A light sneutrino rescues the light stop

Stop searches in supersymmetric frameworks with $R$-parity conservation usually assume the lightest neutralino to be the lightest supersymmetric particle. In this paper we consider an alternative scenario in which the left-handed tau sneutrino is lighter than neutralinos and stable at collider scales, but possibly unstable at cosmological scales. Moreover the (mostly right-handed) stop $\widetilde t$ is lighter than all electroweakinos, and heavier than the scalars of the third generation doublet, whose charged component, $\widetilde\tau$, is heavier than the neutral one, $\widetilde\nu$. The remaining supersymmetric particles are decoupled from the stop phenomenology. In most of the parameter space, the relevant stop decays are only into $t \widetilde\tau \tau$, $t\widetilde\nu\nu$ and $b \widetilde\nu \tau$ via off-shell electroweakinos. We constrain the branching ratios of these decays by recasting the most sensitive stop searches. Due to the"double invisible"kinematics of the $\widetilde t\to t\widetilde\nu\nu$ process, and the low efficiency in tagging the $t\widetilde\tau\tau$ decay products, light stops are generically allowed. In the minimal supersymmetric standard model with $\sim$ 100 GeV sneutrinos, stops with masses as small as $\sim$ 350 GeV turn out to be allowed at 95% CL.


Introduction
In most supersymmetric (SUSY) models, R-parity conservation is implemented to avoid rapid proton decay, which implies that the lightest supersymmetric particle (LSP) is stable. As there are strong collider and cosmological constraints on long-lived charged particles [1][2][3][4][5][6], the LSP is preferably electrically neutral. This, together with the appealing cosmological features of the neutralino, has had a strong influence on the ATLAS and CMS choice on the SUSY searches. Most of them indeed assume the lightest neutralino to be the LSP or, equivalently for the interpretation of the LHC searches, the long-lived particle towards which all produced SUSY particles decay fast.
Searches under these assumptions are revealing no signal of new physics and putting strong limits on SUSY models. The interpretation of these findings in simplified models provides lower bounds at around 900 and 1800 GeV for the stop and gluino masses, respectively [7,8], which are in tension with naturalness in supersymmetry. In this sense, the bias for the neutralino as the LSP, as well as an uncritical understanding of the simplifiedmodel interpretations, is driving the community to believe that supersymmetry can not be a natural solution to the hierarchy problem anymore. In the present paper we break with this attitude and take an alternative direction: we assume that the LSP is not the lightest neutralino but the tau sneutrino 1 . Moreover we avoid peculiar simplified model assumptions and deal with realistic, and somewhat non trivial, phenomenological scenarios. As we will see, the findings in this alternative SUSY scenario make it manifest the strong impact that biases have on our understanding on the experimental bounds and, in turn, on the viability of naturalness.
As the lightest neutralino is not the LSP, we focus on scenarios with all gauginos (gluinos and electroweakinos) heavier than some scalars. These scenarios, discussed in the context of natural supersymmetry, are feasible in top-down approaches, as e.g. in the following supersymmetry breaking mechanisms.

Gauge mediation
In gauge mediated supersymmetry breaking (GMSB) [12] the ratio of the gaugino (m 1/2 ) over the scalar (m 0 ) masses behaves parametrically as m 2 1/2 /m 2 0 ∝ N f (F/M 2 ), where N is the number of messengers, F the supersymmetry breaking parameter and M the messenger mass. The condition F/M 2 1 guarantees the absence of tachyons in the messenger spectrum, and if saturated, it yields f 3. In this way, for large N or F/M 2 close to one, the hierarchy m 1/2 m 0 emerges. Within this hierarchy, gluinos are heavier than electroweakinos, and stops heavier than staus, parametrically by factors of the order of g 2 s /g 2 α at the messenger mass scale M , with g α being the relevant gauge coupling. The renormalization group running to low scales increases these mass splittings for M much above the electroweak scale.
Further enhancements to these mass gaps can be achieved by including also gravity mediation contributions or extending the standard model (SM) group under which the messengers transform [13] 2 .

Scherk-Schwarz
In five-dimensional SUSY theories, supersymmetry can be broken by the Scherk-Schwarz (SS) mechanism [16][17][18][19][20][21][22][23][24]. In this class of theories, one can assume the hypermultiplets of the right handed (RH) stop and the left handed (LH) third generation lepton doublet localized at the brane, and the remaining ones propagating in the bulk of the extra dimension. In such an embedding, gauginos and Higgsinos feel supersymmetry breaking at tree level while scalars feel it through one-loop radiative corrections. As a consequence, the ratio between the gaugino and scalar masses is m 2 1/2 /m 2 0 ∝ 4π/g 2 α . Eventually, gluinos and electroweakinos are very massive and almost degenerate, while the RH stops are light but heavier than the LH staus and the tauonic sneutrinos by around a factor g 2 s /g 2 α .
