumed systematic uncertainty.

Summary and conclusion
Most of the current stop and sbottom searches at the LHC have been performed considering the channels of tt + E T , bbW W + E T for stop and bb + E T for sbottom, assuming the stop and sbottom decay 100% into these channels. However, in many regions of MSSM parameter space, these decay channels are subdominant, resulting in relaxed bounds from current LHC searches. In this work, we studied decays of the stop and sbottom in the cases of a Bino-like LSP with either Wino-like or Higgsino-like NLSPs in the low energy spectrum, for the left-and right-handed stops and left-handed sbottom in the minimal mixing scenario, andt 1,2 ,b 1 in the maximal mixing scenario. We found that new decay channels oft 1 → tχ 0 2,3 ,b 1 → bχ 0 2,3 , tχ ± 1 , Wt 1 open up, which could even dominate over t 1 → tχ 0 1 , bχ ± 1 andb 1 → bχ 0 1 channels. For the heavier stop state,t 2 , a new channel of t 2 → Wb 1 appears in addition tot 2 → Zt 1 in the maximal mixing scenario. Given the further decays of χ 0 2,3 and χ ± 1 , pair production of stops and sbottoms at the LHC typically leads to bb plus multiple gauge bosons plus E T final states. Current search channels of bbW W + E T and bb + E T could be highly suppressed.
We performed a sample collider analysis for the reach of the stop at the 14 TeV LHC with 300 fb −1 integrated luminosity for one particularly interesting channel in the Bino-like LSP with Wino-like NLSP case. We considered left-handed stop pair production mixed stop decay final states oft 1 → tχ 0 2 → thχ 0 1 ,t 1 → bχ ± 1 → bW χ 0 1 , leading to the bbbbjj + E T collider signature. The branching fraction for such decay varies between 25% and 50% for a stop mass larger than 500 GeV with M 2 = M 1 + 150 GeV. Our results show that for a LSP mass of 250 GeV, the 95% C.L. exclusion reach is about 1040 GeV for the stop and the
Considering different low-lying neutralino/chargino spectra provides several promising channels for the stop and sbottom study. In this paper we focused on final states with a Higgs boson. Decays of χ 0 2 to Zχ 0 1 could be dominant with a different choice of sign(µ). Furthermore, a different mass spectrum of neutralino/chargino with LSP being either Wino-like or Higgsino-like might give rise to more interesting final states. 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 analysis can be applied to the study of top partners in other new physics scenarios as well.
[10] CMS collaboration, Search for top-squark pair production in the single-lepton final state in pp collisions at [20] CMS collaboration, Search for supersymmetry in pp collisions at √ s = 8 TeV in events with three leptons and at least one b-tagged jet, CMS-PAS-SUS-13-008 (2013).
[21] ATLAS collaboration, Search for supersymmetry at √ s = 8 TeV in final states with jets and two same-sign leptons or three leptons with the ATLAS detector, JHEP 06 (2014)