A light sneutrino rescues the light stop
Mikael Chala, Antonio Delgado, Germano Nardini, Mariano Quiros
FFTUV-17-0222.4164IFIC/17-08
A light sneutrino rescues the light stop
M. Chala a , A. Delgado b , G. Nardini c , M. Quir´os da Departament de F´ısica T`eorica, Universitat de Val`encia and IFIC, Universitat deVal`encia-CSIC, Dr. Moliner 50, E-46100 Burjassot (Val`encia), Spain b Department of Physics, University of Notre DameNotre Dame, IN 46556, USA c Albert Einstein Center (AEC), Institute for Theoretical Physics (ITP),University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland d Institut de F´ısica d’Altes Energies (IFAE),The Barcelona Institute of Science and Technology (BIST),Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA)Campus UAB, 08193 Bellaterra (Barcelona) Spain
Abstract
Stop searches in supersymmetric frameworks with R -parity conservation usually as-sume the lightest neutralino to be the lightest supersymmetric particle. In this paperwe consider an alternative scenario in which the left-handed tau sneutrino is lighterthan neutralinos and stable at collider scales, but possibly unstable at cosmologicalscales. Moreover the (mostly right-handed) stop (cid:101) t is lighter than all electroweakinos,and heavier than the scalars of the third generation doublet, whose charged compo-nent, (cid:101) τ , is heavier than the neutral one, (cid:101) ν . The remaining supersymmetric particlesare decoupled from the stop phenomenology. In most of the parameter space, therelevant stop decays are only into t (cid:101) τ τ , t (cid:101) νν and b (cid:101) ντ via off-shell electroweakinos. Weconstrain the branching ratios of these decays by recasting the most sensitive stopsearches. Due to the “double invisible” kinematics of the (cid:101) t → t (cid:101) νν process, and thelow efficiency in tagging the t (cid:101) τ τ decay products, light stops are generically allowed.In the minimal supersymmetric standard model with ∼
100 GeV sneutrinos, stopswith masses as small as ∼
350 GeV turn out to be allowed at 95% CL. a r X i v : . [ h e p - ph ] F e b Introduction
In most supersymmetric (SUSY) models, R -parity conservation is implemented to avoidrapid proton decay, which implies that the lightest supersymmetric particle (LSP) isstable. As there are strong collider and cosmological constraints on long-lived chargedparticles [1–6], the LSP is preferably electrically neutral. This, together with the appealingcosmological features of the neutralino, has had a strong influence on the ATLAS and CMSchoice on the SUSY searches. Most of them indeed assume the lightest neutralino to bethe LSP or, equivalently for the interpretation of the LHC searches, the long-lived particletowards which all produced SUSY particles decay fast.Searches under these assumptions are revealing no signal of new physics and puttingstrong limits on SUSY models. The interpretation of these findings in simplified modelsprovides lower bounds at around 900 and 1800 GeV for the stop and gluino masses, respec-tively [7, 8], which are in tension with naturalness in supersymmetry. In this sense, thebias for the neutralino as the LSP, as well as an uncritical understanding of the simplified-model interpretations, is driving the community to believe that supersymmetry can notbe a natural solution to the hierarchy problem anymore. In the present paper we breakwith this attitude and take an alternative direction: we assume that the LSP is not thelightest neutralino but the tau sneutrino . Moreover we avoid peculiar simplified modelassumptions and deal with realistic, and somewhat non trivial, phenomenological scenar-ios. As we will see, the findings in this alternative SUSY scenario make it manifest thestrong impact that biases have on our understanding on the experimental bounds and, inturn, 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 inthe context of natural supersymmetry, are feasible in top-down approaches, as e.g. in thefollowing supersymmetry breaking mechanisms. Gauge mediation
In gauge mediated supersymmetry breaking (GMSB) [12] the ratio of the gaugino( m / ) over the scalar ( m ) masses behaves parametrically as m / /m ∝ N f ( F/M ),where N is the number of messengers, F the supersymmetry breaking parameterand M the messenger mass. The condition F/M (cid:46) f (cid:39)
3. In this way,for large N or F/M close to one, the hierarchy m / (cid:29) m emerges. Within thishierarchy, gluinos are heavier than electroweakinos, and stops heavier than staus,parametrically by factors of the order of g s /g α at the messenger mass scale M ,with g α being the relevant gauge coupling. The renormalization group running tolow scales increases these mass splittings for M much above the electroweak scale. For further studies along similar directions, see e.g. Refs. [9–11]. . Scherk-Schwarz
In five-dimensional SUSY theories, supersymmetry can be broken by the Scherk-Schwarz (SS) mechanism [16–24]. In this class of theories, one can assume thehypermultiplets of the right handed (RH) stop and the left handed (LH) third gen-eration lepton doublet localized at the brane, and the remaining ones propagating inthe bulk of the extra dimension. In such an embedding, gauginos and Higgsinos feelsupersymmetry breaking at tree level while scalars feel it through one-loop radiativecorrections. As a consequence, the ratio between the gaugino and scalar masses is m / /m ∝ π/g α . Eventually, gluinos and electroweakinos are very massive andalmost degenerate, while the RH stops are light but heavier than the LH staus andthe tauonic sneutrinos by around a factor g s /g α .Although the aforementioned ultraviolet embeddings strengthen the motivation of ouranalysis, in