Electroweak superpartners scrutinized at the LHC in events with multi-leptons

We analyze a multi-lepton signal plus missing transverse energy from neutrinos expected at the LHC for a Bino-like neutralino as the lightest supersymmetric particle (LSP), when the left sneutrino is the next-to-LSP and hence a suitable source of Binos. The discussion is carried out in the framework of the $\mu \nu$SSM, where the presence of $R$-parity violating (RPV) couplings involving right-handed neutrinos solves the $\mu$ problem and can reproduce simultaneously the neutrino data. Left sneutrinos/sleptons are pair produced at $pp$ collisions decaying to Binos, with the latter decaying via RPV to $W\ell$ or $Z\nu$. This signal can be compared with LHC searches for electroweak superpartners through chargino-neutralino production. The reduced cross section of the sneutrino/slepton production in comparison with the one of the latter process, limits the sensitivity of the searches to small sneutrino/slepton masses. Although the resulting compressed spectrum typically evades the aforementioned searches, we show that analyses using recursive jigsaw reconstruction are sensitive to these scenarios. As a by-product, we find that the region of Bino masses $110-120$ GeV and sneutrino masses $120-140$ GeV can give rise to a tri-lepton signal compatible with the local excess recently reported by ATLAS.


Introduction
The 'µ from ν' supersymmetric standard model (µνSSM) [1,2], is a natural extension of the minimal supersymmetric standard model (MSSM) [3,4,5], where the µ problem is solved and the neutrino data can be reproduced simultaneously [1,2,6,7,8,9]. This is obtained through the presence of trilinear terms in the superpotential involving righthanded neutrino superfieldsν c i , which relate the origin of the µ-term to the origin of neutrino masses and mixing. The simplest superpotential of the µνSSM [1,2] is built with oneν c : The simultaneous presence of the last three terms in Eq. (1) makes it impossible to assign R-parity charges consistently to the right-handed neutrino ν R , thus producing explicit RPV (harmless for proton decay). Note nevertheless, that in the limit Y ν i → 0,ν c can be identified in the superpotential as a pure singlet superfield without lepton number, similar to the next-to-MSSM [10], and therefore R parity is restored. Thus, the neutrino Yukawa couplings Y ν i are the parameters which control the amount of RPV in the µνSSM, and as a consequence this violation is small. After the electroweak symmetry breaking induced by the soft supersymmetry (SUSY)-breaking terms of the order of TeV, and with the choice of CP conservation, the neutral scalars develop the following vacuum expectation values (VEVs): GeV because of the small contributions Y ν i < ∼ 10 −6 whose size is determined by the electroweak-scale seesaw of the µνSSM [1,2]. Note in this sense that the last term in Eq. (1) generates dynamically Majorana masses m M = 2κ v R √ 2 ∼ TeV. It is also worth noting that µ = λ v R √ 2 ∼ TeV is generated by the fifth term of the superpotential. The new couplings and sneutrino VEVs in the µνSSM induce new mixing of states. The associated mass matrices were studied in detail in Refs. [2,7,11]. Summarizing, in the case of one right-handed neutrino superfield, there are six neutral scalars and five neutral pseudoscalars (Higgses-sneutrinos), seven charged scalars (charged Higgses-sleptons), five charged fermions (charginos-leptons), and eight neutral fermions (neutralinos-neutrinos).
In particular, the neutral fermions have the flavor composition (ν iL , B, W , H d , H u , ν R ). Thus, with the low-energy bino and wino soft masses, M 1 and M 2 , of the order of TeV, and the same for µ and m M as discussed above, this generalized seesaw produces three light neutral fermions dominated by the left-handed neutrino flavor composition, and in agreement with experimental constraints on neutrino masses and mixing angles; while the rest of neutral fermions get masses around the TeV scale. However, if M 1 is small compared with the rest of the parameters, the fourth lightest eigenstate of the mass matrix, which we identify as the lightest neutralino, is mainly bino dominated and the LSP with a mass ≈ M 1 , since the largest off-diagonal mass entry MBH u = 1 √ 2 g ′ v u is small. On the other hand, the neutral scalars have the flavor composition (H d , H u , ν R , ν iL ), but the off-diagonal terms of the mass matrix mixing the left sneutrinos with Higgses and rigth sneutrinos are suppressed by Y ν and v iL , implying that the left sneutrino states will be almost pure. The same happens for the pseudoscalar sneutrino states, which have in addition degenerate masses with the scalars. As discussed in detail in Ref. [11], there is enough freedom in the µνSSM to tune the soft parameters in order to get light sneutrinos. Besides, the left sleptons will also be light, only a little heavier than the left sneutrinos since they are in the same SU(2) doublet, with the mass splitting mainly due to the usual small D-term contribution, −m 2 W cos 2β.
