Constraints on sneutrino dark matter from LHC Run 1

A mostly right-handed sneutrino as the lightest supersymmetric particle (LSP) is an interesting dark matter candidate, leading to LHC signatures which can be quite distinct from those of the conventional neutralino LSP. Using SModelSv1.0.1 for testing the model against the limits published by ATLAS and CMS in the context of so-called Simplified Model Spectra (SMS), we investigate to what extent the supersymmetry searches at Run 1 of the LHC constrain the sneutrino-LSP scenario. Moreover, we discuss the most relevant topologies for which no SMS results are provided by the experimental collaborations but which would allow to put more stringent constraints on sneutrino LSPs. These include, for instance, the mono-lepton signature which should be particularly interesting to consider at Run 2 of the LHC.


Introduction
In this paper, we extend the work of [27] by investigating to what extent the results from SUSY searches at Run 1 of the LHC, published in terms of so-called Simplified Model Spectra (SMS) limits, 2 constrain the sneutrino-LSP scenario. Moreover, we discuss the most promising topologies for which no SMS results exist but would enhance the LHC sensitivity to sneutrino DM. To this aim, we make use of the SModelS v1.0.1 package [31][32][33] to compare the predictions of the MSSM+RN model against the SMS limits published by ATLAS and CMS. The strengths of SModelS v1.0.1 are that it 1.) automatically decomposes the signal of an arbitrary SUSY spectrum into all its SMS-equivalent topologies, and 2.) includes a large database of more than 60 SMS results from ATLAS and CMS SUSY searches. This allows us to test the limits from a large variety of searches and at the same time draw conclusions about which additional topologies should be considered.
The paper is organised as follows. After briefly defining the MSSM+RN in Section 2 we describe the numerical procedure in Section 3. In particular in 3.1 we explain the sampling method and the constraints implemented in the model likelihood function, while in 3.2 we describe the application of SModelS v1.0.1 to the MSSM+RN. Our numerical results are presented in Section 4, and the conclusions in Section 5. Two appendices contain some interesting supplementary material. Appendix A discusses the validity of applying SMS results from slepton searches (dilepton signature) to chargino-pair production followed by decays into leptons and sneutrinos. Appendix B gives some details on scenarios with long-lived heavy charged particles, in particular gluinos or stops, which so far cannot be constrained by SMS results.

The MSSM+RN model
We use the MSSM+RN model as defined in [12,13,24]. (The model used in [21,22,26] differs only slightly in notation.) The superpotential for Dirac RH neutrino superfield is given by where Y IJ ν is a matrix in flavor space (which we choose to be real and diagonal), from which the mass of neutrinos are obtained as m I D = v u Y II ν . Note that lepton-number violating terms are absent in this scheme. The additional scalar fields contribute with new terms in the softbreaking potential where both matrices M 2 N and Λ IJ ν are real and diagonal, M 2 N = diag(m 2 N k ) and Λ IJ ν = diag(A k ν ), with k = 1, 2, 3 being the flavor index. In the sneutrino interaction basis, defined by the vector Φ † = (ν * L ,Ñ * ), the sneutrino mass potential is with the squared-mass matrix M 2 Here, m 2 L k are the soft mass terms for the three SU(2) leptonic doublets, tan β = v u /v d and v 2 = v 2 u + v 2 d = (246 GeV) 2 , with v u,d the usual Higgs vacuum expectation values (vevs). The Dirac neutrino mass m D is small and can be safely neglected.
