A light sneutrino rescues the light stop

Journal of High Energy Physics, Apr 2017

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 \( \overset{\sim }{t} \) is lighter than all electroweakinos, and heavier than the scalars of the third generation lepton doublet, whose charged component, \( \overset{\sim }{\tau } \), is heavier than the neutral one, \( \overset{\sim }{\nu } \). The remaining supersymmetric particles are decoupled from the stop phenomenology. In most of the parameter space, the relevant stop decays are only into \( t\overset{\sim }{\tau}\tau \), \( t\overset{\sim }{\nu}\nu \) and \( b\overset{\sim }{\nu}\tau \) 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 \( \overset{\sim }{t}\to t\overset{\sim }{\nu}\nu \) process, and the low efficiency in tagging the \( t\overset{\sim }{\tau}\tau \) decay products, light stops are generically allowed. In the minimal supersymmetric standard model with ∼ 100 GeV sneutrinos, stops with masses as small as ∼ 350 GeV turn out to be allowed at 95% CL.

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A light sneutrino rescues the light stop

Received: March A light sneutrino rescues the light stop M. Chala 0 1 2 5 6 7 8 9 A. Delgado 0 1 2 3 6 7 8 9 G. Nardini 0 1 2 4 6 7 8 9 M. Quiros 0 1 2 6 7 8 9 kinematics of the 0 1 2 6 7 8 9 t ! t 0 1 2 6 7 8 9 0 Sidlerstrasse 5 , CH-3012 Bern , Switzerland 1 225 Nieuwland Science Hall , Notre Dame, IN 46556 , U.S.A 2 Dr. Moliner 50 , E-46100 Burjassot (Valencia) , Spain 3 Department of Physics, University of Notre Dame 4 Albert Einstein Center (AEC), Institute for Theoretical Physics (ITP), University of Bern 5 Departament de F sica Teorica, Universitat de Valencia and IFIC, Universitat de Valencia-CSIC 6 Open Access , c The Authors 7 350 GeV turn out to be allowed at 8 The Barcelona Institute of Science and Technology (BIST) 9 ed., Cambridge University Press, Cambridge U.K. , (2010), pg. 121 [arXiv:1009.3690] 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. Institucio Catalana de Recerca i Estudis Avancats (ICREA) 1 Introduction 2 3 4 The model and dominant stop decays LHC searches and the dominant decays Single channel bounds Constraints on particular SUSY models A Analysis validation 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{ 6], the LSP is preferably electrically neutral. This, together with the appealing cosmological features of the neutralino, has had a strong in uence 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 ndings in simpli ed 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 simpli edmodel 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 simpli ed model assumptions and deal with realistic, and somewhat non trivial, phenomenological scenarios. As we will see, the ndings 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. 1For further studies along similar directions, see e.g. refs. [9{12]. 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. In gauge mediated supersymmetry breaking (GMSB) [13] the ratio of the gaugino where N is the number of messengers, F the supersymmetry breaking parameter and 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 m1=2 m0 emerges. Within this hierarchy, gluinos are heavier than electroweakinos, and stops heavier than staus, parametrically by facgauge 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 [14].2 ve-dimensional SUSY theories, supersymmetry can be broken by the ScherkSchwarz (SS) mechanism [17{25]. 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 almost degenerate, while the RH stops are light but heavier than the LH staus and the tauonic sneutrinos by around a factor gs2=g2 . 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 2In particular, we assume that the slepton singlet R is much heavier than the slepton doublet (e; e)L. In GMSB scenarios this hypothesis can be ful lled 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 0 [15, 16]. In this model one needs to enlarge the third generation into the 27 fundamental representation and a stau, promptly decaying into soft W -boson products and missing transverse energy. Middle diagram: production of a top and two correlated sources of missing transverse energy. diagram: production of a bottom, tau and missing transverse energy. the electroweakinos and more massive than the third-family slepton doublet.3 This has also been considered in other works (see for example ref. [26]). 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 modi cations thereof. In the considered parameter regime, the phenomenology of the lighter stop, et, is dominated by three-body decays via o -shell electroweakinos into staus and tau sneutrinos, e and e. 