Although the aforementioned ultraviolet embeddings strengthen the motivation of our analysis, in the present paper we do not restrict ourselves to any particular mechanism of supersymmetry breaking. Instead we take a (agnostic) bottom-up approach. We consider a low-energy SUSY theory where the stop phenomenology is essentially the one of the minimal supersymmetric standard model (MSSM) with the lighter stop less massive than the electroweakinos and more massive than the third-family slepton doublet 3 . Gluinos and the remaining SUSY particles are heavy enough to decouple from the collider phenomenology of the lighter stop. In this scenario the LSP at collider scales is therefore the LH tau sneutrino. Of course, subsets of the parameter regions we study can be easily accommodated in any of the previously discussed supersymmetry breaking mechanisms or minor modifications thereof.
In the considered parameter regime, the phenomenology of the lighter stop, t, is dominated by three-body decays via off-shell electroweakinos into staus and tau neutrinos, τ and ν. The viable decay channels are very limited. If the masses of the lightest sneutrino and the lighter stop are not compressed, the only potentially relevant stop decays are 2 In particular, we assume that the slepton singlet τ R is much heavier than the slepton doublet ( ν, τ ) L . In GMSB scenarios this hypothesis can be fulfilled only if the messengers transform under a beyond-thestandard-model group with e.g. an extra U (1) such that the extra hypercharge of the lepton singlet is, in absolute value, larger than the one of the lepton doublet. For instance if we extend the SM gauge group by a U (1), with hypercharge Y , from E 6 one can easily impose the condition that Y (ν L ) = 0 while Y (τ R ) = 0 [14,15]. In this model one needs to enlarge the third generation into the 27 fundamental representation of E 6 decomposed as 27 = 16+10+1 under SO(10), while 16 = 10+5+ν c and 10 = 5 H +5 H under SU (5). Then we get 4 Y = (−1, 0, −2, 2, 1, −3) for the SU (5) representations (10,5, ν c , 5 H ,5 H , 1), respectively.
3 Notice that the mass and quartic coupling of the Higgs do not play a key role in the stop phenomenology. Then, the analysis of the present paper also applies to extensions of the MSSM where the radiative correlation between the Higgs mass and stop spectrum is relaxed. t → t νν, t → t τ τ , t → b ντ and t → b τ ν, the latter being negligible when the interaction between the lighter stop and the Wino is tiny (see more details in Sec. 2) 4 . Thus, for scenarios where the lighter stop has a negligible LH component and/or the Wino is close to decoupling, the relevant stop signatures reduce to those depicted in Fig. 1. This is the stop phenomenology we will investigate in this paper. A comment about dark matter (DM) is here warranted. It is well known that the LH sneutrino is not a good candidate for thermal DM [25,26], as it is ruled out by direct detection experiments [27,28]. Therefore, in a model like the one we study here, one needs a different approach to solve the DM problem. Since many of the available approaches would modify the phenomenology of our scenario only at scales irrelevant for collider observables, incorporating such changes would not modify our results (for more details see Sec. 5).
The outline of the paper is the following. In Sec. 2 we provide further information on the scenario we consider, and on the effects that the electroweakino parameters have on the stop signatures. In Sec. 3 we single out the ATLAS and CMS analyses that, although performed to test different frameworks, do bound our scenario. The consequent constraints on the stop branching ratios and on stop and sneutrino masses are presented in the same section. The implications for some benchmark points and the viability of stops as light as 350 GeV are explained in Sec. 4. Sec. 5 reports on the conclusions of our study, while App. A contains the technical details about our analysis validations.

The model and dominant stop decays
In the MSSM and its minimal extensions, it is often considered that naturalness requires light Higgsinos and stops, and not very heavy gluinos. In fact, in most of the ultraviolet MSSM embeddings, the Higgsino mass parameter, µ, enters the electroweak breaking conditions at tree level, and only if µ is of the order of the Z boson mass the electroweak scale is naturally reproduced. This however solves the issue only at tree level, as also the stops can radiatively destabilize the electroweak breaking conditions. For this reason stops must be light, and the argument is extended to gluinos since, when they are very heavy, they efficiently renormalize the stop mass towards high values. Therefore stops cannot be light in the presence of very massive gluinos without introducing some fine tuning.
Remarkably, the above argument in favor of light Higgsinos, light stops and not very heavy gluinos, is not general. There exist counter examples where the Higgs sector, and thus its minimization conditions, is independent of µ [22][23][24], and where heavy gluinos do not imply heavy stops [19,24,29]. In view of these "proofs of principle", there appears to be no compelling reason why the fundamental description of nature should not consist of a SUSY scenario with light stops and heavy gluinos and electroweakinos. It is thus surprising that systematic analyses on the latter parameter regime have not been performed 5 .