The phenomenology of the left sneutrino as the LSP in the µνSSM has been analyzed in Ref. [11]. In particular, the pair production and prompt decays of sneutrinos/sleptons producing signals with diphoton plus missing transverse energy (MET) from neutrinos, di-lepton plus MET, and multi-leptons, in the range of 100 GeV to 300 GeV, was studied. Displaced-vertex decays of the sneutrino LSP have also been recently studied in Ref. [12] through signals with di-lepton pairs, covering senutrino masses between 45 and 100 GeV. The phenomenology of a neutralino LSP was analyzed in the past in Refs. [6,7,13,14].
In this work, we analyze the interesting case when the bino-like neutralino is the LSP, with the sneutrino the next-to-LSP (NLSP). Thus the decaysν → νχ 0 andl → ℓχ 0 dominate over the RPV ones, which are suppressed by the smallness of Y ν . Thereby pair production of sneutrinos/sleptons at the LHC will be a source of bino pairs. Subsequently, binos will decay via RPV couplings to W ℓ or Zν, giving rise to signals with multi-leptons plus MET from neutrinos. We will compare these µνSSM signals with recent searches for electroweak superpartners at the LCH using an integrated luminosity of 36.1 fb −1 , through chargino-neutralino pair production in R-parity conserving (RPC) models [15,16]. We will obtain that the reduced cross section of sneutrino/slepton pair production in comparison with the latter, makes these searches insensitive if the mass of the sneutrinos is large. However, for a small sneutrino mass, the small difference with the masses of the gauge bosons and binos makes these searches also ineffective. We will show nevertheless, that there exist optimized ATLAS analyses [17] to detect chargino-neutralino pair production in the MSSM when the mass spectrum is compressed, that have a promising sensitivity to our scenario. In fact, we will also obtain regions of bino and sneutrino masses in the µνSSM producing a tri-lepton signal compatible with the local excess reported by ATLAS [17], where it was studied in the context of simplified RPC models, assuming wino-like charginoneutralino production with a bino-like LSP. This scenario was further elaborated in Ref. [18] including dark matter constraints and the measured anomalous magnetic moment of the muon.
The paper is organized as follows. In Section 2 we will introduce the phenomenology of the bino-like LSP with the sneutrino as the NLSP, studying their relevant pair production at the LHC, as well as the signals. On the way, we will analyze the decay widths, BRs and decay lengths of the bino. In Section 3, we will consider the recent ATLAS searches for multi-leptons plus MET, and discuss their feasibility and significance on bino searches in the µνSSM. We will also show our prescription for recasting the ATLAS result [17] to the case of the sneutrino-bino scenario. We then will show the prospects for the 100 and 300 fb −1 searches in Section 4. Our conclusions are presented in Section 5.

Bino-like LSP phenomenology in the µνSSM
The pair production cross section of bino-like neutralinos at large hadron colliders is very small, since there is no direct coupling between the bino flavor state and the gauge bosons, and we are assuming that the rest of the spectrum remains decoupled. Binos are produced mainly through virtual Z bosons in the s channel exploiting their small Higgsino flavor composition, or through the t channel interchange of virtual first generation squarks, strongly suppressed by their large masses. Nevertheless, the bino-like LSP can be produced in the decay of other SUSY particles, which although heavier, have a higher production cross sec-tion at the LHC. That is the case when the left sneutrino is the NLSP. After production, the left sneutrinos decay to the bino LSP.