the present paper we do not restrict ourselves to any particular mechanism ofsupersymmetry breaking. Instead we take a (agnostic) bottom-up approach. We considera low-energy SUSY theory where the stop phenomenology is essentially the one of theminimal supersymmetric standard model (MSSM) with the lighter stop less massive thanthe electroweakinos and more massive than the third-family slepton doublet . Gluinosand the remaining SUSY particles are heavy enough to decouple from the collider phe-nomenology of the lighter stop. In this scenario the LSP at collider scales is thereforethe LH tau sneutrino . Of course, subsets of the parameter regions we study can be easilyaccommodated in any of the previously discussed supersymmetry breaking mechanismsor minor modifications thereof.In the considered parameter regime, the phenomenology of the lighter stop, (cid:101) t , is dom-inated by three-body decays via off-shell electroweakinos into staus and tau neutrinos, (cid:101) τ and (cid:101) ν . The viable decay channels are very limited. If the masses of the lightest sneutrinoand the lighter stop are not compressed, the only potentially relevant stop decays are In particular, we assume that the slepton singlet (cid:101) τ R is much heavier than the slepton doublet ( (cid:101) ν, (cid:101) τ ) L .In GMSB scenarios this hypothesis can be fulfilled only if the messengers transform under a beyond-the-standard-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 gaugegroup by a (cid:101) U (1), with hypercharge (cid:101) Y , from E one can easily impose the condition that (cid:101) Y ( ν L ) = 0while (cid:101) Y ( τ R ) (cid:54) = 0 [14,15]. In this model one needs to enlarge the third generation into the 27 fundamentalrepresentation of E 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 (cid:101) Y = ( − , , − , , , −
3) for the SU (5) representations (10 , ¯5 , ν c , H , ¯5 H , Notice that the mass and quartic coupling of the Higgs do not play a key role in the stop phenomenol-ogy. Then, the analysis of the present paper also applies to extensions of the MSSM where the radiativecorrelation between the Higgs mass and stop spectrum is relaxed. t → t (cid:101) νν , (cid:101) t → t (cid:101) τ τ , (cid:101) t → b (cid:101) ντ and (cid:101) t → b (cid:101) τ ν , the latter being negligible when the interactionbetween the lighter stop and the Wino is tiny (see more details in Sec. 2) . Thus, forscenarios where the lighter stop has a negligible LH component and/or the Wino is closeto decoupling, the relevant stop signatures reduce to those depicted in Fig. 1. This is thestop phenomenology we will investigate in this paper. e t t g χ τ f τ W ∗ f ν τ e t t g χ ν τ f ν τ e t b g χ ± τ f ν τ Figure 1:
The dominant stop decays in our analysis. Left diagram: Production of a top,a tau and a stau, promptly decaying into soft W -boson products and missing transverseenergy. Middle diagram: Production of a top and two correlated sources of missing trans-verse energy. Right diagram: Production of a bottom, tau and missing transverse energy. A comment about dark matter (DM) is here warranted. It is well known that theLH sneutrino is not a good candidate for thermal
DM [25, 26], as it is ruled out by directdetection experiments [27,28]. Therefore, in a model like the one we study here, one needsa different approach to solve the DM problem. Since many of the available approacheswould modify the phenomenology of our scenario only at scales irrelevant for colliderobservables, incorporating such changes would not modify our results (for more detailssee Sec. 5).The outline of the paper is the following. In Sec. 2 we provide further informationon the scenario we consider, and on the effects that the electroweakino parameters haveon 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 consequentconstraints on the stop branching ratios and on stop and sneutrino masses are presentedin the same section. The implications for some benchmark points and the viability ofstops as light as 350 GeV are explained in Sec. 4. Sec. 5 reports on the conclusions of ourstudy, while App. A contains the technical details about our analysis validations. As a practical notation, we are not differentiating particles from antiparticles when indicating thedecay final states. The model and dominant stop decays
In the MSSM and its minimal extensions, it is often considered that naturalness requireslight Higgsinos and stops, and not very heavy gluinos. In fact, in most of the ultravioletMSSM embeddings, the Higgsino mass parameter, µ , enters the electroweak breakingconditions at tree level , and only if µ is of the order of the Z boson mass the electroweakscale is naturally reproduced. This however solves the issue only at tree level, as alsothe stops can radiatively destabilize the electroweak breaking conditions. For this reasonstops must be light, and the argument is extended to gluinos since, when they are veryheavy, they efficiently renormalize the stop mass towards high values. Therefore stopscannot be light in the presence of very massive gluinos without introducing some finetuning.Remarkably, the above argument in favor of light Higgsinos, light stops and not veryheavy gluinos, is not general. There exist counter examples where the Higgs sector, andthus its minimization conditions, is independent of µ [22–24], and where heavy gluinosdo not imply heavy stops [19, 24, 29]. In view of these “proofs of principle”, there ap-pears to be no compelling reason why the fundamental description of nature should notconsist of a SUSY scenario with light stops and heavy gluinos and electroweakinos. Itis thus surprising that systematic analyses on the latter parameter