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 between the lighter stop and the Wino is tiny (see more details in section 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 gure 1. This is the , the latter being negligible when the interaction 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 [27, 28], as it is ruled out by direct detection experiments [29, 30]. Therefore, in a model like the one we study here, one needs a di erent 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 section 5). The outline of the paper is the following. In section 2 we provide further information on the scenario we consider, and on the e ects that the electroweakino parameters have on the stop signatures. In section 3 we single out the ATLAS and CMS analyses that, although performed to test di erent frameworks, do bound our scenario. The consequent 3Notice 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. 4As a practical notation, we are not di erentiating particles from antiparticles when indicating the decay 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 section 4. Section 5 reports on the conclusions of our study, while appendix 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, , enters the electroweak breaking conditions at tree level, and only if 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 e ciently renormalize the stop mass towards high values. Therefore stops cannot be light in the presence of very massive gluinos without introducing some ne 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 [23{25], and where heavy gluinos do not imply heavy stops [20, 25, 31]. 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 (simpli ed model) constraints. Speci cally, 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 o -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 5For recent theoretical analyses in the case of light electroweakinos and their bounds see e.g. [32, 33]. 6These features naturally happen in GMSB and SS frameworks. For GMSB, the trilinear parameter A the SS breaking produces a large tree-level mass for the LH stop and the RH stau elds in the bulk, and parametrically O(g2=gs2) in such GMSB and SS embeddings. stop decay signature. Nevertheless, in practice, avor-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 + 70 GeV, with 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 is free from any direct constraint coming from collider searches and, as stressed in section 1, we refrain from considering bounds that depend on cosmological scale assumptions. On the other hand, numerous collider-scale dependent observables a ect 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 di erent searches, they obtain the stau & 90 GeV [1{4]. A further constraint comes from the CMS and ATLAS searches for disappearing charged tracks, for which m life-time is long [5, 6]. However, in the present scenario with small sparticle mixings, the m2 = can be su ciently large to lead to a fast stau decay, and in fact the charged track LHC bound is eventually overcome for m other hand, a light stau with mass close to the LEP bound modi es the 125 GeV Higgs > 1 (see section 5). On the signal strength R(h ! 100 [37]. All together these bounds hint at an intermediate (not very large) choice of tan , as e.g. tan Finally, a light stau, as well as a light stop, can modify the electroweak precision observables [38]. One expects the corresponding corrections to be within the experimental uncertainties for m t & 300 GeV and negligible sparticle mixing, since the stop is mostly RH and the light stau is su ciently 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 o -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 electheir SM counter-partners:8 troweak basis, by the relevant interaction Lagrangian involving the Bino, Wino, Higgsinos, tau sneutrino, the LH and RH stops and staus (Be; Wf; He1;2; eL, etL;R and eL;R) as well as LI = 7Notice that in an extreme parameter regime, the stop is long lived and leads to stoponium, whose signatures are qualitatively di erent from those we are discussing here [34{36]. Including this (small) parameter regime is irrelevant for our purposes, and we thus exclude it from our analysis. 8We use two-component Weyl spinor notation for spinors. By de nition R Ry are undotted spinors. L;R, where L are undotted spinors and R dotted Here ht;b; are the SM Yukawa couplings while, following the usual MSSM notation, He2 (He1) is the SUSY partner of the Higgs with up-type (down-type) Yukawa interactions. The rst 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 elds. This Lagrangian helps to pin down the Bino, Wino and Higgsino (o -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 M1, M2, mZ , the Bino, Winos and Higgsinos are almost mass eigenstates. The Bino and the electrically-neutral components of Winos and Higgsinos contribute di erent branching ratios into anti-stau tau and into stau anti-tau. This is a consequence of the fact that the decaying particle in the rst diagram of gure 1 is a stop and not an anti-stop. This di erence in the branching ratios can be understood from