The present paper aims at triggering further attention on the subject by highlighting that the present searches poorly constrain the stop sector of this parameter scenario. For this purpose we focus on the LHC signatures of the lighter stop being mostly RH. The illustrative parameter choice we consider is the one where the stop and slepton mixings are small, and the light third generation slepton doublet is lighter than the lighter stop 6 . The remaining squarks, sleptons and Higgses are assumed to be very heavy, in agreement with the (naive) interpretation of the present LHC (simplified model) constraints. Specifically, these particles, along with gluinos, are assumed to be decoupled from the relevant light stop phenomenology. Moreover, possible R-parity violating interactions are supposed to be negligible at detector scales.
In the present parameter scenario the light stop phenomenology only depends on the interactions among the SM particles, the lighter (mostly RH) stop, the lighter (mostly LH) stau, the tau sneutrino and the electroweakinos. The stop decays into sleptons via off-shell charginos and neutralinos. In principle, due to the interaction between the stop and the neutralinos (charginos), any up-type (down-type) quark can accompany the light 5 For recent theoretical analyses in the case of light electroweakinos and their bounds see e.g. [30,31]. 6 These features naturally happen in GMSB and SS frameworks. For GMSB, the trilinear parameter A arises at two loops whereas m 0 appears at one loop. Thus the ratio A/m 0 is one-loop suppressed. Similarly, the SS breaking produces a large tree-level mass for the LH stop and the RH stau fields in the bulk, and generates A at one loop, such that A/m 0 is small due to a one-loop factor. Moreover, the ratio m ν /m t is parametrically O(g 2 /g 2 s ) in such GMSB and SS embeddings.
stop decay signature. Nevertheless, in practice, flavor-violating processes arise only for a very compressed slepton-stop mass spectrum. For our main purpose, which is to prove that pretty light stops are allowed in the present scenario, the analysis of this compressed region is not essential 7 . To safely avoid this region, we impose m t m ν + 70 GeV, with m t and m ν being the masses of the lighter stop and the tau sneutrino, respectively. The kinematic distributions associated to the stop decays strongly depend on the stau and sneutrino masses. In particular, the sneutrino mass m ν is free from any direct constraint coming from collider searches and, as stressed in Sec. 1, we refrain from considering bounds that depend on cosmological scale assumptions. On the other hand, numerous collider-scale dependent observables affect the stau as we now discuss.
The ALEPH, DELPHI, L3 and OPAL Collaborations interpreted the LEP data in view of several SUSY scenarios and, depending on the different searches, they obtain the stau mass bound m τ 90 GeV [1][2][3][4]. A further constraint comes from the CMS and ATLAS searches for disappearing charged tracks, for which m τ 90 GeV is ruled out if the stau life-time is long [5,6]. However, in the present scenario with small sparticle mixings, the mass splitting m τ − m ν , given by can be sufficiently large to lead to a fast stau decay, and in fact the charged track LHC bound is eventually overcome for m τ 90 GeV and tan β > 1 (see Sec. 5). On the other hand, a light stau with mass close to the LEP bound modifies the 125 GeV Higgs signal strength R(h → γγ) unless tan β 100 [35]. All together these bounds hint at an intermediate (not very large) choice of tan β, as e.g. tan β ∼ 10.
Finally, a light stau, as well as a light stop, can modify the electroweak precision observables [36]. One expects the corresponding corrections to be within the experimental uncertainties for m τ 90 GeV, m t 300 GeV and negligible sparticle mixing, since the stop is mostly RH and the light stau is almost degenerate in mass with the tau sneutrino. The latter degeneracy plays a fundamental role also in the collider signature of the stau decay: due to the compressed spectrum, the stau can only decay into a stable (at least at detector scales) sneutrino and an off-shell W boson, giving rise to soft leptons or soft jets.
At the quantitative level, the decay processes of the stop are described, in the electroweak basis, by the relevant interaction Lagrangian involving the Bino, Wino, Higgsinos, tau sneutrino, the LH and RH stops and staus ( B, W , H 1,2 , ν L , t L,R and τ L,R ) as well as their SM counter-partners 8 : Here h t,b,τ are the SM Yukawa couplings while, following the usual MSSM notation, H 2 ( H 1 ) is the SUSY partner of the Higgs with up-type (down-type) Yukawa interactions. The first two lines in Eq. (2.2) come from D-term interactions, the third and fourth lines from F -terms Yukawa couplings and the last line from the covariant derivative of the corresponding fields. This Lagrangian helps to pin down the Bino, Wino and Higgsino (off-shell) roles in the stop decays. In order to understand the magnitude of the single contributions, it is important to remind that the stop (stau) is mostly RH (LH). Moreover, for our scenario with electroweakino mass parameters M 1 , M 2 , µ m Z , the Bino, Winos and Higgsinos are almost mass eigenstates.