The off-diagonal term determines the mixing of the LH and RH fields. If A k ν = ηY ν , that is if the trilinear term is aligned to the neutrino Yukawa, this term is certainly very small as compared to the diagonal entries and is therefore negligible. However, A k ν can in general be a free parameter and may naturally be of the order of the other entries of the matrix [12,13], thus inducing a sizable mixing among the interaction eigenstates. The sneutrino mass eigenstates are then given by  [40] m χ + 1 , mẽ ,μ > 101 GeV (95% CL) [38] mg > 308 GeV (95% CL) [41] σ SI n < σ SI LUX (90% CL) [28] 3 Numerical procedure

Sampling method over the model parameters
For definiteness, we study the MSSM+RN with soft terms defined at a high scale M ∼ M GUT as in [27]. Allowing for non-universalities in the gaugino and scalar sectors, our set of free parameters is Here the M i are the gaugino masses, m L , m R , m N are the charged slepton and sneutrino masses, m Q is a common squark mass parameter, m H ≡ m Hu = m H d denotes the common entry for the two Higgs doublet masses, and A l and A q are the scalar trilinear couplings for the sleptons and squarks respectively. The computation of the mass spectrum follows that explained in [27], where all details are provided. The list of constraints implemented in the model likelihood function is given in Table 1. In particular, besides consistency with B-physics constraints, we require the Higgs mass m h to be compatible with the ATLAS and CMS measurements [1,2], which we combine by a statistical mean, as obtained in [42]. Its uncertainty is dominated by the theoretical error, estimated to be around 4 GeV [43]. We also require that chargino and charged slepton masses fulfill the LEP bounds at 95% confidence level (CL) -notice that the tau slepton has a slightly less stringent lower bound of 85 GeV [40] as compared to selectrons and smuons-and we include the gluino mass bound from the D0 collaboration [41]. Ifν τ 1 is light enough to be produced in Z decay, we require its contribution to the Z invisible decay width to be smaller than 2 MeV [44]. Similarly, when the sneutrino mass is lighter than m h /2, the Higgs can decay invisibly into sneutrino pairs. We require that such decays do not contribute more than 20% to the Higgs invisible branching ratio [39].
Regarding DM constraints, we require consistency with the measured relic abundance and with the bounds from direct detection experiments (constraints from indirect DM detection are also fulfilled). The experimental error on Ω DM h 2 has become incredibly small due to the Planck measurement [15], while the theoretical one is still large. We use a conservative estimate of the order 20% [45] for the latter. Furthermore, we enforce the sneutrino SI scattering cross section off nuclei, σ SI n , to be compatible with the recent 90% CL bound from LUX [28]. To evaluate the experimental observables we first computed the supersymmetric particle spectrum with a modified version of SoftSusy [46]. For the computation of the sneutrino relic density and elastic scattering cross-section the model has been implemented in FeynRules [47,48], by adding the appropriate term in the superpotential and in the soft SUSY breaking potential. We generate output files compatible with CalcHep in order to use the public code micrOMEGAS 3.2 [49]. The B-physics observables are computed by interfacing the program with SuperIso [50].
The likelihood is constructed in a simple way. For measured quantities, we assume a Gaussian likelihood function with a variance given by combining in quadrature the theoretical and experimental variances. For observables for which only lower or upper limits are available, we use a likelihood modelled as a step function on the x% CL of the exclusion limit. The total likelihood function is then the product of the individual likelihoods associated to each experimental result. In order to save time in the sampling procedure, the slepton, chargino and gluino mass limits are, however, absorbed into the prior probability density functions: each parameter point generating a mass spectrum that violates one of these bounds is immediately discarded.
Given the likelihood function, we sample the posterior probability density function with the MultiNest algorithm [51][52][53]. In order to cover all phenomenological interesting classes, we run separate chains that look either for light(ish) EW-inos (mχ± 1 < 900 GeV), light sleptons (ml < 600 GeV), or for light squark or gluinos (mq < 1.5 TeV or mg < 1.5 TeV). As for the choice of priors, we always take logarithmic priors on M 3 , m Q , A Q , m H , while we use both logarithmic and flat priors for M 1 , M 2 , m L , m R , m N , A L , Aν, tan β (details on the prior ranges are provided in [27]). In particular we perform two chains, one with log and one with flat priors, for each relevant data set: two chains for light EW-inos (these two data sets coincide with the ones used in [27]), two chains for light sleptons and two chains for light squarks or gluinos. In each case, the other masses are left to vary freely from high to low values. The motivation for this is, as mentioned, to cover all potentially interesting cases; the results we will present in Section 4 are for all chains combined together.
The sampled points correspond to a 95% CL in volume of the posterior. (Since in this study we are not interested in statistical statements on the parameter space, we will however not exploit this feature.) The limits imposed by a step function are of course strictly obeyed by all scan points. Moreover, we have checked that none of the individual constraints implemented by a Gaussian gets a large pull in the final sample. In particular, BR(B → X s γ) and BR(B s → µ + µ − ) are in full agreement with the 95% CL experimental results [36,37] for all points in the samples.