regime have not beenperformed .The present paper aims at triggering further attention on the subject by highlightingthat the present searches poorly constrain the stop sector of this parameter scenario. Forthis purpose we focus on the LHC signatures of the lighter stop being mostly RH. Theillustrative parameter choice we consider is the one where the stop and slepton mixings aresmall, and the light third generation slepton doublet is lighter than the lighter stop . Theremaining squarks, sleptons and Higgses are assumed to be very heavy, in agreement withthe (naive) interpretation of the present LHC (simplified model) constraints. Specifically,these particles, along with gluinos, are assumed to be decoupled from the relevant lightstop phenomenology. Moreover, possible R -parity violating interactions are supposed tobe negligible at detector scales.In the present parameter scenario the light stop phenomenology only depends on theinteractions among the SM particles, the lighter (mostly RH) stop, the lighter (mostlyLH) stau, the tau sneutrino and the electroweakinos. The stop decays into sleptons viaoff-shell charginos and neutralinos. In principle, due to the interaction between the stopand the neutralinos (charginos), any up–type (down–type) quark can accompany the light For recent theoretical analyses in the case of light electroweakinos and their bounds see e.g. [30, 31]. These features naturally happen in GMSB and SS frameworks. For GMSB, the trilinear parameter A arises at two loops whereas m appears at one loop. Thus the ratio A/m is one-loop suppressed.Similarly, the SS breaking produces a large tree-level mass for the LH stop and the RH stau fields in thebulk, and generates A at one loop, such that A/m is small due to a one-loop factor. Moreover, the ratio m (cid:101) ν /m (cid:101) t is parametrically O ( g /g s ) in such GMSB and SS embeddings. . To safely avoid this region, we impose m (cid:101) t (cid:38) m (cid:101) ν + 70 GeV, with m (cid:101) t and m (cid:101) 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 stauand sneutrino masses. In particular, the sneutrino mass m (cid:101) ν is free from any direct con-straint coming from collider searches and, as stressed in Sec. 1, we refrain from consideringbounds that depend on cosmological scale assumptions. On the other hand, numerouscollider-scale dependent observables affect the stau as we now discuss.The ALEPH, DELPHI, L3 and OPAL Collaborations interpreted the LEP data inview of several SUSY scenarios and, depending on the different searches, they obtain thestau mass bound m (cid:101) τ (cid:38)
90 GeV [1–4]. A further constraint comes from the CMS andATLAS searches for disappearing charged tracks, for which m (cid:101) τ (cid:39)
90 GeV is ruled outif the stau life-time is long [5, 6]. However, in the present scenario with small sparticlemixings, the mass splitting m (cid:101) τ − m (cid:101) ν , given by m (cid:101) τ − m (cid:101) ν = tan β − β + 1 cos θ W m Z + O ( m τ ) , (2.1)can be sufficiently large to lead to a fast stau decay, and in fact the charged track LHCbound is eventually overcome for m (cid:101) τ (cid:38)
90 GeV and tan β > R ( h → γγ ) unless tan β (cid:28)
100 [35]. All together these bounds hint at anintermediate (not very large) choice of tan β , as e.g. tan β ∼ m (cid:101) τ (cid:38)
90 GeV, m (cid:101) t (cid:38)
300 GeV and negligible sparticle mixing, since thestop 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 staudecay: due to the compressed spectrum, the stau can only decay into a stable (at leastat detector scales) sneutrino and an off-shell W boson, giving rise to soft leptons or softjets.At the quantitative level, the decay processes of the stop are described, in the elec-troweak basis, by the relevant interaction Lagrangian involving the Bino, Wino, Higgsinos,tau sneutrino, the LH and RH stops and staus ( (cid:101) B, (cid:102) W , (cid:101) H , , (cid:101) ν L , (cid:101) t L,R and (cid:101) τ L,R ) as well as Notice that in an extreme parameter regime, the stop is long lived and leads to stoponium, whosesignatures are qualitatively different from those we are discussing here [32–34]. Including this (small)parameter regime is irrelevant for our purposes, and we thus exclude it from our analysis. : L I = − g (cid:16)(cid:101) t ∗ L b L (cid:102) W + + (cid:101) τ ∗ L ν L (cid:102) W − + (cid:101) ν ∗ L τ L (cid:102) W + (cid:17) − g √ (cid:0)(cid:101) t ∗ L t L + (cid:101) ν ∗ L ν L − (cid:101) τ ∗ L τ L (cid:1) (cid:102) W − g (cid:48) √ (cid:18) (cid:101) t ∗ L t L + 43 (cid:101) t ∗ R t R + (cid:101) ν ∗ L ν L + (cid:101) τ ∗ L τ L − (cid:101) τ ∗ R τ R (cid:19) (cid:101) B − (cid:26) h t sin β (cid:101) t ∗ R b L (cid:101) H +2 + h b cos β (cid:101) t L ¯ b R (cid:101) H − + h t sin β (cid:0)(cid:101) t ∗ R t L + (cid:101) t L ¯ t R (cid:1) (cid:101) H + h τ cos β (cid:104) ( (cid:101) τ ∗ R ν L + (cid:101) ν L ¯ τ R ) (cid:101) H − − ( (cid:101) τ ∗ R τ L + (cid:101) τ L ¯ τ R ) (cid:101) H (cid:105)(cid:27) − i g √ (cid:2) ( ∂ µ (cid:101) ν ∗ L ) W + µ (cid:101) τ + ( ∂ µ (cid:101) τ ∗ L ) W − µ (cid:101) ν L (cid:9) + h.c. . (2.2)Here h t,b,τ are the SM Yukawa couplings while, following the usual MSSM notation, (cid:101) H ( (cid:101) H ) 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 linesfrom F -terms Yukawa couplings and the last line from the covariant derivative of thecorresponding fields.This Lagrangian helps to pin down the Bino, Wino and Higgsino (off-shell) roles inthe stop decays. In order to understand the magnitude of the single contributions, it isimportant to remind that the stop (stau) is mostly RH (LH). Moreover, for our scenariowith electroweakino mass parameters M , M , µ (cid:29) m Z , the Bino, Winos and Higgsinosare almost mass eigenstates.The Bino and the electrically-neutral components of Winos and Higgsinos contributeto the decays (cid:101) t → t (cid:101) τ τ and (cid:101) t → t (cid:101) νν (see the first two diagrams in Fig. 1). We expectdifferent branching ratios into anti-stau tau and into stau anti-tau. This is a consequenceof the fact that the decaying particle in the first diagram of Fig. 1 is a stop and not ananti-stop. This difference in the branching ratios can be understood from the point ofview of effective operators obtained in the limit that the neutralinos are enough heavythat 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 (cid:101) t → t (cid:101) τ τ the decaying stop is RH, i.e. thefield (cid:101) t R in Eq. (2.2). If the neutralinos are mainly gauginos ( (cid:101) B, (cid:102) W ), as the RH stopis an SU (2) L singlet, the process has to be mediated by the Binos. In this case theproduced top will be RH and the lowest order (dimension-five) effective operator can bewritten as ( (cid:101) t ∗ R (cid:101) τ L )( t R ¯ τ 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 andthe effective operator is ( (cid:101) t ∗ R (cid:101) τ L )( t L ¯ τ R ), and again the stop decay products are staus and We use two-component Weyl spinor notation for ψ L,R , where ψ L are undotted spinors and ψ R dottedspinors. By definition ¯ ψ R ≡ ψ † R are undotted spinors. O ( v/µ ). Now let us instead assume that the decayingstop is LH, that is, (cid:101) t L in Eq. (2.2). In this case the effective operators for the exchange ofgauginos and Higgsinos in (cid:101) t → t (cid:101) τ τ would be ( (cid:101) t ∗ L (cid:101) τ R )( t L ¯ τ R ) and ( (cid:101) t ∗ L (cid:101) τ R )( t R ¯ τ L ) respectively,implying again that the decay products are staus and anti-taus. The contribution to thelatter effective operators is small if the RH stau is heavy (and/or the LH component ofthe stop is small), as happens in the considered model, leading again to the productionof staus and anti-taus with either chirality.In reality, in our scenario with mostly RH light stops, since neutralinos are notcompletely decoupled, full calculations of the stop decays exhibit also some anti-stauand tau contributions. These proceed from dimension-six effective operators such ase.g. ( (cid:101) t ∗ R ∂ µ (cid:101) τ ∗ R )( t R ¯ σ µ τ L ), which contain an extra suppression factor O ( v/µ, v/M , ) with re-spect to the leading result. We can finally say that the decay of stops is dominated by theproduction of anti-taus while the production of taus is chirality suppressed . Althoughinteresting, this effect escapes from the most constraining stop searches, which do nottag the charge of taus or other leptons (see Sec. 3). For the purposes of the detectorsimulations the stop branching ratios can thus be calculated without differentiating theprocesses yielding taus or anti-taus.The chirality suppression is instead crucial for the three-body decays via off-shellcharginos. In principle both decays (cid:101) t → b (cid:101) τ ν and (cid:101) t → b (cid:101) ντ are allowed but, due to thechirality 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 decayinginto b L and an off-shell charged Higgsino is the RH one . The only five-dimensionaleffective operator that can be constructed is ( (cid:101) t ∗ R (cid:101) ν L )( b L ¯ τ R ) which appears from the mixingbetween (cid:101) H +2 and ( (cid:101) H − ) ∗ , after electroweak symmetry breaking, and is thus suppressed bya factor O ( v/µ ). Now instead assume that the stop is LH. At leading order, the decayinto b L and (cid:102) W + gives rise to the operator ( (cid:101) t ∗ L (cid:101) τ ∗ L )( b L ν L ) . Moreover, the (cid:101) t L decay into b R and ( (cid:101) H − ) ∗ can only be generated by a dimension-six operator which is further suppressedby the (tiny) factor h b h τ / cos β . Thus, in general, only the decay (cid:101) t → b (cid:101) ντ can be relevantin scenarios where the light stop is practically RH (or the Wino is much heavier than theHiggsinos), as we are considering throughout this work. For this reason the decay (cid:101) t → b (cid:101) 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 scenarioswith light stops predominantly decaying into t (cid:101) τ τ , t (cid:101) νν and b (cid:101) ντ , while in Sec. 4 we will The same effect arises also in the (cid:101) t → t (cid:101) νν decay (second diagram in Fig. 1), but the collider signa-tures of these different products are not relevant, for neutrinos or anti-neutrinos are indistinguishable atcolliders. As (cid:101) t R is an SU (2) L singlet it cannot decay via a charged gaugino (cid:102) W ± . Notice that in our convention both b L and ν L are undotted spinors and thus b L ν L ≡ b αL (cid:101) (cid:15) αβ ν βL , with (cid:101) (cid:15) αβ being the Levi-Civita tensor, is Lorentz invariant.
100 200 300 400 500 600 E miss T [GeV] . . . . . . . . . . N d N d E m i ss T [ G e V − ]
100 200 300 400 500 m T [GeV] . . . . . . . . N d N d m T [ G e V − ] Figure 2:
Left panel: Normalized distribution of E miss T in the simplified model of Refs. [37,38] (dashed green line) and our scenario (solid orange line) with BR ( (cid:101) t → t (cid:101) νν ) = 1 . Inboth cases, m (cid:101) t = 625 GeV and m LSP = 200
GeV. Right panel: Normalized distributionof m T in the stop decay of the simplified model in Ref. [39] (dashed green line) andof our scenario when BR ( (cid:101) t → b (cid:101) ντ ) = 1 (solid orange line), with m (cid:101) t = 700 GeV and m (cid:101) τ = m (cid:101) ν = 400 GeV in both cases. provide some parameter regions exhibiting this feature and relaxing the bounds on lightstops.