the point of view of e ective operators obtained in the limit that the neutralinos are heavy enough that can be integrated out. We show that this is so by considering the two (opposite) regimes where (see the rst two diagrams in gure 1). We expect the light stop is either mostly RH or mostly LH. Let us rst assume that in the process et ! t etR in eq. (2.2). If the neutralinos are mainly gauginos (Be; Wf0), 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- ve) e ective operator can be written as (etReL)(tR L), by which only staus and anti-taus are produced, but not anti-staus and taus. For diagrams mediated by Higgsinos, the produced top will be LH and the e ective operator is (etReL)(tL R), and again the stop decay products are staus and anti-taus. However, in the limit of heavy electroweakino masses, the coe cient of the latter operator is suppressed by this case the e ective operators for the exchange of gauginos and Higgsinos in et ! t be (etLeR)(tL R) and (etLeR)(tR L) respectively, implying again that the decay products are staus and anti-taus. The contribution to the latter e ective 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. the decaying stop is RH, i.e. the eld 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 e ective operators such as L), which contain an extra suppression factor O(v= ; v=M1;2) with respect to the leading result. We can nally 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 e ect escapes from the most constraining stop searches, which do not tag the charge of taus or other leptons (see section 3). For the purposes of the detector simulations the stop branching ratios can thus be calculated without di erentiating the processes yielding taus or anti-taus. The chirality suppression is instead crucial for the three-body decays via o -shell charginos. In principle both decays et ! b chirality suppression, only the latter (which corresponds to the third diagram in gure 1) are allowed but, due to the can be sizeable in our scenario. Indeed, let us consider the case where the stop decaying into bL and an o -shell charged Higgsino is the RH one.10 The only the (tiny) factor hbh = cos2 . Thus, in general, only the decay et ! b fective operator that can be constructed is (etReL)(bL R) which appears from the mixing between He2+ and (He1 ) , after electroweak symmetry breaking, and is thus suppressed by bL and Wf+ gives rise to the operator (etLeL)(bL L).11 Moreover, the etL decay into bR and (He1 ) can only be generated by a dimension-six operator which is further suppressed by 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 et ! b is absent in gure 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 , while in section 4 we will provide some parameter regions exhibiting this feature and relaxing the bounds on light 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 p 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 nal states performed by the ATLAS and CMS Collaborations, in refs. [39, 40], respectively, as well as searches for pair-produced stops in a nal state with tau leptons carried out by the ATLAS Collaboration in ref. [41]. 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 et ! t (see the rst diagram in gure 1), as the nal state is di erent from any other nal state studied by current searches, in particular with more taus involved. In the et ! t nal state, a top plus missing transverse energy Emiss, coincides with e.g. the one of the et ! t e0 process, with the neutralino as the LSP studied in refs. [39, decay (see the second diagram decay (second diagram in gure 1), but the collider signatures of these di erent products are not relevant, for neutrinos or anti-neutrinos are indistinguishable at colliders. 11Notice that in our convention both bL and 10As etR is an SU(2)L singlet it cannot decay via a charged gaugino Wf . L are undotted spinors and thus bL L being the Levi-Civita tensor, is Lorentz invariant. Figure 2. Left panel: normalized distribution of ETmiss in the simpli ed model of refs. [39, 40] (solid orange line), with m t = 700 GeV and m = m = 400 GeV in both cases. (dashed green line) and our scenario (solid orange line) with BR(et ! t e ) = 1. In both cases, 40]. Nevertheless, since the neutralino is o -shell in our case, most of the discriminating variables behave very di erently, and therefore the experimental bound on et ! t e0 does not strictly apply [42]. And even the existing analyses for stops decaying into several invisible particles, which also refs. [39{41] investigate, turn out to be based on kinematic cuts with e ciencies that are unreliable in our case. This for instance holds for the et ! b (see the third diagram in gure 1) whose invisible particle does not exactly mimic the ones Ge (where Ge is a massless gravitino) analyzed in ref. [41]. = m = 400 GeV and gravitino mass m For the sake of comparison, in the left panel of