First, the input to SModelS v1.0.1 can be simulated events or an SLHA [63] file containing the full mass spectrum and decay tables as well as the SUSY production cross sections, σ, in the format specified at [64]. We choose the latter option. We use the MSSM+RN model implemented in micrOMEGAs 3.2 [49] (see [27]) to compute the decay branching ratios, B. The production cross sections for sleptons and sneutrinos (i.e. the sector modified with respect to the MSSM) are also computed with micrOMEGAs 3.2. For all other production processes, we use the default SModelS v1.0.1 cross section calculator based on Pythia 6.4 [54] and NLL-fast [55][56][57][58][59][60][61]. Electroweak cross sections are thus computed at leading order while strong productions are computed at NLO+NLL order.
Given the information on σ and B in the SLHA files, SModelS v1.0.1 computes σ × B for each topology that occurs. Here, a topology is characterised by the SM particles originating from each vertex, and the mass vector of the SUSY particles in the decays. In order to avoid dealing with a large number of irrelevant processes, which is expensive in terms of computing time, topologies for which σ × B < σ cut , with σ cut = 0.05 fb, are discarded.
When dealing with an arbitrary spectrum of SUSY particles, it is possible that a part of the decay chain leads to completely invisible decays, e.g. a decay of a heavy sneutrino to a lighter one plus neutrinos in the current scenario. In such cases, SModelS v1.0.1 compresses the invisible part of the decay chain as illustrated in Fig. 1. All decays to neutrinos appearing after the last visible decay are disregarded, yielding an "effective LSP" for the particular event, which can be different from the true LSP. This procedure is called "invisible compression". Likewise, a neutralino may decay invisibly to a sneutrino and a neutrino; in this case the compressed topology resembles an MSSM topology.
In addition, if the mass gap between mother and daughter particles is small, the decay products will be too soft to be detected at the LHC. This is taken care of by the so-called "mass compression" in SModelS v1.0.1, discarding any SM particle that come from a vertex for which the mass splitting of the R-odd particles is less than a certain threshold. We use 5 GeV as the minimum required mass difference for the decay products to be visible.
Another comment is in order. The experimental constraints currently implemented in the SModelS v1.0.1 database require final states containing missing transverse energy (MET). This means that scenarios with long-lived particles (cτ > 10 mm) leading to signatures with displaced vertices or heavy charged particle tracks cannot be tested with SModelS v1.0.1. In the MSSM, this problem occurs, e.g., in wino-LSP scenarios where the χ ± 1 is highly massdegenerate with the χ 0 1 and thus becomes long-lived. In the sneutrino LSP case, not only charginos can be long lived if the mass splitting with the sneutrino is small enough; other possibilities are, e.g., long-lived gluinos or stops, if they are the next-to-lightest SUSY particle (NLSP). We perform a detailed check of all input points to avoid the erroneous application of SMS limits to such cases. Points that have visible decays from long-lived particles or heavy charged particle tracks with cross sections larger than σ cut are discarded. (A brief discussion of such scenarios can be found in Appendix B.) Once the decomposition into SMS topologies, including mass and invisible compression, is completed and the checks that the SMS results actually apply are passed, a given point is confronted against the SMS results in the SModelS v1.0.1 database. For each experimental constraint that exists, SModelS v1.0.1 reports among other things the analysis name, the Tx name identifying the topology, 3 the predicted signal cross section for the point under consideration and the 95% CL experimental upper limit on it. Finally, the ratio r of the signal cross-section and the upper limit, r = σ(predicted)/σ(excluded), is given, where σ effectively means σ × B or the weight of the topology. A value of r ≥ 1 means that the input model is likely excluded by the corresponding analysis.