The data collected during the LHC Run II, even at small luminosity, have proven tobe more sensitive to SUSY signals than their counterpart at √ s = 8 TeV. Among thesearches with the most constraining expected reach, we will be interested in those forpair-produced stops in fully hadronic final states performed by the ATLAS and CMSCollaborations, in Refs. [37, 38], respectively, as well as searches for pair-produced stopsin 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 constrainthe signal processes under consideration.This reinterpretation issue is clear for the decay (cid:101) t → t (cid:101) τ τ (see the first diagram inFig. 1), as the final state is different from any other final state studied by current searches,in particular with more taus involved. In the (cid:101) t → t (cid:101) νν decay (see the second diagram inFig. 1), the final state, a top plus missing transverse energy E miss T , coincides with e.g. theone of the (cid:101) t → t (cid:101) χ 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 discriminatingvariables behave very differently, and therefore the experimental bound on (cid:101) t → t (cid:101) χ does9ot strictly apply [40]. And even the existing analyses for stops decaying into severalinvisible particles, which also Refs. [37–39] investigate, turn out to be based on kinematiccuts with efficiencies that are unreliable in our case. This for instance holds for the (cid:101) t → b (cid:101) ντ decay (see the third diagram in Fig. 1) whose invisible particle does not exactlymimic the ones of (cid:101) t → bτ ν (cid:101) G (where (cid:101) 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 (cid:101) t → t (cid:101) χ (dashed green line) and (cid:101) t → t (cid:101) νν (orange solid line) with m (cid:101) t = 625 GeV and m LSP = 200 GeV. In the right panel we contrast the shapes of thetransverse mass m T constructed out of the tagged light tau lepton, without any furthercut, coming from the decays (cid:101) t → b (cid:101) ντ (dashed green line) and (cid:101) t → bτ ν (cid:101) G (orange solidline) for m (cid:101) τ = m (cid:101) ν = 400 GeV and gravitino mass m (cid:101) G = 0. These kinematic variablesare of fundamental importance for the aforementioned ATLAS and CMS searches. Inparticular, as Fig. 2 illustrates, the stringent cuts on these quantities reduce the efficiencyon the signal in our model, with respect to the standard benchmark scenarios for whichthe 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 homemaderoutines based on a combination of MadAnalysis v5 [41, 42] and
ROOT v5 [43], withboosted 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 fullyhadronic analysis [38] considers, instead, a signal region consisting of 60 independentbins. Finally, the ATLAS analysis involving tau leptons carries out a simple countingexperiment. Details on the validation of our implementation of these three analyses canbe found in App. A. We find that our recast of the ATLAS search for stops in the hadronicfinal state leads to slightly smaller limits, while the ones of the other searches very preciselyreproduce the experimental bounds.
ATLAS [37] (only SRB) CMS [38] ATLAS [39] (cid:101) t → t (cid:101) τ τ √ √ ∗ (cid:101) t → t (cid:101) νν √ √ ∗ (cid:101) t → b (cid:101) ντ √ √ ∗ Table 1:
Analyses employed for testing the different decay modes. The most sensitive onein each case is tagged with an asterisk.
Thus, as shown in Tab. 1, we combine the whole CMS set of bins with the abovesignal region SRB for probing the decay (cid:101) t → t (cid:101) νν , and with the single bin of the ATLAScounting experiment for testing the (cid:101) t → t (cid:101) τ τ and (cid:101) t → b (cid:101) ντ processes . Limits at differentconfidence levels are obtained by using the CL s method [45]. The expected number of In principle, the two ATLAS analyses could be combined into a single statistics. They are indeed
MadGraph v5 [46] that are subsequently decayed by
Pythia v6 [47]. Theparameter cards are produced by means of
SARAH v4 [48] and
SPheno v3 [49]. When eachchannel is studied separately, the corresponding branching ratio has been fixed manuallyto one in the parameter card. When several channels are considered, the amount of signalevents is rescaled accordingly.
As discussed in the previous sections, in our scenario the possible decay channels are (cid:101) t → t (cid:101) τ τ , (cid:101) t → t (cid:101) νν and (cid:101) t → b (cid:101) ντ . In this section we consider each individual decay channeland use the LHC data to bound the corresponding branching ratio in the plane ( m (cid:101) t , m (cid:101) 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 (cid:101) t , m (cid:101) ν ). Everypanel contains the exclusion curves corresponding to several values of the branching ratiointo the considered channel. For a given branching ratio, the allowed region stands outsidethe respective curve (marked as in the legend) and within the kinematically allowed area(below the thin dashed line).For the decay (cid:101) t → t (cid:101) τ τ (upper panels of Fig. 3) the most sensitive analysis is theATLAS counting experiment. We combine it with the CMS signal region into a singlestatistics. As Fig. 3 shows, the bound on this channel is very weak. In particular, amongthe searches that we identified as the most sensitive ones to this channel, there is no oneconstraining this decay mode at 95% CL for m (cid:101) t (cid:38)
300 GeV and m (cid:101) ν (cid:46)
100 GeV.For the decay channel (cid:101) t → t (cid:101) νν (middle panels of Fig. 3) the most sensitive analysis isthe CMS analysis, though the ATLAS search for hadronically decayed stops is also ratherconstraining. The bound provided in Fig. 3 is based on the combination of both. Asalready pointed out, the stringent cuts optimized for the searches for stops into on-shellLSP neutralinos have rather low efficiency on the “double invisible” three-body decaysignal involving an off-shell mediator [40].Finally, the bounds for the (cid:101) t → b (cid:101) ντ decay channel are presented in the lower panelsof Fig. 3. As summarized in Tab. 1, it turns out that the most sensitive analysis to thischannel 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 combiningthe CMS signal regions with the ATLAS counting one into a single statistics (we do notexpect relevant improvements by also including the excluded ATLAS analysis).We expect the findings to be qualitatively independent of the particular SUSY realiza- independent, for one of them concentrates on the fully hadronic topology while the other tags lightleptons. If we only combine with the CMS analysis is because the validation of this search gives betterresults. At any rate, no big differences are expected.
