Stop searches in flavourful supersymmetry

Natural realisations of supersymmetry require light stops ${\tilde t}_1$, making them a prime target of LHC searches for physics beyond the Standard Model. Depending on the kinematic region, the main search channels are ${\tilde t_1}\to t \tilde \chi^0_1$, ${\tilde t_1}\to W b \tilde \chi^0_1$ and ${\tilde t_1}\to c \tilde \chi^0_1$. We first examine the interplay of these decay modes with ${\tilde c_1}\to c \tilde \chi^0_1$ in a model-independent fashion, revealing the existence of large regions in parameter space which are excluded for any ${\tilde t_1}\to c \tilde \chi^0_1$ branching ratio. This effect is then illustrated for scenarios with stop-scharm mixing in the right-handed sector, where it has previously been observed that the stop mass limits can be significantly weakened for large mixing. Our analysis shows that once the LHC bounds from ${\tilde c_1}\to c \tilde \chi^0_1$ searches are taken into account, non-zero stop-scharm mixing leads only to a modest increase in the allowed regions of parameter space, with large areas excluded for arbitrary mixing angles.


Introduction
A key feature of supersymmetric extensions of the Standard Model (SM) is the fact that radiative corrections to the Higgs potential can induce electroweak symmetry breaking in a technically natural fashion. Since top quarks and top squarks dominate the radiative corrections, naturalness requires their masses to be of similar magnitudes to ensure a sufficient cancellation of quadratic divergences. Apart from the gluino, Higgsinos and the left-handed bottom squark, the rest of the superpartners are less important for naturalness, and may well have masses above the reach of the LHC [1][2][3][4][5][6]. A spectrum with the above hierarchy is a typical starting point for phenomenological analyses in supersymmetry (SUSY).
Although light stops are required for naturalness, they can reintroduce fine-tuning in minimal SUSY because the Higgs is typically predicted to be light. For instance, to accommodate a Higgs mass of 125 GeV in the Minimal Supersymmetric SM (MSSM), the stop masses must be around 1 TeV, at the cost of tuning at the percent level or worse. Reconciling these two features, light stops for naturalness and heavier stops for the Higgs mass, constitutes the "little hierarchy problem". However, in contrast to naturalness, the little hierarchy problem is model dependent and tightly bound to the MSSM. SUSY models that can generate a sufficiently heavy Higgs with improved naturalness include scenarios with non-decoupling D-terms [7] and the next-to-minimal supersymmetric SM with special parameter choices [8].
Naturalness considerations aside, there are additional reasons to expect light stops if SUSY is realised in nature. For instance, the renormalisation group evolution from a high scale with universal squark masses typically drives the masses of the third generation squarks to small values [9]. Light stops also help accommodate the observed dark matter relic density [10,11] and are an essential ingredient in realising baryogenesis [12][13][14].
Experimentally, the bounds on the lightest stop mass mt 1 are much weaker than the limits on the other coloured superpartners, i.e. the squarks of the first two generations and the gluino [15,16]. There are three main kinematic regions where different channels are used to search for stops, namely Here mχ0 1 denotes the mass of the lightest neutralino, constituting the lightest superpartner (LSP), while m W , m b and m c are the mass of the W boson, the bottom quark and the charm quark, respectively.
In each region, the results from the ATLAS and CMS searches are interpreted in the context of simplified models, where the branching ratio for each decay mode is fixed to 100% and flavour violation is assumed to be absent. Under these assumptions, the resulting limits on mt 1 in the region R1 are strong, reaching up to stop masses close to 800 GeV [17][18][19][20][21][22][23][24][25][26]. It has been observed [27][28][29][30], however, that these limits can be weakened if nonminimal sources of flavour violation are present. This occurs because flavour-violating effects enhance the decay width fort 1 → cχ 0 1 , and thereby reduce the branching ratio for t 1 → tχ 0 1 from unity. On the other hand, if the decay width oft 1 → cχ 0 1 becomes large, the limits from directc 1 pair production and subsequent scharm decayc 1 → cχ 0 1 [31] become relevant, which apply tot 1 → cχ 0 1 as well once the branching ratio is large. In the second region R2, the situation is similar. The limits on mt 1 reach only up to around 300 GeV [17,19,20] and the three-body decayt 1 → W bχ 0 1 is suppressed by phase space, so thatt 1 → cχ 0 1 can compete for relatively small off-diagonal elements in the squark mass matrix [32]. Again, once stop-scharm mixing and therefore the decay width fort 1 → cχ 0 1 is sizeable, searches for charm signatures [33] can become relevant. Finally, in the third region R3,t 1 → cχ 0 1 is typically the dominant decay mode and the four-body decayt 1 → bf f χ 0 1 [19,33] can only compete for scenarios resembling Minimal Flavour Violation (MFV) [34].