The Bino and the electrically-neutral components of Winos and Higgsinos contribute to the decays t → t τ τ and t → t νν (see the first two diagrams in Fig. 1). We expect different branching ratios into anti-stau tau and into stau anti-tau. This is a consequence of the fact that the decaying particle in the first diagram of Fig. 1 is a stop and not an anti-stop. This difference in the branching ratios can be understood from the point of view of effective operators obtained in the limit that the neutralinos are enough heavy that can be integrated out. We show that this is so by considering the two (opposite) regimes where the light stop is either mostly RH or mostly LH.
Let us first assume that in the process t → t τ τ the decaying stop is RH, i.e. the field t R in Eq. (2.2). If the neutralinos are mainly gauginos ( B, W 0 ), as the RH stop is an SU (2) L singlet, the process has to be mediated by the Binos. In this case the produced top will be RH and the lowest order (dimension-five) effective operator can be written as ( t * R τ L )(t RτL ), by which only staus and anti-taus are produced, but not antistaus and taus. For diagrams mediated by Higgsinos, the produced top will be LH and the effective operator is ( t * R τ L )(t LτR ), and again the stop decay products are staus and anti-taus. However, in the limit of heavy electroweakino masses, the coefficient of the latter operator is suppressed by O(v/µ). Now let us instead assume that the decaying stop is LH, that is, t L in Eq. (2.2). In this case the effective operators for the exchange of gauginos and Higgsinos in t → t τ τ would be ( t * L τ R )(t LτR ) and ( t * L τ R )(t RτL ) respectively, implying again that the decay products are staus and anti-taus. The contribution to the latter effective operators is small if the RH stau is heavy (and/or the LH component of the stop is small), as happens in the considered model, leading again to the production of staus and anti-taus with either chirality.
In reality, in our scenario with mostly RH light stops, since neutralinos are not completely decoupled, full calculations of the stop decays exhibit also some anti-stau and tau contributions. These proceed from dimension-six effective operators such as e.g.
, which contain an extra suppression factor O(v/µ, v/M 1,2 ) with respect to the leading result. We can finally say that the decay of stops is dominated by the production of anti-taus while the production of taus is chirality suppressed 9 . Although interesting, this effect escapes from the most constraining stop searches, which do not tag the charge of taus or other leptons (see Sec. 3). For the purposes of the detector simulations the stop branching ratios can thus be calculated without differentiating the processes yielding taus or anti-taus.
The chirality suppression is instead crucial for the three-body decays via off-shell charginos. In principle both decays t → b τ ν and t → b ντ are allowed but, due to the chirality suppression, only the latter (which corresponds to the third diagram in Fig. 1) can be sizeable in our scenario. Indeed, let us consider the case where the stop decaying into b L and an off-shell charged Higgsino is the RH one 10 . The only five-dimensional effective operator that can be constructed is ( t * R ν L )(b LτR ) which appears from the mixing between H + 2 and ( H − 1 ) * , after electroweak symmetry breaking, and is thus suppressed by a factor O(v/µ). Now instead assume that the stop is LH. At leading order, the decay into b L and W + gives rise to the operator ( t * L τ * L )(b L ν L ) 11 . Moreover, the t L decay into b R and ( H − 1 ) * can only be generated by a dimension-six operator which is further suppressed by the (tiny) factor h b h τ / cos 2 β. Thus, in general, only the decay t → b ντ can be relevant in scenarios where the light stop is practically RH (or the Wino is much heavier than the Higgsinos), as we are considering throughout this work. For this reason the decay t → b τ ν is absent in Fig. 1, that only depicts the relevant decays in our scenario.
In the next section we will study in detail how the present LHC data constrain scenarios with light stops predominantly decaying into t τ τ , t νν and b ντ , while in Sec. 4 we will 9 The same effect arises also in the t → t νν decay (second diagram in Fig. 1), but the collider signatures of these different products are not relevant, for neutrinos or anti-neutrinos are indistinguishable at colliders. 10 As t R is an SU (2) L singlet it cannot decay via a charged gaugino W ± . 11 Notice that in our convention both b L and ν L are undotted spinors and thus b L ν L ≡ b α L αβ ν β L , with αβ being the Levi-Civita tensor, is Lorentz invariant. provide some parameter regions exhibiting this feature and relaxing the bounds on light stops.