gure 2 we show the distributions of ETmiss in the decays et ! t e0 (dashed green line) and et ! t transverse mass mT 2 constructed out of the tagged light tau lepton, without any further cut, coming from the decays et ! b (dashed green line) and et ! b Ge (orange solid line) (orange solid line) with fundamental importance for the aforementioned ATLAS and CMS searches. In particular, as gure 2 illustrates, the stringent cuts on these quantities reduce the e ciency 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. [42]. In the light of this discussion, we recast the aforementioned analyses using homemade routines based on a combination of MadAnalysis v5 [43, 44] and ROOT v5 [45], with boosted techniques implemented via Fastjet v3 [46]. Two signal regions, SRA and SRB, each one divided in three categories, are considered in the ATLAS fully hadronic search [39] (note that SRA and SRB are not statistically independent, though). The di erent categories vary on the requested amount of Emiss, as well as on the cut on the mass of the tagged fat jets. The CMS fully hadronic analysis [40] 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 ATLAS [39] (only SRB) case is tagged with an asterisk. these three analyses can be found in appendix A. We nd that our recast of the ATLAS search for stops in the hadronic nal state leads to slightly smaller limits, while the ones of the other searches very precisely reproduce the experimental bounds. Thus, as shown in table 1, we combine the whole CMS set of bins with the above signal region SRB for probing the decay et ! t counting experiment for testing the et ! t , and with the single bin of the ATLAS processes.12 Limits at di erent con dence levels are obtained by using the CLs method [47]. 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 [48] that are subsequently decayed by Pythia v6 [49]. The parameter cards are produced by means of SARAH v4 [50] and SPheno v3 [51]. When each channel is studied separately, the corresponding branching ratio has been 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 and use the LHC data to bound the corresponding branching ratio in the plane (mt; m ). The results are reported in gure 3 where, for every given channel, the bounds at the 90% CL (left panels) and 95% CL (right panels) are presented in the plane (mt; m ). 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 . In this section we consider each individual decay channel (below the thin dashed line). (upper panels of gure 3) the most sensitive analysis is the ATLAS counting experiment. We combine it with the CMS signal region into a single statistics. As gure 3 shows, the bound on this channel is very weak. In particular, among the searches that we identi ed as the most sensitive ones to this channel, there is no one constraining this decay mode at 95% CL for mt & 300 GeV and m 12In principle, the two ATLAS analyses could be combined into a single statistics. They are indeed independent, 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 di erences are expected. same for BR(et ! b e ) = 1; 0:8; 0:6; 0:4. 95% CL (right panel) in the plane (mt; m ). For each value of the branching ratio the excluded region is the one enclosed by the corresponding curve. Above the thin dashed line the channel is For the decay channel et ! t (middle panels of gure 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 gure 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 e ciency on the \double invisible" three-body decay signal involving an o -shell mediator [42]. Finally, the bounds for the et ! b of gure 3. As summarized in table 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 gure 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). decay channel are presented in the lower panels We expect the ndings to be qualitatively independent of the particular SUSY realization 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 speci c 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 section 4. Nevertheless, in practice, our results should qualitatively apply to all SUSY realizations with prompt decays of staus with mass m 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 section 4. In such a situation, we can consider BR(et ! te ) and BR(et ! be ) as two independent variables, BR(et ! te ) = 1 The total number of signal events after cuts is given by It is then possible to use the aforementioned ATLAS and CMS searches to constrain the two-dimensional plane BR(et ! t e ) for some set of values of mt and m . e e N = X Nij (mt) ij (mt; m ) ; where L = 13 fb 1 stands for the integrated luminosity, is the stop pair production cross section, and the indices i and j run over the three decay modes. The quantity ij is the the constraints on et ! t prove this feature in full generality. 