Results
We now turn to analysing the impact of the LHC searches on the MSSM+RN parameter space. As explained in the previous Section, we here consider only points for which the SMS results apply, i.e. we discard points with non-prompt visible decays as well as points with longlived charged particles. Scanning over the parameter space, we can then distinguish several cases: • the SMS results in principle apply but no SMS constraints actually exist for the specific topologies of the point -these points will be labelled as not tested; 4 • there exist (one or more) SMS results that test the specific topologies of the point but for each topology the total σ × B is below the corresponding 95% CL upper limit -these points will be considered as allowed; and • at least one topology has a σ × B equal or above its 95% CL upper limit (r ≥ 1) -these points will be considered as excluded.  Let us start with the question which analyses are the most important ones for constraining the model. To this end, Figs. 2 and 3 show a breakdown of most constraining analyses in thẽ ν τ 1 versusg andν τ 1 versus χ ± 1 mass planes, respectively. Looking first at Fig. 2, we see that (the SMS interpretations of) the hadronic SUSY searches [65][66][67][68][69][70][71] are constraining gluino masses up to about mg ≈ 1200 GeV and LSP masses up to about mν τ 1 ≈ 500 GeV. These searches mostly exclude points where eitherg → bb χ 0 i ,g → tt χ 0 i org → qq χ 0 i decays are dominant, followed by an invisible decay of the neutralino, χ 0 i → νν. Moreover, dilepton + MET searches [72,73] exclude sneutrino LSP masses up to about mν τ 1 ≈ 210 GeV, independent of the gluino mass. The process that is constrained here is Drell-Yang production of χ + 1 χ − 1 followed by χ ± 1 → l ±ν l1 Figure 4: Scatter plots of points for which SMS results apply. The top row shows theν τ 1 vs. g, the bottom row theν τ 1 vs. χ ± 1 mass plane. In the panels on the left, the points excluded by the SMS constraints (red) are plotted on top of those which are not excluded (blue); in panels on the right this plotting order is inverted. Also shown (in grey) are the "not tested" points, for which no SMS constraints exist.
(l = e or µ), with theν l1 →ν τ 1 + X decay being invisible (because of X being genuinely invisible or very soft). Consequently, in Fig. 3 we see that chargino masses can be excluded up to about m χ ± 1 ≈ 440 GeV by the dilepton + MET limits. (There is also a small region of parameter space at low masses where τ + τ − + MET [74] gives the strongest limit.) It is important to note here that the constraints on χ + 1 χ − 1 → l + l − + MET actually stem from thel +l− → l + l − χ 0 1 χ 0 1 simplified model (and analogously for τ + τ − + MET), which has the opposite spin configuration than chargino-pair production followed by chargino decays into sneutrinos. The validity of applying the limits from the slepton searches to the case of charginopair production is discussed in Appendix A.
Also noteworthy is the fact that most of the excluded points in Figs. 2 and 3 have some grey points lying below them, which are not excluded or not tested at all. This is corroborated in Fig. 4, where we present the summary of not tested, allowed and excluded points in theν τ 1 versusg andν τ 1 versus χ ± 1 mass planes. In the plots on the left, the excluded points (red) are plotted on on top of the allowed points (blue), while in the plots on the right this plotting order is inverted. As can be seen, only a small part of the parameter space can genuinely be For the dilepton signature originating from chargino-pair production, the chargino mixing plays an important rôle: wino-like charginos have a higher production cross section, and a higher branching fraction into lν l1 . The limits from l + l − + MET searches therefore mostly affect scenarios with wino-like χ ± 1 , while higgsino scenarios are much less constrained. For illustration see Fig. 5, which shows the SMS-allowed points in theν τ 1 versus χ ± 1 mass planehere the color map gives the size of the U 11 entry of the chargino mixing matrix, indicating to the wino/higgsino content of the χ ± 1 . As can be seen, in the region that is in principle constrained by the SMS results the surviving points feature χ ± 1 s that have a large higgsino admixture (|U 11 | < ∼ 0.5). These points have a lower χ + 1 χ − 1 production cross section and the χ ± 1 decays preferably into τν τ 1 since the higgsino decay to e, µ is Yukawa suppressed; τ + τ − + MET is however a more difficult signature experimentally and thus only constrains a small strip at lowν mass, cf. the purple points in Fig. 3.

Missing topologies
The next question to ask is which are the most important signatures not covered by SMS results. Such information can be used to improve on the interpretation of the LHC searches for new physics. We call these uncovered signatures "missing topologies". For any point passed through SModelS v1.0.1, we keep up to ten missing topologies sorted by their σ × B. To avoid double counting, missing topologies are evaluated after mass and invisible compressions. The total weight is computed by summing over all diagrams giving the same topology, i.e. ignoring the mass vector of the SUSY states involved. Moreover, l = e, µ lepton flavors appearing in the final state are summed over (light quark flavors are always summed over). In the following, we only consider MSSM+RN scan points which are not excluded, and we demand that missing topologies have σ × B ≥ 1 fb. The results can be presented in two ways, either by showing the most frequent missing topologies in a certain parameter space, or by selecting for each parameter point the missing topology with the highest cross section.
