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CMS kinematic edge from s-bottoms

We present two scenarios in the Minimal Supersymmetric Extension of the Standard Model (MSSM) that can lead to an explanation of the excess in the invariant mass distribution of two opposite charged, same flavor leptons, and the corresponding edge at an energy of about 78 GeV, recently reported by the CMS collaboration. In both scenarios, s-bottoms are pair produced, and decay to neutralinos and a b-jet. The heavier neutralinos further decay to a pair of leptons and the lightest neutralino through on-shell s-leptons or off-shell neutral gauge bosons. These scenarios are consistent with the current limits on the s-bottoms, neutralinos, and s-leptons. Assuming that the lightest neutralino is stable we discuss the predicted relic density as well as the implications for Dark Matter direct detection. We show that consistency between the predicted and the measured value of the muon anomalous magnetic moment may be obtained in both scenarios. Finally, we define the signatures of these models that may be tested at the 13 TeV run of the LHC.


I. INTRODUCTION
After the Higgs discovery [1,2] hypothesis to data in the range of 20 GeV < m ll < 300 GeV. The best fit to the SFOS event distribution is obtained for an edge at an energy of 78.7± 1. 4 GeV. An alternative search is done by a counting experiment, without any assumption of the signal and background shape. The counting experiment is performed in the mass range of 20 < m ll < 70 GeV, and an excess of 130 +48 −49 events are seen in the central region, corresponding to a local significance of 2.6 σ.
In this article, we shall interpret the presence of this edge as a signature of the production of third generation supersymmetric particles at the LHC 1 . Supersymmetry is an attractive framework [5][6][7], that leads to the unification of couplings at high scales and provides Dark Matter candidates in terms of the superpartners of the neutral Higgs and gauge bosons. Moreover, for supersymmetric particle masses of the order of the TeV scale, low energy supersymmetry leads to the radiative breaking of the electroweak symmetry with a light, 1 During the completion of this work, an alternative explanation of this kinematic edge in terms of first and second generation s-quarks together with light s-leptons was presented [4]. mostly SM-like Higgs boson with a mass which may be consistent with the value observed at the LHC [8][9][10][11][12][13]. It has been pointed out that the study of kinematic edges can be important for the detection of light supersymmetric particles (for recent work, see [14,15]), and several kinematic variables have been proposed to distinguish new physics from background. In this article, we shall focus on the edge in the m ll distribution.
The kinematic edge can be explained by the presence of a light s-bottom 2 . The s-bottoms are pair produced in the detector, and one of the s-bottoms decays to a b-jet and the LSP. The other one decays to a heavier neutralino and a b-jet, and the heavier neutralino subsequently decays to the lightest neutralino and a pair of SFOS leptons through a s-lepton or an offshell Z, depending on the mass of the s-leptons and the composition of the neutralinos.
We therefore defined two scenarios. In scenario A, the s-bottom decays through the decay chain ofb 1 → bχ 0 2 → bll → bl + l −χ0 1 . In scenario B, instead, the s-bottom decay features the cascade decay ofb 1 → bχ 0 2,3 → bZ * χ0 1 → bl + l −χ0 1 . Thus, the two s-bottoms together give 2 b-jets, a pair of SFOS leptons and missing energy. Under these conditions, the m ll distribution will feature a kinematic edge.
This article is organized as follows : In section II, we will analyze the two possible scenarios in more detail, and study the resultant contributions to the kinematic edge. We also discuss the implications of these scenarios for Dark Matter and the muon anomalous magnetic moment. In section III we consider possible constraints on both scenarios from the LHC. We reserve section IV for our conclusions.

II. S-BOTTOM CONTRIBUTIONS TO THE DILEPTON KINEMATIC EDGE
Scenarios with pair produced s-bottoms are able to explain the kinematic edge. The spectra in Fig 1 and Fig 3 are examples of possible scenarios, where the particle masses necessary to explain the data in each of these scenarios are presented in Table I. 2 The explanation of the edge events with via the decay of s-bottoms is consistent with the benchmarks proposed by CMS in Ref [3]. However, the CMS benchmarks, based on the heavier neutralinos decay to an off-shell Z and the lightest neutralino, are in tension with the ATLAS limits on b-jet + E miss T channel.