The dominant pair production channels of sleptons at hadron colliders were studied in Refs. [19,20,21,22,23,24]. The main production channels at the LHC are through a virtual Z boson on the s channel for the pair production of scalar and pseudoscalar left sneutrinosνν, a virtual W boson for the production of a left slepton and a (scalar or pseudoscalar) sneutrinolν, and both virtual Z and γ for the pair production of left sleptons ℓl. Note that although the left sneutrino is lighter than its corresponding left slepton as discussed in the Introduction, since the mass separation is always smaller than m W , the phase space suppression makes the decayl →χ 0 + ℓ dominant.
In Fig. 1, we show the production channels as well as the decay of the sneutrino and slepton to produce the bino LSP. The right sleptons can be also a source of bino LSP at the LHC. If their masses are similar to the ones of the left sleptons, an additional diagram as the third one of Fig. 1 will be present. However, the production cross section corresponding to this extra diagram is significantly smaller than for those shown in Fig. 1. Altogether, the number of binos produced after the decay of right sleptons is around a tenth of the number produced through left sneutrinos/sleptons.
If the mass of the bino-like neutralino lies between the Higgs and Z masses, the possible two body decays are to W ℓ and Zν, as shown also in Fig. 1. There we only depicted the decay of each neutralino pair to W and Z, and the leptonic decays of the latter. Note that both neutralinos can also decay to Z or W indistinctly, and that the hadronic decay of the W boson, as well as the invisible decay of one of the Z's, contribute to the signal of leptonic searches, in addition to the diagrams displayed. The bino decays are mediated through the RPV mixing between the bino and neutrinos. Although three body decays involving virtual Higgs boson or other virtual heavier scalars are possible, all of them suffer from kinematic suppression. Thus the relevant diagrams will be the two body decays, and approximate formulas for the partial decay widths are as follows: where U V is the matrix that diagonalizes the mass matrix for the neutral fermions [2,11]. If we neglect the kinematic factors, and sum over the two light families of leptons, Γχ0 →W ℓ /Γχ0 →Zν ≈ 2 cos 2 θ W . Thus the decay to W ℓ will always be at least about a factor of 1.5 larger than the decay to Zν. On the other hand, when the mass of the LSP is close to the masses of the gauge bosons, the difference in mass can have a significant impact on the relative size of the partial widths through those kinematic factors. All in all, for values of the left sneutrino VEVs that produce an acceptable mass scale for neutrinos, and given the small value of M 1 , Eqs. (2) and (3) predict widths 5 × 10 −13 GeV corresponding to cτ < ∼ 0.3 mm. This is short enough to expect most of the decays to happen inside the fiducial region defined by the values of the transverse impact parameter (d P V 0 ) and the longitudinal impact parameter (z P V 0 ) relative to the primary vertex, considered in prompt ATLAS and CMS searches. Subsequently, the W and Z bosons will decay promptly producing leptons, neutrinos or jets. Thus the neutralino could be detectable in events including leptons, jets and/or MET. Note that if the mass of the LSP drops below the mass of the W boson, its decay is still possible and will proceed through three-body decays mediated by off-shell gauge bosons and scalars. The total width will be in this case smaller, due to the reduced phase space, and will lead to leptons and/or quarks originated at displaced vertices. This signal cannot be tested with the usual sparticles searches, but rather with dedicated analysis. The study of this possibility, although interesting, is beyond the scope of this work.
If the mass of the bino-like neutralino is larger than the one of the Higgs boson, the decayχ 0 → hν is also possible, with the dominant diagram mediated by the sneutrino-Higgs mixing. The approximate formula for the corresponding partial decay width is given by: where Z H is the matrix that diagonalizes the mass matrix for the neutral scalars [2,11]. On the one hand, the relative size of the decay of neutralino to Higgs compared to the decay to gauge bosons, is suppressed by the kinematic factors when mχ0 m h . On the other hand, the contribution of the sneutrino-Higgs mixing is not necessarily small compared with the bino-neutrino mixing. As discussed in detail in Ref. [11], this mixing can be enhanced when the mass separation between mν and m h 0 is small, and as a result, in this case the decays of neutralinos to gauge bosons is smaller. Although we take into account the channelχ 0 → hν in our numerical computation, from the perspective of the searches for the neutralino at the LHC using events with leptons, it is not useful since the BR of the Higgs boson to light leptons is small.