We choose the latter approach to show in Fig. 6 the missing topologies in the sneutrino-vs. gluino-mass plane. The various processes are denoted in the bracket notation of SModelS, explained in [31]. The structure is [branch1, branch2] for the decay chains ("branches") of the two initially produced SUSY particles; each branch contains inner brackets for each vertex, con- denotes gluino-pair production with the first gluino decaying viag → qq χ 0 , χ 0 → νν and the other one viag → qq χ ± , χ ± → lν. 5 It is apparent that many points with gluino masses below about 1.2 TeV, for which the LHC searches should have good sensitivity, are not excluded by the SMS results because they feature "mixed topologies", where the two pair-produced gluinos undergo different decays (e.g. one gluino decaying into bb and the other one into light jets). Since the SMS results for pairproduced sparticles always assume two identical branches, these cases cannot be constrained by SModelS v1.0.1. Moreover, hadronic final states with additional leptons, as they arise from gluino decays into charginos and the chargino decaying further into a charged lepton (e, µ or τ ) plus the LSP, do not have any SMS equivalent. Finally, there are no SMS results available forg → tb χ ± j , no matter of whether the chargino has any visible decays. It is also worth noting that over a large part of the parameter space single lepton + MET from χ 0 i χ ± j production; its importance is corroborated in Fig. 7, where one can see that it is indeed dominating the whole sneutrino-vs. chargino-mass plane. (There are also cases where single W + MET is dominant.) The cross section for single lepton + MET production, shown in Fig. 8, can be very large and should give important additional constraints on the model. While searches for single lepton + MET were performed by both ATLAS [75] and CMS [76], unfortunately no suitable SMS interpretation exists for these analyses. It would be extremely interesting if the experimental collaborations provided upper limit maps and/or efficiency maps for their single lepton + MET analyses in the context of a chargino-sneutrino simplified model.

This appears as [[[nu],[W]],[[ta],[W]]] (yellow points) in
Before proceeding it is instructive to take another look at the missing topologies arising from EW-ino and slepton production, but this time ordered by their frequency of occurrence. This is done in Fig. 9. Not surprisingly we see that besides single lepton (e or µ), single τ is an important signature. Although it is less clean experimentally, the relative weight of single e, µ or τ + MET might potentially give information on the mass pattern of the mostly RH sneutrinos.

Another important class of "missing topologies" are different-flavor dileptons ([[[l]],[[ta]]] and [[[l]],[[l']]])
. Different-flavor dileptons + MET have in principle been considered by ATLAS and CMS in the context of chargino-pair production in the MSSM with the charginos decaying either into W ( * ) χ 0 1 [72] or into lν χ 0 1 via on-shell sleptons/sneutrinos [72,73]. However, the associated SMS limits do not apply to the sneutrino LSP case for various reasons. For example, the leptons from χ ± 1 → W ( * ) χ 0 1 are generally softer than those from χ ± 1 → l ±ν l decays (for the same χ ± 1 and LSP masses) because of the additional neutrinos in the W decay. The limits for the χ + 1 χ − 1 → 2 ×lν(orνl) → 2 × lν χ 0 1 simplified model are also not applicable because they involve an additional intermediate mass scale.  (black stars). In this case, after χ 0 i χ ± j production, the decay chain is and χ ± j → τ ±ν τ 1 . The panel on the right shows the breakdown of most constraining analyses for the points that are excluded by the SMS limits (for the sake of comparison, the allowed points are shown in grey). In both panels, the solid magenta lines and the dashed blue lines are the current exclusion limit by LUX and the forecasted sensitivity of XENON1T experiment respectively, while the dashed light green line corresponds to the predicted neutrino coherent scattering on nuclei.