The purpose of this article is to examine the complementarity ofc 1 → cχ 0 1 searches with the standard channelst 1 → W bχ 0 1 andt 1 → cχ 0 1 in the presence of non-minimal sources of flavour violation. In Section 2, we introduce the basic ideas behind our combination procedure and apply it to set model-independent limits on mt 1 , mχ0 1 and the branching ratio oft 1 → cχ 0 1 in the kinematic region R1 using ATLAS Run I data. The very same exercise is performed in Section 3 for the region R2. Focusing on flavour mixing in the right-handed up-squark sector, which is largely unconstrained by quark flavour observables, we then quantify in Section 4 the interplay between the different search strategies. As we are interested in non-MFV scenarios in this article, we use the ATLAS bounds fort 1 → cχ 0 1 directly in region R3. This allows us to provide interesting exclusions in large parts of the entire mt 1 -mχ0 1 plane. Our conclusions and an outlook are presented in Section 5. In order to make our article self-contained, Appendix A provides details on the Monte Carlo (MC) simulations that were used to obtain the numerical results presented in our work.
2 Stop search combination for mt 1 We begin our numerical analysis in the kinematic region R1. In this region the two-body decayt 1 → tχ 0 1 dominates unless non-minimal sources of flavour violation in the up-squark sector are present that lead to an appreciable rate fort 1 → cχ 0 1 . As illustrated in Figure 1, in such cases one faces three different decay configurations: one that involves two top quarks (configuration 1), one with an intermediate top and a charm quark (configuration 2), and finally one with two charm quarks (configuration 3). Since the final state contains two LSPs in all configurations, the visible decay products will be augmented by large amounts of missing transverse momentum (E T,miss ).
In order to find combined model-independent limits on mt 1 , mχ0 1 and the branching ratio Br t 1 → cχ 0 1 in the region R1, we employ three different ATLAS searches that are all based on around 20 fb −1 of √ s = 8 TeV data. Specifically, these are a) 2 c-tags + E T,miss [31]: This ATLAS search is originally designed for the decay configuration 3 in Figure 1. In order to maximise the sensitivity of this search, three distinct signal regions (SRs) called mct150, mct200 and mct250 are defined. In all SRs, events have to have a reconstructed primary vertex consistent with the beam positions and to meet basic quality criteria. Furthermore, events are required to contain no residual electron or muon candidate and at least two jets with radius R = 0.4 and p T > 130, 100 GeV and |η| < 2.5. The multijet background contribution with large E T,miss is suppressed by requiring a minimum azimuthal separation |∆φ( p T,j 1,2,3 , p T,miss )| > 0.4 between any of the three leading jets and the E T,miss direction p T,miss . The third jet is exempted from this angular requirement, if it has p T < 50 GeV, |η| < 2.4 and less than half of the sum of its track p T is associated with tracks matched to the primary vertex. The two highest-p T jets are required to be identified as arising from a charm quark (c-tagged). The algorithm used in the ATLAS analysis achieves a c-tagging efficiency of 20% with a b-jet and light-jet rejection fraction of 8 and 200 (medium operating point) [36]. The E T,miss selections are E T,miss > 150 GeV and E T,miss / i=1,2 |p T,j i | > 1/3. To further discriminate between signal and background the invariant mass of the two c-tagged jets has to satisfy m cc > 200 GeV and a selection based on the boost-corrected contransverse mass m CT [35] is employed. Depending on the SR, m CT > 150 GeV, m CT > 200 GeV or m CT > 250 GeV is required.