00 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ]
90% CL
BR = 1BR = 0.8
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ]
95% CL
BR = 1BR = 0.8
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ]
90% CL
BR = 1BR = 0.8BR = 0.6
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ]
95% CL
BR = 1BR = 0.8BR = 0.6
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ]
90% CL
BR = 1BR = 0.8BR = 0.6BR = 0.4
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ]
95% CL
BR = 1BR = 0.8BR = 0.6BR = 0.4
Figure 3:
Upper panels: Excluded region for BR ( (cid:101) t → t (cid:101) τ τ ) = 1 , . at the 90% CL (leftpanel) and 95% CL (right panel) in the plane ( m (cid:101) t , m (cid:101) ν ) . For each value of the branchingratio the excluded region is the one enclosed by the corresponding curve. Above the thindashed line the channel is kinematically forbidden. Middle panels: The same for BR ( (cid:101) t → t (cid:101) νν ) = 1 , . , . . Lower panels: The same for BR ( (cid:101) t → b (cid:101) ντ ) = 1 , . , . , . . m (cid:101) τ (cid:46) m (cid:101) ν + 30 GeV and BR ( (cid:101) τ → (cid:101) νW ∗ ) (cid:39) . In concrete models, it is feasible that the branching ratios of the three aforementionedstop decay channels sum up to essentially 100%, as we will explicitly see in Sec. 4. In sucha situation, we can consider BR( (cid:101) t → t (cid:101) νν ) and BR( (cid:101) t → b (cid:101) ντ ) as two independent variables,and fix BR( (cid:101) t → t (cid:101) τ τ ) asBR( (cid:101) t → t (cid:101) τ τ ) = 1 − BR( (cid:101) t → t (cid:101) νν ) − BR( (cid:101) t → b (cid:101) ντ ) . (3.1)It is then possible to use the aforementioned ATLAS and CMS searches to constrain thetwo-dimensional plane (cid:2) BR( (cid:101) t → t (cid:101) νν ) , BR( (cid:101) t → b (cid:101) ντ ) (cid:3) for some set of values of m (cid:101) t and m (cid:101) ν .The total number of signal events after cuts is given by N = (cid:88) i,j N ij ( m (cid:101) t ) (cid:15) ij ( m (cid:101) t , m (cid:101) ν ) , (3.2)with N ij ( m (cid:101) t ) = L σ ( pp → (cid:101) t (cid:101) t ∗ ) × BR( (cid:101) t → i ) × BR( (cid:101) t ∗ → j ) , (3.3)where L = 13 fb − stands for the integrated luminosity, σ is the stop pair production crosssection, and the indices i and j run over the three decay modes. The quantity (cid:15) ij is theefficiency that our recast analyses have on the (cid:101) t (cid:101) t ∗ → ij events and is strongly dependenton the mass spectrum. To determine (cid:15) ij in some given mass spectrum scenarios, we runsimulations of (cid:101) t (cid:101) t ∗ → ij following the procedure discussed above. As the searches do notdiscriminate between ij and its hermitian conjugate, it holds (cid:15) ij = (cid:15) ji .The results are shown in Fig. 4. The regions above the horizontal dashed green lineswould be the excluded ones had we assumed the signal to consist of only (cid:101) t (cid:101) t ∗ → b (cid:101) ντ b (cid:101) ντ events. Analogously, the areas to the right of the vertical green dashed lines would be the To clarify this issue, we repeated the (cid:101) t → t (cid:101) τ τ simulations for a few parameter points featuring atiny stau sneutrino mass splitting. For these few points, the constraints on (cid:101) t → t (cid:101) τ τ presented in thispaper turn out to be comparable, i.e. ruling out a similar region of the parameter space in the plane( m (cid:101) t , m (cid:101) ν ). Moreover the constraints on (cid:101) t → t (cid:101) νν and (cid:101) t → b (cid:101) ντ are of course the same. This suggests thatthe presented bounds can be applied to other scenarios. Extensive parameter space simulations would behowever required to prove this feature in full generality. . . . . . . BR (˜ t → t ˜ νν ) . . . . . . B R ( ˜ t → b ˜ τ ν ) m ˜ t = 300 GeV m ˜ ν = 70 GeV . . . . . . BR (˜ t → t ˜ νν ) . . . . . . B R ( ˜ t → b ˜ τ ν ) m ˜ t = 390 GeV m ˜ ν = 170 GeV . . . . . . BR (˜ t → t ˜ νν ) . . . . . . B R ( ˜ t → b ˜ τ ν ) m ˜ t = 430 GeV m ˜ ν = 110 GeV . . . . . . BR (˜ t → t ˜ νν ) . . . . . . B R ( ˜ t → b ˜ τ ν ) m ˜ t = 480 GeV m ˜ ν = 200 GeV Figure 4:
Excluded regions at 95% CL in the plane of BRs for different pairs of ( m (cid:101) t , m (cid:101) ν ) .The areas below (to the left of ) the horizontal (vertical) green dashed lines would be allowedif only the (cid:101) t → b (cid:101) τ ν ( (cid:101) t → t (cid:101) νν ) mode was considered. The areas enclosed by the orangesolid lines are excluded when all channels are combined. The areas above the diagonalblack solid straight lines are forbidden by the condition of Eq. (3.1). excluded ones under the assumption that only the events (cid:101) t (cid:101) t ∗ → t (cid:101) ννt (cid:101) νν are bounded. Theregions enclosed by the orange solid lines are instead excluded considering the whole signal,including also the stop decay into t (cid:101) τ τ and the mixed channels. For such comprehensiveexclusion bounds, a common CL s is constructed out of the bins in the ATLAS signalregion SRB, all bins in the CMS analysis and the single bin in the ATLAS countingexperiment.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 constraints14n the isolated signals, ruling out the region above and on the right of the horizontaland vertical dashed lines, respectively. This even reaches points close to the origin,where the main decay channel is (cid:101) t → t (cid:101) τ τ . The main reason is the inclusion of themixed channels. • ii) The fact that no single decay necessarily dominates, makes sizeable regions ofthe parameter space to still be allowed by current data. This is further reinforced bythe smaller efficiencies that current analyses have on these processes in comparisonto the standard channels. Thus, even small masses such as m (cid:101) t (cid:39)