LHC searches and the dominant decays
The data collected during the LHC Run II, even at small luminosity, have proven to be more sensitive to SUSY signals than their counterpart at √ s = 8 TeV. Among the searches with the most constraining expected reach, we will be interested in those for pair-produced stops in fully hadronic final states performed by the ATLAS and CMS Collaborations, in Refs. [37,38], respectively, as well as searches for pair-produced stops in a final state with tau leptons carried out by the ATLAS Collaboration in Ref. [39]. However, the results provided by these experiments can not simply be used to constrain the signal processes under consideration.
This reinterpretation issue is clear for the decay t → t τ τ (see the first diagram in Fig. 1), as the final state is different from any other final state studied by current searches, in particular with more taus involved. In the t → t νν decay (see the second diagram in Fig. 1), the final state, a top plus missing transverse energy E miss T , coincides with e.g. the one of the t → t χ 0 process, with the neutralino as the LSP studied in Refs. [37,38]. Nevertheless, since the neutralino is off-shell in our case, most of the discriminating variables behave very differently, and therefore the experimental bound on t → t χ 0 does not strictly apply [40]. And even the existing analyses for stops decaying into several invisible particles, which also Refs. [37][38][39] investigate, turn out to be based on kinematic cuts with efficiencies that are unreliable in our case. This for instance holds for the t → b ντ decay (see the third diagram in Fig. 1) whose invisible particle does not exactly mimic the ones of t → bτ ν G (where G is a massless gravitino) analyzed in Ref. [39].
For the sake of comparison, in the left panel of Fig. 2 we show the distributions of E miss T in the decays t → t χ 0 (dashed green line) and t → t νν (orange solid line) with m t = 625 GeV and m LSP = 200 GeV. In the right panel we contrast the shapes of the transverse mass m T 2 constructed out of the tagged light tau lepton, without any further cut, coming from the decays t → b ντ (dashed green line) and t → bτ ν G (orange solid line) for m τ = m ν = 400 GeV and gravitino mass m G = 0. These kinematic variables are of fundamental importance for the aforementioned ATLAS and CMS searches. In particular, as Fig. 2 illustrates, the stringent cuts on these quantities reduce the efficiency on the signal in our model, with respect to the standard benchmark scenarios for which the LHC searches have been optimized. This issue was previously pointed out in Ref. [40].
In the light of this discussion, we recast the aforementioned analyses using homemade routines based on a combination of MadAnalysis v5 [41,42] and ROOT v5 [43], with boosted techniques implemented via Fastjet v3 [44]. Two signal regions, SRA and SRB, each one containing three bins, are considered in the ATLAS fully hadronic search [37] (note that SRA and SRB are not statistically independent, though). The CMS fully hadronic analysis [38] considers, instead, a signal region consisting of 60 independent bins. Finally, the ATLAS analysis involving tau leptons carries out a simple counting experiment. Details on the validation of our implementation of these three analyses can be found in App. A. We find that our recast of the ATLAS search for stops in the hadronic final state leads to slightly smaller limits, while the ones of the other searches very precisely reproduce the experimental bounds. Thus, as shown in Tab. 1, we combine the whole CMS set of bins with the above signal region SRB for probing the decay t → t νν, and with the single bin of the ATLAS counting experiment for testing the t → t τ τ and t → b ντ processes 12 . Limits at different confidence levels are obtained by using the CL s method [45]. The expected number of background events, as well as the actual number of observed events, are obtained from the experimental papers. Signal events, instead, result from generating pairs of stops in the MSSM with MadGraph v5 [46] that are subsequently decayed by Pythia v6 [47]. The parameter cards are produced by means of SARAH v4 [48] and SPheno v3 [49]. When each channel is studied separately, the corresponding branching ratio has been fixed manually to one in the parameter card. When several channels are considered, the amount of signal events is rescaled accordingly.

Single channel bounds
As discussed in the previous sections, in our scenario the possible decay channels are t → t τ τ , t → t νν and t → b ντ . In this section we consider each individual decay channel and use the LHC data to bound the corresponding branching ratio in the plane (m t , m ν ).
The results are reported in Fig. 3 where, for every given channel, the bounds at the 90% CL (left panels) and 95% CL (right panels) are presented in the plane (m t , m ν ). Every panel contains the exclusion curves corresponding to several values of the branching ratio into the considered channel. For a given branching ratio, the allowed region stands outside the respective curve (marked as in the legend) and within the kinematically allowed area (below the thin dashed line).
For the decay t → t τ τ (upper panels of Fig. 3) the most sensitive analysis is the ATLAS counting experiment. We combine it with the CMS signal region into a single statistics. As Fig. 3 shows, the bound on this channel is very weak. In particular, among the searches that we identified as the most sensitive ones to this channel, there is no one constraining this decay mode at 95% CL for m t 300 GeV and m ν 100 GeV.