b) 1 lepton + 4 jets + 1 b-tag + E T,miss [19]: In its original form, this ATLAS search has been tailored for the decay configuration 1 in Figure 1 with one top quark decaying hadronically and the other one leptonically. It implements four SRs that target different regions in the mt 1 -mχ0 1 plane and implement different analysis strategies. In our case it turns out that only the SRs called tN diag and tN med are relevant in the combination. The following preselection criteria are common to the two SRs. Events are required to have a reconstructed primary vertex, E T,miss > 100 GeV, exactly one isolated lepton with p T > 25 GeV and at least four R = 0.4 jets with p T > 25 GeV. Events that do not pass certain data quality requirements are re- jected. In the SR tN diag, the cuts on the three hardest jets are p T > 60, 60, 40 GeV and |η| < 2.5. The two leading jets have to satisfy |∆φ( p T,j 1,2 , p T,miss )| > 0.8 and at least one jet has to be identified as a bottom-quark jet (b-tagged), assuming an average tagging efficiency of 70% [37,38]. In addition, we require in our analysis E T,miss > 150 GeV, E T,miss / √ H T > 5 GeV 1/2 , m T > 140 GeV, m had-top ∈ [130, 205] GeV and impose a veto on loose τ leptons. Here H T is defined as the scalar p T of the four hardest jets in the event, m T denotes the transverse mass constructed from the lepton transverse momentum and p T,miss , while m had-top represents the hadronic top mass. The selection requirements in tN med that differ from to that of tN diag are p T > 80, 60, 40 GeV for the three leading jets, |∆φ( p T,j 2 , p T,miss )| > 0.8, E T,miss > 200 GeV and m had-top ∈ [130, 195] GeV. A cut on E T,miss / √ H T and a τ -veto is not imposed, but H sig T,miss > 12.5 and am T 2 > 170 GeV is required. Here H sig T,miss is an object-based missing transverse momentum that is normalised by the per-event resolution of the jets [19] and am T 2 is an asymmetric variant of the generalised transverse mass [39][40][41][42]. c) 6 jets+2 b-tags+E T,miss [18]: This ATLAS search aims to provide the best sensitivity for the decay configuration 1 in Figure 1 with both top quarks decaying hadronically. In our analysis, we consider only the SR A1 and the SR A2 out of the possible nine SRs. All events that pass certain quality requirements and do not contain a reconstructed electron or muon with p T > 10 GeV are subjected to the following common selection criteria. They have to have at least six R = 0.4 jets with p T > 80, 80, 35,35,35,35 GeV and |η| < 2.8, and out of these jets, two or more have to be b-tagged (70% efficiency). The number of events with mismeasured E T,miss is reduced by requiring |∆φ( p T,j 1,2,3 , p T,miss )| > π/5 and |∆φ( p T,miss , p track T,miss )| < π/3, where p track T,miss denotes the missing transverse momentum direction determined from the calorimeter system. To further sculpt the signal, the transverse mass calculated from the b-tagged jet closest in the azimuthal angle φ to p T,miss has to satisfy m b,min T > 175 GeV, the mass cuts m 0 bjj < 225 GeV and m 1 bjj < 250 GeV on the first and second top candidate [18] are imposed and loose τ leptons are vetoed. The SRs A1 and A2 only differ in the imposed E T,miss selection. In the former case, events with E T,miss > 150 GeV suffice, while in the latter case the stronger requirement E T,miss > 250 GeV is imposed.     To combine the searches a, b and c, we work in the narrow-width approximation and assume that only the decay modest 1 → tχ 0 1 andt 1 → cχ 0 1 are relevant, so that Br t 1 → tχ 0 1 = 1 − Br t 1 → cχ 0 1 . Both assumptions are satisfied in the kinematic region R1. Using the shorthand notations Br = Br t 1 → cχ 0 1 and σt 1t * 1 = σ pp →t 1t * 1 , the fiducial cross sections (σ fid ) s corresponding to the three different ATLAS searches can then be written in the following way Here ts denotes the efficiency with which the decay configuration t = 1, 2, 3 (see Figure 1) is detected by the search s = a, b, c.