Complementarity with direct DM searches
Let us finally turn to the complementarity of LHC and direct DM searches-recall that all points in our scans are consistent with DM constraints, as described in Table 1. In Fig. 10, left panel, we plot the allowed (gray), excluded (red) and not tested points (cyan) as a function of the sneutrino mass and the SI scattering cross section. In the same plot we also show the forecasted sensitivity of XENON1T after two years of scientific run [77] and the predicted value for neutrino coherent scattering on nuclei [78], which can be an irreducible background for direct detection experiments. From this plot, the complementarity between the two type of searches is striking. Points with a SI elastic cross section well below the neutrino background, and hence not detectable by direct detection experiments, are already excluded by SMS results. On the other hand, a bulk of points allowed (or even more interestingly, not tested) by SMS results is well in the reach of XENON1T, expected to start running in 2015. Notice however that there still exist combinations of parameters that allow sneutrino DM to escape both direct detection and LHC searches, represented by the cyan points below the neutrino background curve. In the MSSM+RN, DM direct searches are basically sensitive to the mass of the LSP and its couplings with the Higgs and Z bosons. The rest of the SUSY mass spectrum is not relevant. This is different with respect to the MSSM with the neutralino LSP, where the interaction with the quarks is mediated as well by squarks on t-channel. This is clearly visible in the right panel of Fig. 10, which shows the most constraining SMS analyses. In Figs. 2 and 3 these SMS analyses are typically correlated with the gluino or chargino mass, while now they are scattered all over the σ SI n versus mν τ 1 plane. Figure 11: On the left allowed (grey), excluded (red) and not tested (blue and cyan) points are shown in the plane of sneutrino mass versus mixing angle. The subset of points with exceedingly small σ × B at the LHC but in the reach of XENON1T is visualised in blue. On the right, we show the SMS allowed points in the sneutrino mass versus mixing angle plane, subdivided in blue points, which are in the reach of XENON1T and in light green (light grey) points, which are above (below) the neutrino background.
The same set of allowed, excluded and not tested points are plotted as a function of the sneutrino mixing angle in the left panel of Fig. 11. The bulk of not tested points in the reach of XENON1T (dark blue points) has, as expected, relatively large mixing angles, corresponding to sizeable contributions from Z boson exchange to the SI scattering cross section. Excluded red points are scattered everywhere in the sin θν vs. mν τ 1 plane and probe also very RH sneutrinos. In the right panel of Fig. 11 we see that among the allowed points, XENON1T can constrain a large portion of the sneutrino parameter space, while the very RH sneutrinos will remain inaccessible to future direct detection detectors. In general the points with negligible mixing angles haveν τ 1 as LSP and the neutralino as NLSP, which tends to be almost degenerate with chargino. The relic density is then actually achieved by co-annihilation of neutralino-chargino and then communicated to the mostly sterile LSP (see [27] for details). Such scenarios are very difficult to test.

Conclusions
Scenarios with a sneutrino as the LSP are an interesting alternative to MSSM models with neutralino LSPs. Indeed in SUSY models with a RH neutrino superfield (MSSM+RN) the fermionic field contributes to neutrino masses while the scalar field contributes to the DM candidate, which is a mixed, however mostly RH, sneutrino.
The collider phenomenology of the MSSM+RN can be quite different from the typical MSSM case. It is therefore interesting and relevant to ask how the SUSY search results from Run 1 of the LHC, which were mostly designed with the MSSM in mind, constrain sneutrino LSP scenarios. To address this question, we used SModelS v1.0.1 for testing the MSSM+RN against more than 60 results from CMS and ATLAS searches in the context of so-called Simplified Model Spectra (SMS). More precisely, by considering the model parameter space where the sneutrino is a good DM candidate compatible with all current constraints, we assessed 1.) the constraining power of the current SMS results on such scenarios and 2.) the most relevant signatures not covered by the SMS approach.
Concerning point 1.), we found that the dilepton + MET searches are among the most relevant ones, constraining sneutrino masses up to about 210 GeV and mostly wino-like charginos up to m χ ± 1 ≈ 440 GeV. It is important to note here that this amounts to re-interpreting the ATLAS and CMS searches for pp →l +l− → l + l − χ 0 1 χ 0 1 in terms of pp → χ + 1 χ − 1 → l + l −ν lνl (the validity of this is discussed in Appendix A). Hadronic SUSY searches exclude gluinos masses up to mg ≈ 1200 GeV and LSP masses up to mν 1 ≈ 500 GeV. Nonetheless in general we find that only a very limited portion of the parameter space can be properly excluded by SMS results. For most points in the (mg, mν 1 ) or (m χ ± 1 , mν 1 ) planes there exist parameter combinations that allow to avoid all limits. Indeed, most of the parameter space is either allowed (SMS constraints exist for the specific topologies of the point but all σ × B of these topologies are below their 95% CL upper limits) or not tested at all (there are no existing SMS constraints for the specific topologies of the point or each topology has a σ × B which is smaller than 1 event at LHC Run 1). Direct DM searches are complementary to the SMS constraints: many points that are not tested by SMS results can potentially be excluded by XENON1T. Vice versa, points well below the neutrino background, hence not reachable by future DM detectors, are already excluded by SMS results.