300 GeV and m (cid:101) ν (cid:39)
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 valuesof BR( (cid:101) t → t (cid:101) τ τ ). This effect can be easily understood from the first row plots inFig. 3: there is little sensitivity of the present experimental searches to the channel (cid:101) t → t (cid:101) τ τ when m (cid:101) t and m (cid:101) ν are small. The results of Sec. 3 can be reinterpreted in concrete SUSY scenarios that exhibit stopsdecaying as in Fig. 1, at least at detector scales . The stop, stau, sneutrino and elec- Scenario M M µ A 1.1 TeV 5 TeV 5 TeVB 1.1 TeV 1.1 TeV 1.1 TeV
Table 2:
The value of the electroweakino mass parameters assumed in scenarios A and B. 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 thesecodes, and fix the parameters as follows. We impose tan β = 10, in agreement with thearguments of Sec. 2. The slepton and squark soft-breaking trilinear parameters are set tozero. The soft masses of the RH stop, M U R , and LH stau doublet, M L L , are much lighterthan those of their partners with opposite “chirality”, M Q L and M E R . The electroweakinosoft parameters are set, as shown for scenarios A and B in Tab. 2, above the lighter stopmass. The masses of the remaining SUSY particles are not relevant for our analysis, theyjust 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 massesof the SUSY particles except electroweakinos, light stop and light stau doublet at 3 TeV. As the Higgs plays no role in this study, the origin of electroweak breaking remains genericallyunspecified and not used to constrain the SUSY parameters.
00 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ] . . .
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ] . . . .
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ] . . .
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ] . . .
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ] . . .
300 400 500 600 700 800 900 m ˜ t [GeV] m ˜ ν [ G e V ] . . . Figure 5:
Contour plots of the values of BR ( (cid:101) t → t (cid:101) τ τ ) (left panels), BR ( (cid:101) t → t (cid:101) νν ) (middlepanels) and BR ( (cid:101) t → b (cid:101) ντ ) (right panels) in Scenario A (upper panels) and Scenario B(lower panels). For the above parameter choice, we study two parameter regimes denoted as scenariosA and B, characterized by the values of M , M and µ quoted in Tab. 2. Within eachregime, we vary the masses m (cid:101) t and m (cid:101) ν , by scanning over M U R and M L L , and consequently m (cid:101) τ is determined as well. We discard the parameter points with m (cid:101) t < m (cid:101) ν +70 GeV, whichcorrespond to compressed scenarios that are not investigated in this paper. Contour plotsof dominant stop branching ratios are plotted in Figs. 5 as a function of m (cid:101) t and m (cid:101) ν ,for scenario A (upper row panels) and scenario B (lower row panels). For each scenario,the branching ratios of (cid:101) t → t (cid:101) τ τ , (cid:101) t → t (cid:101) νν , and (cid:101) t → b (cid:101) ντ are plotted in the left, middleand right panels, respectively. As anticipated in Sec. 2, the main effect of decreasing M and µ is to enhance BR ( (cid:101) t → b (cid:101) ντ ), as we can see by comparing the two right panels inFig. 5. Conversely, by increasing the value of M and µ we increase the branching ratiocorresponding to the channel t (cid:101) τ τ , and we expect to make softer the bounds in the plane( m (cid:101) t , m (cid:101) ν ), in agreement with the general behavior in the lower row panels in Fig. 3 andin all plots in Fig. 4. We stress that, within the considered parameter range, the sum ofthese three branching ratios is always above 95% (depending on the range of m (cid:101) t and m (cid:101) ν )which is consistent with our general model assumptions. We also checked numericallythat the total width of the stau is O (10 − GeV) for m (cid:101) ν ≈
500 GeV, and is much largerat smaller sneutrino masses. Analogously, the mass gap between the stau and sneutrinomasses ranges between 5 −
40 GeV, the latter value appearing for m (cid:101) ν ≈
60 GeV.The results of Sec. 3, along with the numerical evaluations of the different stop branch-16
00 350 400 450 500 550 600 650 700 m ˜ t [GeV] m ˜ ν [ G e V ] Scenario A 300 350 400 450 500 550 600 650 700 m ˜ t [GeV] m ˜ ν [ G e V ] Scenario B
Figure 6:
95% CL exclusion plots (inside the orange lines) for scenario A (left panel) andscenario B (right panel). The gray areas correspond to the region with m (cid:101) t < m (cid:101) ν + 70 GeVthat we do not investigate. ing ratios, allow to recast the present LHC constraints on scenarios A and B. At eachparameter point we rescale the amount of signal events, depending on the values of thebranching ratios extracted from the MSSM parameter card corresponding to that point .The final excluded regions at 95% CL in the plane ( m (cid:101) t , m (cid:101) ν ) are shown in Fig. 6. Bothin scenario A (left panel) and B (right panel) the exclusion bounds (orange areas) arerelaxed with respect to their analogous in SUSY scenarios with the neutralino as theLSP. As anticipated, bounds are weaker in scenario A than in scenario B, due the largervalues of BR( (cid:101) t → t (cid:101) τ τ ). Remarkably, in the presence of light sneutrinos, a RH stop ataround 350 GeV is not ruled out by current LHC data, or at least by the ATLAS andCMS 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, amostly right-handed stop with a mass of around 350 GeV is compatible with the presentLHC data. This is mostly due to the coexistence of several branching ratios into channelswhich the LHC searches have weak sensitivity to. Although we have not been concernedabout detailed naturalness issues, light