The efficiency maps relevant for the combination of the different stop channels in the  [GeV]  region R1 are displayed in the four panels of Figure 2. They have been obtained by means of the MC simulations described in Appendix A. From the plots it is evident that the efficiencies ts are not flat, but depend rather sensitively on mt 1 and mχ0 1 . This behaviour is expected because changing the mass of the lightest stop and the LSP will modify the kinematic distributions of the final-state particles, which in turn leads to different signal acceptances in the various SRs. In fact, a qualitative understanding of the obtained efficiencies is possible by studying the cutflow of the analysis a, b and c for the different signal configurations 1, 2 and 3. We start by discussing the efficiencies 1a and 2a shown in the upper left and upper right panel of Figure 2, respectively. The first observation is that in most parts of the mt 1 -mχ0 1 plane, the efficiency 1a is smaller than 2a . This is readily understood by recalling from Figure 1 that configuration 1 (2) leads to a final state with two bottom quarks (one bottom quark). In the former case, two b quarks have to be misidentified as c-jets in order to produce an event in the SRs of search a, while in the latter case one mis-tag is sufficient. Another feature that is evident from the plots is that the efficiencies 1a and 2a both decrease if one approaches the kinematic boundary of region R1. This is due to the fact that the decay chaint 1 → tχ 0 1 → W + bχ 0 1 and its conjugate will not give rise to significant E T,miss if the mass difference mt 1 − mχ0 1 is close to m t , and as a result the corresponding event is less likely to pass the E T,miss requirements that are imposed in the scalar charm search a.
Simple qualitative explanations of the efficiency maps 2b and 2c presented in the lower left and lower right panel of Figure 2 can also be given. In the case of 2b , the requirement to have an isolated lepton strongly suppresses the acceptance for final states arising from the configuration 2, which involves both at 1 → tχ 0 1 → W + bχ 0 1 and at * 1 → cχ 0 1 decay or the combination of charge-conjugated processes. For these decays, the fact that a lepton with p T > 25 GeV can only arise from a leptonic decay of a W boson also explains the finding that 3b 0 in the whole kinematic region R1. That 2b increases when approaching the kinematic boundary mt 1 − mχ0 1 = m t has to do with the fact that   this efficiency is defined relative to the acceptance corresponding to a signal from the configuration 1 in the search b see (2.1) . The latter acceptance is however suppressed close to the kinematic boundary because there is only little E T,miss available. Similar arguments hold for 2c . In this case the requirement that events have to contain two btags plays the role that the single-lepton tag played before. In fact, events resulting from configuration 2 can end up in the SR, if the final-state charm quark is erroneously b-tagged. The corresponding probability is non-negligible and taking into account that the relative acceptance for detecting the configuration 2 in the search c again increases for decreasing mass splitting mt 1 −mχ0 1 , one obtains numerically 2c 1 for points with mt 1 −mχ0 1 not too far from m t . Since the probability to mistake two charm quarks for two b-jets is essentially zero, we furthermore find that 3c 0 for all points of interest in the mt 1 -mχ0 1 plane. With the efficiency maps at hand, one can then use (2.1) and combine the individual searches to obtain model-independent exclusion limits on Br t 1 → cχ 0 1 . The outcome of such an exercise is shown in Figure 3. The red region in both panels is excluded at 95% confidence level (CL) for any value of thet 1 → cχ 0 1 branching ratio. We observe that depending on the LSP (stop) mass, values of mt 1 up to 530 GeV (mχ0 1 up to 160 GeV) are ruled out by our combination of ATLAS Run I data. Outside the excluded region our procedure can be used to set lower and upper model-independent limits on Br t 1 → cχ 0 1 as indicated by the coloured contours in the left and right panel of the figure. This information will be used in Section 4 to put bounds in the mt 1 -mχ0 1 plane for the case of the MSSM with a bino-like LSP and purely right-handed stop-scharm mixing.
It is also interesting to quantify the impact that each individual search has in the combination that leads to the final 95% CL exclusion limit. For the kinematic region R1, we illustrate the power of the different searches in the left panel of Figure 4. The naive combination corresponds to the choice ts = 0 in (2.1) and is indicated by the dark red contour in the figure. We see that a successive inclusion of the searches a, b and c enlarges the excluded area in the mt 1 -mχ0 1 plane considerably. In fact, it is evident from the three additional red contours that the inclusion of search a has the most pronounced effect in the combination, while adding searches b and c to the mix leads to either no or only a minor improvement of the exclusion limits in the mt 1 -mχ0 1 plane. This feature nicely illustrates one of the main findings of our work, i.e. the observation that the recent ATLAS search forc 1 → cχ 0 1 [31] can be recast as a search fort 1 → cχ 0 1 , and that this procedure can be used to set stringent bounds on mt 1 and mχ0 1 in models with non-minimal flavour mixing in the up-squark sector.