The second main result of this paper concerns point 2.), i.e. the study of the allowed points in terms of missing topologies. In the hadronic sector, pair-produced gluinos with masses well in the reach of LHC Run 1 are not constrained because they feature one or more of the following: • additional leptons: since the gluino cannot directly decay into the sneutrino LSP, the hadronic final state is often accompanied by leptons; • mixed topologies: each of the pair-produced gluinos undergoes a different decay; • the gluinos decay into tb final states.
None of these possibilities are covered by the current SMS results. Note here that the last two items are also common in the MSSM, as described in [31]. For EW production, missing topologies include: • single leptons; • single W s; • different-flavour opposite-sign leptons; • same-sign W 's or same-sign taus (accompanied respectively by additional leptons/taus, or W s).
While such signatures have been searched for by the SUSY and/or exotics groups in ATLAS and CMS, the results do not exist in terms of appropriate SMS interpretations. Such an SMS interpretation would be very interesting in particular for the mono-lepton + MET case, which promises to have a considerable impact for constraining the MSSM+RN model. A final comment is in order. While the SMS approach is very convenient for the characterisation of new physics signatures and vast surveys of parameter spaces, it clearly has its limitations. Given the high interest in non-standard SUSY (and other new physics) scenarios, we urge the experimental collaborations to document their analyses in a way that they can conveniently be re-casted in public simulation frameworks like CheckMATE [79] or the MadAnalysis 5 PAD [80]. (See also the recommendations in [80] and [81] in this context). This would allow to go beyond the limitations of SMS approach and give a much more rigorous assessment of the constraints in a large variety of new physics models, including the sneutrino DM scenario discussed in this paper. Unfortunately we are still a long way from this.

A Validity of slepton search results for chargino-pair production with decay into lepton+sneutrino
In the spirit of the SModelS v1.0.1 philosophy, we apply SMS constraints for the l + l − + MET topology, obtained in the context of pair production of charged sleptons, pp →l +l− followed byl ± → l ±χ0 1 to the case of chargino-pair production pp →χ + 1χ − 1 followed by χ ± 1 → l ±ν l1 , despite the opposite spin configuration. This can only be valid if the signal selection efficiencies in both scenarios are comparable. To test this assumption, we use the recast code [82] for ATLAS search in final states with two leptons and missing transverse momentum, ATLAS-SUSY-2013-11 [72], which is available in the framework of the Mad-Analysis 5 "Public Analysis Database" [80]. We consider two benchmark scenarios in the simplified-model spirit, an MSSM one with (ml ± , mχ0 1 ) = (270, 100) GeV and an MSSM+RN one with (m χ ± 1 , mν 1 ) = (270, 100) GeV. Events are generated with MadGraph 5 [83,84] and Pythia 6.4 [54] and then passed through Delphes 3 [85] for the simulation of the detector effects. 6 For simplicity, in the following we restrict our study to pair-production of selectrons for the MSSM case, and pair-production of charginos decaying exclusively via electrons in the MSSM+RN case.
The event selection requires two opposite sign (OS), same flavor (SF) leptons with high transverse momentum, concretely p T > 35 GeV and p T > 20 GeV. 7 Figure 12 compares the p T distributions in the two benchmark scenarios, in the left panel for the harder electron, e 1 , in the right panel for the second electron, e 2 . The bin sizes are chosen such that the first bin corresponds to the events that do not pass the p T > 35 GeV (left panel) or p T > 20 GeV (right panel) requirement. We see that the electrons originating from selectron-pair production tend to be harder than those originating from chargino-pair production.
The analysis further requires the invariant mass of the lepton pair to be outside the Z window, and τ s and jets are vetoed. Finally, three signal regions are defined by thresholds on the m T 2 ("stransverse mass") variable [86,87] that is used for reducing the tt and W t backgrounds: m T 2 > 90, > 120 and > 150 GeV. The m T 2 distributions after the preselection cuts are shown in Fig. 13. It can be seen that the distributions intersect around the minimum required value of m T 2 = 90 GeV; events with electrons originating from chargino decays are more likely to pass this cut.