For the decay channel t → t νν (middle panels of Fig. 3) the most sensitive analysis is the CMS analysis, though the ATLAS search for hadronically decayed stops is also rather constraining. The bound provided in Fig. 3 is based on the combination of both. As already pointed out, the stringent cuts optimized for the searches for stops into on-shell LSP neutralinos have rather low efficiency on the "double invisible" three-body decay signal involving an off-shell mediator [40].
Finally, the bounds for the t → b ντ decay channel are presented in the lower panels of Fig. 3. As summarized in Tab. 1, it turns out that the most sensitive analysis to this channel is the ATLAS counting one, although the other two searches can also (slightly) probe this mode. In Fig. 3, the exclusion curves for this channel are obtained by combining the CMS signal regions with the ATLAS counting one into a single statistics (we do not expect relevant improvements by also including the excluded ATLAS analysis).
We expect the findings to be qualitatively independent of the particular SUSY realizaindependent, for one of them concentrates on the fully hadronic topology while the other tags light leptons. If we only combine with the CMS analysis is because the validation of this search gives better results. At any rate, no big differences are expected. tion we consider. The only model dependence is the mass splitting between the stau and the sneutrino, which determines the kinematic distribution of the stau decay products. In specific SUSY models such a splitting is determined, and due to the numerical approach of the present analysis, our results are obtained for a concrete stau-sneutrino mass splitting, as detailed in Sec. 4. Nevertheless, in practice, our results should qualitatively apply to all SUSY realizations with prompt decays of staus with mass m τ m ν + 30 GeV and BR( τ → νW * ) 100% 13 .

Combined bounds
In concrete models, it is feasible that the branching ratios of the three aforementioned stop decay channels sum up to essentially 100%, as we will explicitly see in Sec. 4. In such a situation, we can consider BR( t → t νν) and BR( t → b ντ ) as two independent variables, and fix BR( t → t τ τ ) as It is then possible to use the aforementioned ATLAS and CMS searches to constrain the two-dimensional plane BR( t → t νν), BR( t → b ντ ) for some set of values of m t and m ν . The total number of signal events after cuts is given by where L = 13 fb −1 stands for the integrated luminosity, σ is the stop pair production cross section, and the indices i and j run over the three decay modes. The quantity ij is the efficiency that our recast analyses have on the t t * → ij events and is strongly dependent on the mass spectrum. To determine ij in some given mass spectrum scenarios, we run simulations of t t * → ij following the procedure discussed above. As the searches do not discriminate between ij and its hermitian conjugate, it holds ij = ji . The results are shown in Fig. 4. The regions above the horizontal dashed green lines would be the excluded ones had we assumed the signal to consist of only t t * → b ντ b ντ events. Analogously, the areas to the right of the vertical green dashed lines would be the 13 To clarify this issue, we repeated the t → t τ τ simulations for a few parameter points featuring a tiny stau sneutrino mass splitting. For these few points, the constraints on t → t τ τ presented in this paper turn out to be comparable, i.e. ruling out a similar region of the parameter space in the plane (m t , m ν ). Moreover the constraints on t → t νν and t → b ντ are of course the same. This suggests that the presented bounds can be applied to other scenarios. Extensive parameter space simulations would be however required to prove this feature in full generality.  excluded ones under the assumption that only the events t t * → t ννt νν are bounded. The regions enclosed by the orange solid lines are instead excluded considering the whole signal, including also the stop decay into t τ τ and the mixed channels. For such comprehensive exclusion bounds, a common CL s is constructed out of the bins in the ATLAS signal region SRB, all bins in the CMS analysis and the single bin in the ATLAS counting experiment.
In light of these results, several comments are in order: • i) The comprehensive bounds, which exclude the region outside the orange curves, are much stronger than those obtained by the simple superposition of the constraints on the isolated signals, ruling out the region above and on the right of the horizontal and vertical dashed lines, respectively. This even reaches points close to the origin, where the main decay channel is t → t τ τ . The main reason is the inclusion of the mixed channels.
• ii) The fact that no single decay necessarily dominates, makes sizeable regions of the parameter space to still be allowed by current data. This is further reinforced by the smaller efficiencies that current analyses have on these processes in comparison to the standard channels. Thus, even small masses such as m t 300 GeV and m ν 70 GeV, illustrated in the top left panel, can be allowed.
• iii) As we can see from all panels in Fig. 4, the allowed regions favor large values of BR( t → t τ τ ). This effect can be easily understood from the first row plots in Fig. 3: there is little sensitivity of the present experimental searches to the channel t → t τ τ when m t and m ν are small.