13To clarify this issue, we repeated the et ! t e simulations for a few parameter points featuring a tiny stau sneutrino mass splitting. For these few points, the constraints on et! t out to be comparable, i.e. ruling out a similar region of the parameter space in the plane (mte; me). Moreover presented in this paper turn 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 Figure 4. Excluded regions at 95% CL in the plane of BRs for di erent pairs of (mt; m ). The areas below (to the left of) the horizontal (vertical) green dashed lines would be allowed if only excluded when all channels are combined. The areas above the diagonal black solid straight lines e ) mode was considered. The areas enclosed by the orange solid lines are are forbidden by the condition of eq. (3.1). e ciency that our recast analyses have on the etet ! ij events and is strongly dependent on the mass spectrum. To determine ij in some given mass spectrum scenarios, we run simulations of etet ! 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 gure 4. The regions above the horizontal dashed green lines would be the excluded ones had we assumed the signal to consist of only etet events. Analogously, the areas to the right of the vertical green dashed lines would be the excluded ones under the assumption that only the events etet ! t regions enclosed by the orange solid lines are instead excluded considering the whole signal, are bounded. The including also the stop decay into t and the mixed channels. For such comprehensive exclusion bounds, a common CLs 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 { 12 { 1.1 TeV 1.1 TeV 5 TeV 1.1 TeV 1.1 TeV 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 et ! te . The main reason is the inclusion of the 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 e ciencies that current analyses have on these processes in comparison to the illustrated in the top left panel, can be allowed. standard channels. Thus, even small masses such as met ' 300 GeV and m iii) As we can see from all panels in gure 4, the allowed regions favor large values of there is little sensitivity of the present experimental searches to the channel et ! te e ). This e ect can be easily understood from the rst row plots in gure 3: Constraints on particular SUSY models The results of section 3 can be reinterpreted in concrete SUSY scenarios that exhibit stops decaying as in gure 1, at least at detector scales. The stop, stau, sneutrino and electroweakino mass spectrum and their partial widths are determined by means of SARAH v4 and SPheno v3. More speci cally, we use the MSSM implementation provided by these x the parameters as follows. We impose tan = 10, in agreement with the arguments of section 2. The slepton and squark soft-breaking trilinear parameters are set to zero. The soft masses of the RH stop, MU2R , and LH stau doublet, ML2L , are much lighter than those of their partners with opposite \chirality", M Q2L and ME2R . The electroweakino soft parameters are set, as shown for scenarios A and B in table 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.14 14As the Higgs plays no role in this study, the origin of electroweak breaking can remain generically unspeci ed and not used to constrain the SUSY parameters. With the underlying assumption that the Higgs quartic coupling receives a beyond-the-MSSM F or D term contribution, the choice M Q2L is possible in the absence of stop mixing. Otherwise, without beyond-the-MSSM, the observed Higgs mass would be compatible with MU2R (300 GeV)2 and tiny stop mixing only for M Q2L (3 TeV)2 [52], i.e. at the expense of an unpleasant ne tuning. Figure 5. Contour plots of the values of BR(et ! te ) (left panels), BR(et ! te ) (middle panels) and BR(et ! be ) (right panels) in Scenario A (upper panels) and Scenario B (lower panels). For the above parameter choice, we study two parameter regimes denoted as scenarios A and B, characterized by the values of M1, M2 and quoted in table 2. Within each of dominant stop branching ratios are plotted in scenario A (upper row panels) and scenario B (lower row panels). For each scenario, the branching ratios of et ! t right panels, respectively. As anticipated in section 2, the main e ect of decreasing M2 is to enhance BR(et ! b e ), as we can see by comparing the two right panels in gure 5. Conversely, by increasing the value of M2 and we increase the branching ratio are plotted in the left, middle and gures 5 as a function of mt and m , for regime, we vary the masses mt and m , by scanning over MU2R e e m is determined as well. We discard the parameter points with m and ML2L , and consequently correspond to compressed scenarios that are not investigated in this paper. Contour plots , and we expect to make softer the bounds in the plane (mt; m ), in agreement with the general behavior in the lower row panels in in all plots in gure 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 m ) 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 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 500 GeV, and is much larger The results of section 3, along with the numerical evaluations of the di erent stop branching ratios, allow to recast the present LHC constraints on scenarios A and B. At each parameter point we rescale the amount of signal events, depending on the values of the branching ratios extracted from the MSSM parameter card corresponding to that point.15 The nal excluded regions at 95% CL in the plane (mt; m ) are shown in gure 6. 