To see the net effect on the signal efficiencies, Table 2 shows the complete cut-flow comparison for the two benchmark scenarios. As expected, differences arise in the first cut, selecting high p T OS lepton pairs, and when applying the lower bounds for m T 2 . Because of the softer p T distribution in case of chargino production+decay, there are fewer events passing the first cut for this scenario. However, the opposite is true for the m T 2 cut. Ultimately, the efficiencies are comparable in all signal regions, and even somewhat higher for the MSSM+RN scenario.
To check that this is still true closer to the kinematic edge, we reproduce the cut-flows for a second set of benchmark scenarios with an LSP mass of 200 GeV. As can be seen in Table 3, we find a similar behaviour in this case. We conclude that we can safely apply the SMS upper  limits given by the experimental collaborations in the context of slepton-pair production in the MSSM to constrain chargino-pair production followed by decays into lν l in the MSSM+RN.

B Lifetimes of long-lived particles
As mentioned in Sec. 3.2, a considerable number of the scan points comprise long-lived sparticles. These occur mostly when enforcing light gluinos or squarks; in this case about 30 % of the points feature long-lived particles, while the fraction is below 1 % without this constraint. The long-lived particles are predominantly gluinos (85 %), mostly in the case where it is the NLSP, and in a few points whereχ 0 1 is slightly (up to about 50 GeV) lighter than the gluino. Apart from that we find points with long-lived stops or staus in case they are the NLSP, as well as single points with long-lived charginos. Here we will focus on the long-lived gluinos and stops, long-lived staus have been discussed before in [27]. In the MSSM long-lived gluinos appear when all squarks are extremely heavy, e.g. in split-SUSY scenarios. In case of the MSSM+RN with a sneutrino LSP additional causes come into play. If the gluino is the NLSP, its decay will proceed only via virtual squarks and gauginos, yielding an effective four body decay,g → qqνν (virtualq andχ 0 ) org → qq lν (virtualq and χ ± ). The gluino lifetime will therefore depend not only on the squark mass, but also on the gaugino masses and mixings, as well as the sneutrino mixing angle. Meta-stable gluinos can thus appear even if the squarks are not completely decoupled. The gluino lifetime as a function of its mass is shown in Fig. 14. The left plot illustrates the depencence on the sneutrino mass, the right plot the dependence on the sneutrino mixing. We can distinguish two general regions. First, we observe an exponential dependence of the lifetime on the gluino mass for decay lengths of 10 mm up to 10 4 m. Here the lifetime is largely independent of the sneutrino mass. Moreover lifetimes at constant gluino masses are longer for heavier squarks and gauginos. In this region we generally find large mixing angles sin θν, but heavy gauginos and squarks. Points with very small mixing angles may also appear in this region, in the case that the mass of the lightest neutralino is below the gluino mass. The second region, with lifetimes longer than 10 4 m, and up to 10 17 m, shows a very different behaviour. We can see a clear correlation between gluino and sneutrino masses in this region, with longer lifetimes found for smaller mass splittings. The lifetimes moreover increase when going to very small sneutrino mixing angles, with the maximum lifetimes achieved for sin θν going to zero.
Likewise, if the stop is the NLSP 8 and has a small mass difference with the sneutrino, it can be long-lived, see Fig. 15. As seen for the gluinos, the lifetime depends strongly on the sneutrino mixing. Both long lived gluinos and long lived stops can be constrained by searches for R-hadrons, see [88,89] for R-hadrons escaping the detector, [90] for stopped R-hadrons, or [91] for metastable gluinos decaying in flight inside the detector. However, large uncertainties arise from modeling both the hadronisation and the strong interaction of the R-hadron with the detector. Therefore no collider constraints on long-lived sparticles have been included. Additionally, cosmological constraints become important for gluino lifetimes of about 100 s (10 10 m) [92]. Lifetimes of that order would affect the fraction of heavy nuclei produced during the Big Bang nucleosynthesis. Longer lifetimes can further be constrained by searches for diffuse gamma ray background, distortions in the CMBR and heavy isotopes.