Constraints on particular SUSY models
The results of Sec. 3 can be reinterpreted in concrete SUSY scenarios that exhibit stops decaying as in Fig. 1  troweakino mass spectrum and their partial widths are determined by means of SARAH v4 and SPheno v3. More specifically, we use the MSSM implementation provided by these codes, and fix the parameters as follows. We impose tan β = 10, in agreement with the arguments of Sec. 2. The slepton and squark soft-breaking trilinear parameters are set to zero. The soft masses of the RH stop, M 2 U R , and LH stau doublet, M 2 L L , are much lighter than those of their partners with opposite "chirality", M 2 Q L and M 2 E R . The electroweakino soft parameters are set, as shown for scenarios A and B in Tab. 2, above the lighter stop mass. The masses of the remaining SUSY particles are not relevant for our analysis, they just need to be heavy enough to not intervene in the stop phenomenology. Nevertheless, for practical purposes, all SUSY parameter have to be chosen and then we set all masses of the SUSY particles except electroweakinos, light stop and light stau doublet at 3 TeV. For the above parameter choice, we study two parameter regimes denoted as scenarios A and B, characterized by the values of M 1 , M 2 and µ quoted in Tab. 2. Within each regime, we vary the masses m t and m ν , by scanning over M 2 U R and M 2 L L , and consequently m τ is determined as well. We discard the parameter points with m t < m ν +70 GeV, which correspond to compressed scenarios that are not investigated in this paper. Contour plots of dominant stop branching ratios are plotted in Figs. 5 as a function of m t and m ν , for scenario A (upper row panels) and scenario B (lower row panels). For each scenario, the branching ratios of t → t τ τ , t → t νν, and t → b ντ are plotted in the left, middle and right panels, respectively. As anticipated in Sec. 2, the main effect of decreasing M 2 and µ is to enhance BR( t → b ντ ), as we can see by comparing the two right panels in Fig. 5. Conversely, by increasing the value of M 2 and µ we increase the branching ratio corresponding to the channel t τ τ , and we expect to make softer the bounds in the plane (m t , m ν ), in agreement with the general behavior in the lower row panels in Fig. 3 and in all plots in Fig. 4. We stress that, within the considered parameter range, the sum of these three branching ratios is always above 95% (depending on the range of m t and m ν ) which is consistent with our general model assumptions. We also checked numerically that the total width of the stau is O(10 −8 GeV) for m ν ≈ 500 GeV, and is much larger at smaller sneutrino masses. Analogously, the mass gap between the stau and sneutrino masses ranges between 5 − 40 GeV, the latter value appearing for m ν ≈ 60 GeV. The

Conclusions
The bottom line in this paper is that, in the minimal supersymmetric standard model (MSSM) scenario with heavy electroweakinos, light staus and light tau sneutrinos, a mostly right-handed stop with a mass of around 350 GeV is compatible with the present LHC data. This is mostly due to the coexistence of several branching ratios into channels which the LHC searches have weak sensitivity to. Although we have not been concerned about detailed naturalness issues, light stops certainly help in this sense. Heavy electroweakinos are instead considered unnatural, but this is not necessarily true for low scale supersymmetric (SUSY) breaking. In particular, heavy electroweakinos are feasible without inducing a hierarchy problem in some supersymmetry breaking embeddings based on Scherk-Schwarz (SS) and low scale gauge mediated supersymmetry breaking (GMSB) mechanisms.
In the investigated scenario, the light spectrum only includes the Standard Model particles, the mostly right-handed stop, the tau sneutrino and the mostly left-handed stau. Among these SUSY particles, the light stop is heavier than the left-handed stau, which is in turn heavier than the tau sneutrino. The charginos and neutralinos might be at the TeV scale or below, but in any case heavier than the light stop. The number of dominant stop decay channels is only a few. These decays occur via off-shell electroweakinos, and ATLAS and CMS fully hadronic searches for stops into hadronic or tau lepton states [37][38][39], although designed for a different scope, are the searches that are expected to be most sensitive to them. Remarkably, their constraints do not rule out stops with masses as small as 350 GeV, when the stau mass is around 100 GeV, the sneutrino mass is approximately 60 GeV, and the electroweakinos are at the TeV scale. Neither further bounds do apply: such staus are heavy enough to be compatible with the LEP bounds [1][2][3][4], and decay fast, in agreement with the LHC bounds on disappearing tracks [5,6].
The only constraint comes from cosmological scale observables. In the present study the tau sneutrino is the lightest SUSY particle, stable (at least) at collider scales. If it also is stable at cosmological scales, its thermal relic density is below the dark matter (DM) abundance [25,26] and, moreover, it is also ruled out by direct detection experiments [27,28]. So the scenario has to be completed somehow, to provide a reliable explanation of the surveyed DM relic density and/or avoid the strong bounds from direct detection experiments.