3 Electroweak searches at the LHC As shown in the previous section, the production and decay of the sneutrino (and slepton) NLSP when the neutralino is the LSP can produce signals including up to six leptons plus MET. These µνSSM signals can be compared with searches for electroweak SUSY partners at the LHC. The ATLAS analyses [15] and [16] use an integrated luminosity of 36.1 fb −1 of protonproton (pp) collision data delivered by the LHC at a center-of-mass energy of √ s = 13 TeV, to search for events with two or three leptons and four or more leptons, respectively. The former analysis targets direct chargino/neutralino and slepton production in R-parity conserving (RPC) models, whereas the latter includes the study of simplified R-parity violating (RPV) scenarios with a lepton-number violating term [25], targeting direct production of chargino/neutralino, slepton/sneutrino, and gluinos. In the case of sleptons/sneutrinos analyzed in Ref. [16], the result puts a lower bound of 1.06 TeV on their masses assuming a single RPV channel available for the decay of the neutralino LSP. Although this assumption is allowed in simplified trilinear RPV scenarios, it is not in fact possible in the µνSSM where the small BRs of the leptonic decays of the gauge bosons contribute to the computation. We have checked that no constraint on the   [17] and [29].
sneutrino/slepton mass is obtained from these searches in the cases studied in this work. The ATLAS analyses also use a moderate to large amount of MET to discriminate against backgrounds, thus they are not sensitive to a compressed spectrum where this amount is not large. Production cross sections for chargino/neutralino pairs at the LHC [26,27] are much larger than the production cross sections for slepton pairs [28]. Thus the kinematic requirement for a mass separation between sleptons and neutralinos to have enough MET, forces the sleptons in the µνSSM to have masses where the expected number of pairs produced at the LCH is not enough to obtain bounds.
A novel approach for the identification of events coming from the production of sparticles in compressed spectra, where the decay products carry low momenta, is the recursive jigsaw reconstruction (RJR) technique [29,30]. This has made possible to design competitive searches for chargino-neutralino pairs even in scenarios where the mass splitting is close to the mass of the gauge bosons [17]. As we will analyze below, the same analysis can be used to put constraints on the slepton/sneutrino NLSP pair production when the neutralino is the LSP in the µνSSM.
The ATLAS chargino-neutralino search using RJR in Ref. [17] is based on the 13-TeV data with 36.1 fb −1 . All the search channels analyzed require two or three leptons originated from the decay of the gauge bosons plus MET. The different signal regions are optimized to target specific mass splittings between the produced chargino-neutralino and the neutralino LSP, for which the initial state radiation (ISR) signal regions are designed to maximize the sensitive to the case where ∆m = mχ± 1 /χ 0 2 − mχ0 1 is in the range between 100 and 160 GeV. Since the production cross section of the left sneutrino/slepton is much smaller than the chargino-neutralino one, the ISR signal regions have the largest sensitivity to the mass range where the production cross section is not negligible, and mχ0 m Z .
In the ISR signal regions, the events have to fit in the "compressed decay tree" described in Ref. [17]. A signal sparticle system S decays to a set of visible momenta V and invisible momentum I recoils from a jet-radiation system ISR. The preselection criteria require exactly three light leptons (electron or muon), and between one and three non b-tagged jets. The transverse momentum of the leptons must fulfill p ℓ 1/2 T > 25 and p ℓ 3 T > 20 GeV. The selection criteria applied to the events after preselection are given in Table 1.
At first at least one same-flavor opposite sign (SFOS) pair is required, and from the formed SFOS pairs the one with invariant mass closest to M Z should be in the range (75, 105). The remaining lepton is used to construct the W -boson transverse mass, m W T , as follows: where ∆φ is the azimuthal opening angle between the lepton associated with the W boson  and our implementation. and the missing transverse momentum. After that, the following variables are used as discriminant: • p CM T ISR : The magnitude of the vector-summed transverse momenta of the jets assigned to the ISR system.