Stop search combination for
We now turn our attention to the kinematic region R2. If stop-scharm mixing is present, both the two-body decayt 1 → cχ 0 1 and the three-body decayt 1 → W bχ 0 1 can be phenomenologically relevant. As a result, the final states emerging from two stop decays can contain either two charm quarks (configuration 3), two bottom quarks (configuration 4) or one charm quark and one bottom quark (configuration 5). The additional decay configurations with bottom quarks are depicted in Figure 5. As indicated by the small grey blobs in this figure, thet 1 → W bχ 0 1 transitions proceeds through an effective four-point vertex which involves the exchange of off-shell particles. In our analysis, we include for simplicity only top-quark exchange, but neglect chargino and sbottom contributions, assuming that these states are sufficiently heavy and decoupled from the spectrum.
In the kinematic region R2, we constrain the mt 1 -mχ0 1 parameter space by again combining three different ATLAS analyses. They are all based on 20.3 fb −1 of total integrated luminosity collected at 8 TeV centre-of-mass energy, and implement the following search strategies: d) 4 jets + c-tags + E T,miss [33]: Originally, this ATLAS search has been designed to gain sensitivity to the decay configuration 3 in Figure 1. In our analysis, we consider the c-tagged selections C1 and C2. The events have to meet basic quality criteria and are vetoed if they contain isolated muons or isolated electrons with p T > 10 GeV. As a further preselection E T,miss > 150 GeV and least one R = 0.4 jet with p T > 150 GeV and |η| < 2.5 in the final state is required. To be contained in the SRs, the events are required to have at least four jets with p T > 30 GeV, |η| < 2.5 and |∆φ( p T,j , p T,miss )| > 0.4. A b-jet veto (2.5 rejection factor) is applied to the selected jets by using a loose c-tag requirement (95% efficiency) [36]. In addition, at least one of the three subleading jets has to pass the medium c-tag criteria mentioned earlier in the description of search a. The leading jet is then required to have p T > 290 GeV and the two SRs C1 and C2 are defined with E T,miss > 250 GeV and E T,miss > 350 GeV, respectively. e) 2 leptons + jets + E T,miss [17]: This ATLAS search targets the decay configuration 4 in Figure 5 with both W bosons decaying leptonically. Our analysis includes the SR L90 and L100 of this search. After passing certain quality requirements, events are preselected if they have exactly two oppositely charged leptons (muons, electrons or one charged lepton of each flavour). At least one of these leptons must have p T > 25 GeV and the invariant mass of the lepton pair has to satisfy m ll > 20 GeV. After applying these preselections, events with m ll ∈ [71, 111] GeV, |∆φ( p T,j , p T,miss )| > 1, where j denotes the jet closest to the E T,miss direction, and |∆φ( p T,llb , p T,miss )| < 1.5 with p T,llb = p T,l 1 + p T,l 2 + p T,miss are rejected. The SR L90 requires m T2 > 90 GeV but has no jet requirement, while L100 has a tight jet selection with at least two R = 0.4 jets with p T > 100, 50 GeV and |η| < 2.5. Furthermore, the cut m T2 > 100 GeV on the lepton-based stransverse mass [43,44] is set in L100.
f) 1 lepton+3 jets+b-veto+E T,miss [19]: At the outset, this ATLAS search is intended for the decay configuration 4 in Figure 5 with one leptonic and one hadronic Wboson decay. In our combination we use the bcC diag SR of this analysis, which requires one central lepton with p T > 25 GeV and |η| < 1.2 as well as at least three R = 0.4 jets with p T > 80, 40, 30 GeV and |η| < 2.5. Out of the three jets, none are allowed to be b-tagged (70% efficiency) and the two hardest jets have to satisfy |∆φ( p T,j 1,2 , p T,miss )| > 2.0, 0.8. The other cuts in our analysis are E T,miss > 140 GeV, E T,miss / √ H T > 5 GeV 1/2 , m T > 120 GeV and ∆R( p T,l , p T,j 1 ) ∈ [0.8, 2.4]. The angular separation in the η -φ plane is defined as ∆R = (∆η) 2 + (∆φ) 2 .