stops certainly help in this sense. Heavy elec-troweakinos are instead considered unnatural, but this is not necessarily true for low scale In order to check the consistency of our procedure, we also perform the collider simulations describedin Sec. 3 for numerous parameter configurations of each scenario. We find perfect consistency, meaningthat the contribution from any channel to the search of any other is negligible. unstableat cosmological scales . In theories with R -parity conservation this can be realized only ifthere 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 (cid:101) G . It is a candidateto warm DM and its cosmological abundance is given by Ω / h (cid:39) . m / / . F (cid:39) m / M P . In this casethe sneutrino decays as (cid:101) ν → ν (cid:101) G and, as far as collider phenomenology is concerned, itlooks stable. In theories with a heavy gravitino, as e.g. in theories with SS breaking, onecould always introduce a right-handed sneutrino ν R , lighter than the left-handed sneu-trino . On the other hand, the right-handed sneutrino can in principle play the role ofDM [9, 11]. If its fermionic partner is light, also the decay (cid:101) t → b (cid:101) τ ν R appears although This can be achieved for instance by localizing the right-handed neutrino multiplet in the brane andthus receiving its mass from higher order radiative corrections. . In this case, in order to overcome the direct detec-tion bounds, the initial density of sneutrinos in thermal equilibrium should be diluted bysome mechanism, as e.g. an entropy production (or simply a non-standard expansion ofthe universe), before the big bang nucleosynthesis [54, 55]. Finally the simplest solutionto avoid the direct detection bounds is if there is a small amount of R -parity breaking andthe 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 (cid:101) ν → e j ¯ e k . Depending on the value of the coupling λ the sneutrino can decay at cosmological times. Needless to say, in this case one wouldneed some additional candidate to DM.Remarkably, the present bounds on the stop mass in the considered scenario are soweak 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 channelsresponsible for the poorly efficient current LHC searches, should also (partially) apply tothe left-handed third-family squarks. The presence of these additional squarks in the lightspectrum would effectively increase the number of events ascribable to the channels wehave analyzed. Nonetheless, since the obtained constraints are very weak, there shouldbe room for a sizeable number of further events before reaching TeV-scale bounds. Insuch a case, in the heavy electroweakino scenario considered in this paper, present datacould still allow for a full squark third-family generation much lighter than what is naivelyinferred 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 wherevery light stops are compatible with the present LHC searches without relying on ar-tificial (e.g. compressed) parameter regions. It is not clear whether this simply occursbecause of lack of dedicated data analyses. In summary, the possibility that the bias forthe neutralino as lightest SUSY particle have misguided the experimental community to-wards partial searches, and that clear SUSY signatures are already lying in the collecteddata, is certainly intriguing. For discussions in this direction see e.g. Refs. [50–53]. cknowledgments The work of MC is partially supported by the Spanish MINECO under grant FPA2014-54459-P and by the Severo Ochoa Excellence Program under grant SEV-2014-0398. Thework of AD is partially supported by the National Science Foundation under grant PHY-1520966. The work of GN is supported by the Swiss National Science Foundation undergrant 200020-168988. The work of MQ is also partly supported by the Spanish MINECOunder grant CICYT-FEDER-FPA2014-55613-P, by the Severo Ochoa Excellence Pro-gram under grant SO-2012-0234, by Secretaria d’Universitats i Recerca del Departamentd’Economia i Coneixement de la Generalitat de Catalunya under grant 2014 SGR 1450,and by the CERCA Program/Generalitat de Catalunya.
A Analysis validation
In order to validate our implementations of the experimental analyses of Refs. [37–39],we apply them to Monte Carlo events generated using the same benchmark models ofthose searches. Specifically, these are pair-produced stops decaying as (cid:101) t → t (cid:101) χ [37, 38]and (cid:101) t → bν (cid:101) τ ( (cid:101) τ → τ (cid:101) G ) [39]. The signal samples are obtained by generating pairs of stopevents in the MSSM with MadGraph v5 at leading order. Such events are subsequentlydecayed by
Pythia v6 . In the parameter cards produced with
SARAH v4 and
SPheno v3 ,the branching ratio BR( (cid:101) t → t (cid:101) χ ) is fixed manually to 100% in the first two analyses. In thesame vein, for the analysis of Ref. [39] we fix both BR( (cid:101) t → bν (cid:101) τ ) = 1 and BR( (cid:101) τ → τ ν ) = 1.Notice that, in this last case, the neutrino plays the role of the (massless) gravitino, thusmimicking 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 singlestatistics (note that the analysis of Ref. [39] is simply a counting experiment). The only
300 400 500 600 700 800 900 1000 m ˜ t [GeV] m ˜ χ [ G e V ] exper. boundrecast bound
300 400 500 600 700 800 900 1000 m ˜ t [GeV] m ˜ χ [ G e V ] exper. boundrecast bound
400 500 600 700 800 900 1000 m ˜ t [GeV] m ˜ τ [ G e V ] exper. boundrecast bound Figure 7:
Comparison of the bounds reported by the experimental papers (solid orangelines) of Ref. [37] (left panel), Ref. [38] (middle panel) and Ref. [39] (right panel) withthose obtained after recasting the analyses (dashed green lines).
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