• p CM T I : The magnitude of the vector-summed transverse momenta of the invisible system.
• p CM T : The magnitude of the vector-summed transverse momenta of the CM system.
• R ISR ≡ p CM I ·p CM T S /p CM T S : Serves as an estimate of mχ0 1 /mχ0 2 /χ ± 1 . This corresponds to the fraction of the momentum of the system that is carried by its invisible system I, with momentum p CM I in the CM frame. As p CM T S grows, it becomes increasingly hard for backgrounds to possess a large value in this ratio, unlike compressed signals where this feature is exhibited [29].
• ∆φ CM ISR,I : The azimuthal opening angle between the ISR system and the invisible system in the CM frame.
Our analysis is implemented using the Madanalysis v5.17 [31,32,33] package, and validated with simulated Monte Carlo (MC) events corresponding to the production of neutralino-chargino pairs in the context of the MSSM decaying to a neutralino LSP and leptonically decaying gauge bosons, with selected masses of mχ± 1 /χ 0 2 = 200 and mχ0 1 = 100 GeV. Ten thousand events are generated using MadGraph5_aMC@NLO v2.6.3.2 [34] at leading order (LO) of perturbative QCD simulating the production of the described process with the standard model files for the MSSM. Events are then passed for showering and hadronization to PYTHIA v8.201 [35] using the A14 tune [36], and then to DELPHES v3.3.3 [37] for detector simulation. The results of the events selection are compared with the cutflow table provided by the ATLAS collaboration, as shown in Table 2. The first column reproduces the unweighted yields from the ATLAS analysis, the second one presents the unweighted yields from our implementation, and the last one the same yields but normalized to the number of events in the first column. As can be seen from the table, the numbers agree within a 20% error, thus we use this implementation to obtain mχ0 120 GeV mν 125 GeV ml 145 GeV  Table 3: Benchmark point of the µνSSM in Sℓ3_ISR. In the third row the efficiency ǫ passing the selection requirements is shown.
the efficiency map of the ATLAS search for different masses of sneutrinos/sleptons and neutralinos.
The sneutrino/slepton pair production is simulated in a similar way, but with model files generated using a suitable modified version of SARAH code [38,39,40], and the spectrum is generated using SPheno v3.3.6 code [41,42]. Cross sections are calculated at NLO+NLL using Resummino v2.01 [43,44,45,46,27]. For each selected point, ten thousand MC events are generated as explained and passed through the described selection criteria. The results are then compared with the expected (S 95 exp ) and observed (S 95 obs ) upper limits obtained in the ATLAS search.
The processes described in Fig. 1 show the highest yield of the possible combinations of neutralino decays, when the mass separation between slepton/sneutrino and neutralino is not large enough to make the first produced leptons to contribute, which would be excluded from the ATLAS searches. Other possibilities, like W decaying hadronically or both neutralinos decaying to Z bosons, with only one of them decaying leptonically, contribute also to the signal, but with smaller yields. The possibility of both neutralinos decaying to Z bosons, with the latter decaying to leptons, produce a negligible contribution caused both by the small corresponding BR and the excess of predicted signal leptons.
The points analyzed in the µνSSM parameter space show all a worse efficiency passing the selection requirements of SR2ℓ_ISR in comparison with SR3ℓ_ISR. Thus the results discussed in the next section are derived from the limits corresponding to SR3ℓ_ISR.

Results
By using the method described in the previous section, we now calculate the current and potential limits on the two-dimensional parameter space mν − mχ0 of the µνSSM from the searches with the 36.1 fb −1 ATLAS result [17], and discuss the prospects for the 100 and 300 fb −1 searches.