15In order to check the consistency of our procedure, we also perform the collider simulations described in section 3 for numerous parameter con gurations of each scenario. We nd perfect consistency, meaning that the contribution from any channel to the search of any other is negligible. B (right panel). The gray areas correspond to the region with m + 70 GeV that we do not Both in scenario A (left panel) and B (right panel) the exclusion bounds (orange areas) are relaxed with respect to their analogous in SUSY scenarios with the neutralino as the LSP. As anticipated, bounds are weaker in scenario A than in scenario B, due the larger e ). Remarkably, in the presence of light sneutrinos, a RH stop at around 350 GeV is not ruled out by current LHC data, or at least by the ATLAS and CMS analyses performed till now. 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 o -shell electroweakinos, and ATLAS and CMS fully hadronic searches for stops into hadronic or tau lepton states [39{ 41], although designed for a di erent 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{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 [27, 28] and, moreover, it is also ruled out by direct detection experiments [29, 30]. 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 Ge. It is a candidate to warm DM and its cosmological abundance is given by 3=2h2 ' 0:1(m3=2=0:2 keV), Ge 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 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, 12]. If its fermionic partner is light, also the decay et ! b this process is suppressed by the small neutrino Yukawa coupling. Thus, in practice, the stop collider phenomenology would not be di erent from that considered in the present paper. Another possibility is if the cosmological model becomes non-standard, as would happen by assuming modi cations 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 [57, 58]. 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 ijk such that the sneutrino decays as e ! ej ek. Depending on the value of the coupling 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 sub16This can be achieved for instance by localizing the right-handed neutrino multiplet in the brane and thus receiving its mass from higher order radiative corrections. 17For discussions in this direction see e.g. refs. [53{56]. TeV spectrum. Indeed, the kinematic e ects and the coexistence of multi decay channels responsible for the poorly e cient 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 e ectively 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 simpli ed 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 arti cial (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 The work of MC is partially supported by the Spanish MINECO under grant FPA201454459-P and by the Severo Ochoa Excellence Program under grant SEV-2014-0398. The work of AD is partially supported by the National Science Foundation under grant PHY1520966. The work of GN is supported by the Swiss National Science Foundation under grant 200020-168988. The work of MQ is also partly supported by the Spanish MINECO under grant CICYT-FEDER-FPA2014-55613-P, by the Severo Ochoa Excellence Program under grant SO-2012-0234, by Secretaria d'Universitats i Recerca del Departament d'Economia i Coneixement de la Generalitat de Catalunya under grant 2014 SGR 1450, and by the CERCA Program/Generalitat de Catalunya. In order to validate our implementations of the experimental analyses of refs. [39{41], we apply them to Monte Carlo events generated using the same benchmark models of those searches. Speci cally, these are pair-produced stops decaying as et ! t e0 [39, 40] and Ge) [41]. 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(et ! t e0) is xed manually to 100% in the rst two analyses. In the same vein, for the analysis of ref. [41] we x both BR(et ! b e ) = 1 and BR(e ! Notice that, in this last case, the neutrino plays the role of the (massless) gravitino, thus ) = 1. mimicking the channel studied in the experimental work. As stated in the main text, bounds are obtained by combining the di erent bins of a particular search into a single ref. [39] (left panel), ref. [40] (middle panel) and ref. 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A light sneutrino rescues the light stop, Journal of High Energy Physics, 2017, DOI: 10.1007/JHEP04(2017)097