Under the assumption that only the decay modest 1 → W bχ 0 1 andt 1 → cχ 0 1 are relevant in region R2, the searches d, e and f can then be combined by using formulas analogous to those presented in (2.1). The corresponding efficiency maps are depicted in Figure 6. In the upper left and right panel we show the efficiencies for detecting final states with two bottom quarks (configuration 4) or one bottom and one charm quark (configuration 5) by means of the search d. As expected the efficiency 4d is typically smaller than 5d , because the search d involves a c-tagged selection. Another noticeable feature of the latter efficiencies is that they are enhanced close to the kinematic boundary m W +m b = mt 1 −mχ0 1 for relatively light stops with mt 1 250 GeV. This is related to the fact that, compared tot 1 → cχ 0 1 , the decayt 1 → W bχ 0 1 produces a harder E T,miss spectrum for masses in this region of the mt 1 -mχ0 1 plane. As a result, events resulting from configuration 4 or 5 more easily pass the E T,miss requirement of search d than final states arising from configuration 3.
In the lower left panel of Figure 6, we find that the efficiency 5e 0 in the entire R2 region, as a result of the requirement of search e to have two charged leptons in each event.
The very same requirement also leads to 3e 0. The efficiency map for 5f is shown     in the lower right panel of the latter figure. One observes that 5f grows towards masses satisfying mt 1 − mχ0 1 = m t . This feature originates mostly from the fact that for mt 1 and mχ0 1 values close to the boundary between the regions R1 and R2, the leading jet arising from the configuration f is on average harder compared to situations where the masses are close to m W + m b = mt 1 − mχ0 1 . As a result of the central lepton requirement, we also find that 3f 0 in the full R2 part of the mt 1 -mχ0 1 plane. In Figure 7, we show the results of our combination procedure in the case of the kinematic region R2. The parameter space that is excluded at 95% CL for any value of thet 1 → cχ 0 1 branching ratio is shaded red in both panels, while the coloured contours indicate the model-independent limits on Br t 1 → cχ 0 1 . We see that mt 1 values up to around 300 GeV are ruled out by the combined ATLAS Run I data for essentially all LSP masses mχ0 1 satisfying m W + m b < mt 1 − mχ0 1 < m t . The obtained model-independent bounds on thet 1 → cχ 0 1 branching ratio will be used in the next section to set limits in the mt 1 -mχ0 1 plane for MSSM scenarios with a bino-like LSP and purely right-handed stop-scharm mixing. [GeV] [GeV]  As in Section 2, we finally discuss the weight that each search has in our combination. The right panel of Figure 4 shows the 95% CL exclusion contours in the kinematic region R2 that are obtained from a naive combination as well as from a successive inclusion of the searches d, e and f . From the figure it is clear that the search d has by far the strongest effect, and that adding the searches e and f does not significantly improve the exclusion in the mt 1 -mχ0 1 plane. This again shows that c-tagged SUSY searches, like for instance the ATLAS analysis [33], can also be used to set stringent constraints on mt 1 and mχ0 1 even outside the kinematic region that the search was initially designed to cover.

Exclusion limits for purely right-handed up-squark mixing
In order to illustrate the effects of flavour mixing in the up-squark sector, we consider a simplified model consisting of a bino-like LSP and a purely right-handed top-like squarkt 1 that is an admixture oft R andc R flavour eigenstates. Sincet R -c R mixing is induced by flavour non-diagonal entries in the squark mass-squared matrix M 2 u , it is convenient to use the mass insertion method [45] to express flavour constraints in terms of the dimensionless quantity 33 .
In contrast to quantities like δ u LL or δ u RL where mixing witht L is considered, purely righthanded scenarios do not require a light bottom squark, and are hence not subject to strong constraints from direct sbottom searches [26,[46][47][48]. Quark flavour constraints are also avoided if only δ u RR insertions are considered. We note that although the mass insertion parameter δ u LR does not require a light sbottom and is poorly constrained by flavour physics, its effect on the stop decay width is suppressed relative to δ u RR by a factor of 16 due to hypercharges. Using the mass insertion parameter (4.1) as a template thus allows one to illustrate the maximal effects of flavour violation in stop decays. Choosing other possibilities would generically lead to stronger exclusions, once additional direct and/or indirect constraints are included.