We have assumed that the three families of left sneutrinos and sleptons are degenerated and therefore all of them contribute to the signal. Our result in the mass regions considered is that no points can be excluded from current data. It is also worth noting that the observed limit in the 3ℓ_ISR signal region (S 95 obs = 15.3) is significantly larger than the expected limit (S 95 exp = 6.9 +3.1 −2.2 ), due to a 3.02 sigma excess [17]. Points of our parameter space in the region mχ0 ∈ (110, 120) and mν ∈ (120, 140) predict a number of events similar to the observed excess. As an example, Table 3 shows a benchmark point which predicts 5.1 events above  Figure 2: Regions of the µνSSM that will be probed by the signal with three leptons plus MET from neutrinos discussed in the text in the two-dimensional parameter space mν − mχ0, for the 13-TeV search with an integrated luminosity of 100 fb −1 (green) and 300 fb −1 (yellow).
background in Sℓ3_ISR. If the observed local excess were due to a statistical fluctuation, and the observed upper limit converged to the expected limit, we can easily infer the potential bounds on the parameter space of the sneutrino-neutralino mass in the µνSSM. For 100 and 300 fb −1 to be reached at the end of Run 2, we just have to rescale the limits by 100/36.1 and 300/36.1, respectively. The result is shown in Fig. 2. In this figure, the solid black line shows the points where the sneutrino and neutralino are degenerated in mass. The green area enclose the excluded region for 100 fb −1 if no excess is observed, and the yellow area shows the same for 300 fb −1 . The prospects show a potential exclusion of sneutrino masses up to 160 and 185 GeV for 100 and 300 fb −1 , respectively. We can see that this region extends up to the solid line, reflecting the fact that the search will be fully sensitive to the degenerated scenario. For a given sneutrino mass, smaller value of the neutralino mass does not give rise to a worse sensitivity until the kinematic functions in Eq. (3) make the product BR(χ 0 → Zν) × BR(χ 0 → W ℓ) too small and the search becomes ineffective. On the other hand, for a given neutralino mass the larger the value of the sneutrino mass the smaller the production cross section becomes, limiting the exclusion scope. Notice also that in the lower-right corner the limits are weaker due to the mass separation between sneutrino and neutralino, as a consequence of the increased energy of the produced leptons in the decay of sleptons.

Conclusions and outlook
We have analyze a multi-lepton signal plus missing transverse energy from neutrinos expected at the LHC for a bino-like neutralino LSP, in the framework of the µνSSM. Assuming that the left sneutrino is the NLSP, together with left sleptons which are close in mass they decay to binos after pair production at pp collisions. Subsequently, the binos decay promptly to W ℓ or Zν via RPV couplings. All in all, these signals include up to six leptons plus MET. To evaluate the prospects of this search strategy, we have recast the result of the ATLAS chargino-neutralino search using RJR, based on the 13-TeV data with 36.1 fb −1 [17]. This analysis is sensitive to three charged leptons of the two light families produced by a compressed spectrum of electroweak superpartners. This is also our situation, because the reduced cross section of the sneutrino/slepton production in comparison with the chargino-neutralino one, limits the sensitivity of the searches to small sneutrino/slepton masses. Although in these mass regions, no points of the parameter space of the µνSSM can be excluded, the prospects show a potential exclusion of sneutrino masses up to 160 and 185 GeV for 100 and 300 fb −1 , respectively.
These limits can be complemented in the future by searches for displaced decays of the neutralino when its mass is below the threshold of the W mass. In this case, three-body decays mediated by off-shell gauge bosons and scalars will produced a small total width due to the reduced phase space, leading to signals with lepton and/or quarks originated at displaced vertices. Dedicated studies will also be necessary to search for events with high multiplicities of leptons, when the mass separation between sneutrino and neutralino is not small. On the other hand, in this paper, we have focused on the bino-like LSP. Another interesting possibility would be to study the case of a wino-like LSP. The different couplings involved as well as new RPV decays could modify the sensitivity of the searches to the new compressed spectrum. We plan to cover this possibility in a forthcoming publication [47].
Let us finally mention a by-product of our analysis in the region of bino (sneutrino) mass 110 − 120 (120 − 140) GeV, where we find that a tri-lepton signal is compatible with the local excess reported by ATLAS.