There are a limited number of possible mechanisms to circumvent the previous problems without altering the stop phenomenology we have investigated. The simplest possibility is to assume that the sneutrino, even though stable at collider scales, is unstable at cosmological scales. In theories with R-parity conservation this can be realized only if there is a lighter SUSY particle (possibly a DM candidate) which the sneutrino decays to, but such that the sneutrino only decays outside the detector and in cosmological times. In theories with GMSB this role can be played by a light gravitino G. It is a candidate to warm DM and its cosmological abundance is given by Ω 3/2 h 2 0.1(m 3/2 /0.2 keV), which suggests a rather low scale of supersymmetry breaking F m 3/2 M P . In this case the sneutrino decays as ν → ν G and, as far as collider phenomenology is concerned, it looks stable. In theories with a heavy gravitino, as e.g. in theories with SS breaking, one could always introduce a right-handed sneutrino ν R , lighter than the left-handed sneutrino 16 . On the other hand, the right-handed sneutrino can in principle play the role of DM [9,11]. If its fermionic partner is light, also the decay t → b τ ν R appears although this process is suppressed by the small neutrino Yukawa coupling. Thus, in practice, the stop collider phenomenology would not be different from that considered in the present paper. Another possibility is if the cosmological model becomes non-standard, as would happen by assuming modifications of general relativity or with non-standard components of DM, as for instance black holes 17 . In this case, in order to overcome the direct detection bounds, the initial density of sneutrinos in thermal equilibrium should be diluted by some mechanism, as e.g. an entropy production (or simply a non-standard expansion of the universe), before the big bang nucleosynthesis [54,55]. Finally the simplest solution to avoid the direct detection bounds is if there is a small amount of R-parity breaking and the sneutrino becomes unstable at cosmological scales. For instance one can introduce an R-parity violating superpotential as W = λ ijk L i L j E k [56], with a small Yukawa coupling λ ijk such that the sneutrino decays as ν → e jēk . Depending on the value of the coupling λ the sneutrino can decay at cosmological times. Needless to say, in this case one would need some additional candidate to DM.
Remarkably, the present bounds on the stop mass in the considered scenario are so weak that even the complete third-generation squarks might be accommodated in the sub-TeV spectrum. Indeed, the kinematic effects and the coexistence of multi decay channels responsible for the poorly efficient current LHC searches, should also (partially) apply to the left-handed third-family squarks. The presence of these additional squarks in the light spectrum would effectively increase the number of events ascribable to the channels we have analyzed. Nonetheless, since the obtained constraints are very weak, there should be room for a sizeable number of further events before reaching TeV-scale bounds. In such a case, in the heavy electroweakino scenario considered in this paper, present data could still allow for a full squark third-family generation much lighter than what is naively inferred from current constraints based on simplified models. Quantifying precisely this, as well as studying the right-handed neutrino extension, is left for future investigations.
Details aside, our main conclusion highlights the existence of unusual scenarios where very light stops are compatible with the present LHC searches without relying on artificial (e.g. compressed) parameter regions. It is not clear whether this simply occurs because of lack of dedicated data analyses. In summary, the possibility that the bias for the neutralino as lightest SUSY particle have misguided the experimental community towards partial searches, and that clear SUSY signatures are already lying in the collected data, is certainly intriguing.

A Analysis validation
In order to validate our implementations of the experimental analyses of Refs. [37][38][39], we apply them to Monte Carlo events generated using the same benchmark models of those searches. Specifically, these are pair-produced stops decaying as t → t χ 0 [37,38] and t → bν τ ( τ → τ G) [39]. The signal samples are obtained by generating pairs of stop events in the MSSM with MadGraph v5 at leading order. Such events are subsequently decayed by Pythia v6. In the parameter cards produced with SARAH v4 and SPheno v3, the branching ratio BR( t → t χ 0 ) is fixed manually to 100% in the first two analyses. In the same vein, for the analysis of Ref. [39] we fix both BR( t → bν τ ) = 1 and BR( τ → τ ν) = 1. Notice that, in this last case, the neutrino plays the role of the (massless) gravitino, thus mimicking the channel studied in the experimental work. As stated in the main text, bounds are obtained by combining the different bins of a particular search into a single statistics (note that the analysis of Ref. [39] is simply a counting experiment). The only  caveat concerns the analysis of Ref. [37]. The two signal regions considered in that search are not statistically independent. Therefore, the most constraining of the two statistics, each constructed out of the three bins of a particular signal region, is taken. Altogether, the comparison between the bounds reported in Refs. [37][38][39] and ours are displayed in Fig. 7. We have checked that QCD next-to-leading order effects (taken as an overall K-factor) shift the dashed green lines by only a small amount.