In Figure 8, we show the dependence of Br t 1 → tχ 0 1 and Br t 1 → W bχ 0 1 on δ u RR for three different benchmark values of (Mũ) 22 . The left panel corresponds to mt 1 = 500 GeV and mχ0 1 = 200 GeV, i.e. a parameter point that lies in the heart of the kinematic region R1. Similarly, the curves in the right panel are based on the point mt 1 = 300 GeV and mχ0 1 = 200 GeV, which is located in the kinematic region R2. Note that even though we parameterise our results in terms of (4.1), we perform an exact diagonalisation in our numerical analysis. One observes that to reduce Br t 1 → tχ 0 1 = 1 − Br t 1 → cχ 0 1 from 100% to 90% requires large mass insertions δ u RR ∈ [0.6, 0.8], while values of δ u RR 0.02 are sufficient to suppress Br t 1 → W bχ 0 1 = 1 − Br t 1 → cχ 0 1 by approximately 50%. The strong δ u RR -dependence of Br t 1 → W bχ 0 1 is a consequence of the fact thatt 1 → W bχ 0 1 is a three-body decay, whereast 1 → cχ 0 1 is a two-body process. In the case oft 1 → tχ 0 1 , the flavour-conserving decay mode is not phase-space suppressed and as a result a largert Rc R mixing angle is needed to obtain appreciable values of Br t 1 → cχ 0 1 . In the kinematic region R3,t 1 → cχ 0 1 is the dominant decay mode unless δ u RR is below 10 −3 , in which case the four-body modet 1 → bf f χ 0 1 becomes the main channel. In the following, we will not consider such smallt R -c R mixing angles and hence will employ Br t 1 → cχ 0 1 = 100% in the whole region R3.
In the two panels of Figure 9, we show the results of the combined search strategies of Sections 2 and 3 when applied to two representative scenarios oft R -c R mixing. The left panel depicts the case of large mixing δ u RR = 0.7, while the right panel illustrates the case of small mixing δ u RR = 0.02. In both plots, we have fixed (Mũ) 22 = 1.5 TeV and the red contours correspond to the regions in the mt 1 -mχ0 1 plane that are excluded at 95% CL. To guide the eye, the 95% CL exclusion limits obtained in [19] and [31] have been overlaid as green and blue dotted curves. Focusing our attention on the kinematic region R1, we see that for the choice δ u RR = 0.7 the limits on mt 1 are about 50 GeV weaker than the bounds obtained in [19], which assumes no stop-scharm mixing. On the other hand, for δ u RR = 0.02 our exclusion coincides with the limit of the 1 lepton + 4 jets + 1 b-tag + E T,miss search. These features are expected because in the first case one has Br t 1 → tχ 0 1 ∈ [70, 80]% in the parameter space of interest, while Br t 1 → tχ 0 1 100% in the second case. In the kinematic region R2, one observes instead that for larget R -c R mixing our bound resembles that of the analysis [31], while for small mixing the region in the mt 1 -mχ0 1 plane around mt 1 = 300 GeV and mχ0 1 = 200 GeV remains allowed. These properties can be understood by realising that in the first case the lightest stop decays to almost 100% viat 1 → cχ 0 1 , while in the second case the decay modet 1 → W bχ 0 1 is dominant, in particular for values of the stop and LSP mass close to the kinematic boundary mt 1 − mχ0 1 = m t . One furthermore notices, that in region R3 our exclusions match the 95% CL bound from thec 1 → cχ 0 1 analysis [31], since both our choices of δ u RR lead to Br t 1 → cχ 0 1 = 100%. The two scenarios oft R -c R mixing that we have considered nicely illustrate our general finding that by combining various E T,miss search strategies, large regions in the mt 1 -mχ0 1 plane can be excluded for arbitrary mass insertion parameters δ u RR . Notice that quark flavour observables leave the mass insertion parameter δ u RR essentially unconstrained. Althought R -c R mixing will induce flavour-changing top-quark decays like t → cZ and t → ch at the one-loop level, the existing LHC Run I constraints on the relevant processes [49] are too loose to lead to any restriction. The mass insertion parameter δ u RR also modifies B-meson decays via chargino loops. However, the wino couples only to left-handed squarks and the Higgsino coupling to right-handed squarks is proportional to the corresponding Yukawa coupling, which is small in the case of the charm squark. As a result, corrections associated to the δ u RR mass insertion are strongly suppressed in processes like B s → µ + µ − and B → X s γ, making the constraints from stop searches derived above the only relevant restrictions on scenarios with purely right-handed stop-scharm mixing.

Conclusions and outlook
In this article, we have shown that allowing for non-minimal flavour violation in the upsquark sector of the MSSM can weaken the direct LHC bounds on the mass mt 1 of the lightest stop. While large effects were found previously [27][28][29], we have demonstrated that a detailed numerical analysis which includes the recent ATLAS search forc 1 → cχ 0 1 limits the possible impact oft 1 → cχ 0 1 ont 1 → cχ 0 1 andt 1 → W bχ 0 1 . The general idea is that although an enhancedt 1 → cχ 0 1 decay rate decreases the branching ratios oft 1 → tχ 0 1 andt 1 → W bχ 0 1 , the directc 1 → cχ 0 1 bounds become progressively more relevant, and as a result stop and scharm searches cannot be fully decoupled in the presence of up-squark mixing. By combining the different decay channels, we demonstrated that there are large regions in the mt 1 -mχ0 1 plane which are disfavoured by LHC Run I searches, independently of the amount of stop-scharm mixing. In particular, we find a lower limit of mt 1 > 530 GeV at 95% CL for LSP masses mχ0 1 100 GeV. This finding agrees with [30], generalising it to the case of a neutralino with non-zero mass. Stringent exclusion limits can also be derived for all other considered decay scenarios. We have illustrated this point by studying MSSM scenarios with a bino-like LSP and non-zerot R -c R mixing. The two representative cases of the mass insertion parameter δ u RR that we have considered are left unconstrained by quark flavour observables, but by combining various direct E T,miss searches, stringent exclusions in the mt 1 -mχ0 1 plane can be derived. In LHC Run II and beyond, the ATLAS and CMS collaborations are expected to provide new results on stop searches with a siginificantly improved reach in the mt 1 -mχ0 1 plane. Improvements in the sensitivity to stops will not only be due to the increase in the centre-of-mass energy, but is also likely to arise from new analysis strategies or technical developments. For instance, ATLAS has recently installed [50] a new subdetector called Insertable B-Layer or IBL [51]. This new inner pixel layer should allow to improve the c-tagging capabilities of ATLAS and thus pave the way to look for processes likec 1 → cχ 0 1 andt 1 → cχ 0 1 in a more efficient fashion. The complementarity and synergy between the different stop decay channels that exists in the presence of flavour mixing is therefore expected to become phenomenologically even more relevant at later phases of the LHC physics programme.
PIEF-GA-2012-326948) and by an Ambizione Grant of the Swiss National Science Foundation. UH acknowledges the hospitality and support of the CERN theory division. He also would like to thank the KITP in Santa Barbara for hospitality and acknowledges that this research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. LCT is supported by the Swiss National Science Foundation.

A Event generation
Our event generation has been performed at leading order with MadGraph5 aMCNLO [52] starting from a customised version of the implementation of coloured scalar pair production presented in [53] and utilises NNPDF2.3 parton distribution functions [54]. The simulated parton-level events were showered with PYTHIA 6 [55] and analysed with the publicly available code CheckMATE [56], which relies on DELPHES 3 [57] as a fast detector simulation. In order to be able to distinguish charm-quark jets from both bottom-quark and light-flavoured jets, we have implemented the JetFitterCharm algorithm described in [36] into DELPHES 3. In all our analyses jets were clustered with FastJet [58] with the anti-k t algorithm [59] as the standard jet finder.
The efficiency maps presented in Figures 2 and 6 have been obtained by simulating 138 different signal points that fall into the kinematic regions R1 and R2. The actual mapping in the mt 1 -mχ0 1 plane can be found in [60,61]. For each signal point and all relevant final states, 10 5 partonic events have been generated, showered and passed through the fast detector simulation and an analysis containing the selection requirements corresponding to the individual searches described in Sections 2 and 3. The efficiency maps are then obtained by considering the SR that provides the best exclusion limit for a given point in the mt 1 -mχ0 1 plane.