A. Scenario A
The spectrum in Fig 1 features a s-bottom with a mass around 390 GeV and a light s-lepton. The s-bottom can decay to aχ 0 2 and a b-jet. Theχ 0 2 , with a mass around 340 GeV can decay to two leptons and aχ 0 1 through a right-handed s-electron or a s-muon with masses mẽ R = mμ R = ml around 300 GeV. The mass of the LSP is chosen to be 260 GeV.
Those two leptons will have same flavor and opposite signs, and the edge of the invariant mass of the dilepton will be at which is about 80 GeV in this spectrum. In Eq.
(1) ml is the s-lepton mass and mχ0 1 and mχ0 2 are the lightest and second lightest neutralino masses, respectively. The competing decay channel of the s-bottom is a b-jet and the LSP. Therefore, the pair produced s-bottoms, with one s-bottom decaying to a b-jet and the LSP, and the other decaying through the decay chain discussed above, will contribute to the SFOS dilepton + ≥2 jets + missing energy channel with a kinematic edge around 80 GeV. Also, since the s-bottom decays to either a b-jet and missing energy, or a b-jet, two leptons and missing energy, there will be no significant contributions to the 2b-jets plus 2 jets channel from s-bottom pair production. The mass parameters in scenario A were chosen in order to give a sufficiently large cross-section without being in conflict with other experimental constraints, which will be  discussed in more details in section III. We choose mb 1 around 390 GeV so that it has a sizable production cross section. The mass of the lightest neutralino is chosen to be sufficiently low to allow the existence of an edge, but not low enough to lead to a conflict with searches for pair production ofb 1 in the 2 b-jets plus E miss T channel. The mass of the second lightest neutralino is chosen to lead to the required edge while avoiding a degenerate spectrum which will give too soft b-jets. For ab 1 of 390 GeV a decay branching ratio BF (b 1 → bχ 0 1 ) = 1, the bound on the LSP mass is 260 GeV, and in order satisfy the above requirements we chose theχ 0 1 mass to be close to this value, which is consistent with the ATLAS experimental bounds due to the fact that in scenario A BF (b 1 →χ 0 1 ) < 1. In order to induce a large excess of events in the 2 b-jets plus SFOS leptons channel without generating a similarly large number of events in the 2-b-jets plus four leptons channel, we require that BF (b 1 → bχ 0 2 ) BF (b 1 → bχ 0 1 ). A simple way of satisfying this requirement is to assume thatb 1 is mostly right-handed,χ 0 2 is mostly a Wino andχ 0 1 is mostly a Bino. χ ± 1 is wino like. Observe that the chargino contribution to the sbottom decay branching fraction, BF(b 1 → t * χ± 1 ), is highly suppressed due to phase space factors.

The parameters are further constrained by the requirement of obtaining a proper Dark
Matter relic density and a value of the anomalous magnetic moment of the muon consistent with experiment. To obtain the right relic density, we can either mix the bino-like LSP with Higgsinos, so that the LSP can annihilate more efficiently through the Higgsino components, or approach the so-called A-funnel region, where mχ0 Higgs mass, so the LSP can annihilate efficiently through the resonant mediation of the heavy Higgs bosons. For a neutralino mass mχ0 1 260 GeV, the A-funnel region is excluded by the CMS Higgs to τ τ searches [16] for tan β > 20. Then, for large tan β the right relic density requires a small Higgsino mass parameter µ to get a large enough Higgsino component. A small µ and a large tan β make the Higgsino components inχ 0 2 too large to give a BF(b 1 →χ 0 2 b) small enough to be consistent with the 4 lepton + missing energy searches. That means that the right relic density and a small BF(b 1 →χ 0 1 b) together favor moderate values of tan β.
At the same time, to get the right muon anomalous magnetic moment, a larger tan β is favored. So if we put the restriction on the relic density, BF(b 1 →χ 0 1 b) and muon g-2 together, a sizable, but not very large value of tan β is favored. When tan β = 25, as in scenario A, the bound on m A from the CMS Higgs to τ τ searches is about 600 GeV. Then, values of µ around 500 GeV are necessary to give the right relic density. Also, BF(b 1 →χ 0 1 b) is 7.4% for tan β = 25 and µ = 500 GeV, which is consistent with the constraints coming from 4 lepton searches, which we are going to discuss in detail in section III. Then we choose the mass of the right-handed sleptons to be 320 GeV to give the m ll edge at 80 GeV according to Eq (1). In addition, we chose the mass of the left-handed s-leptons to be around 400 GeV to give a larger contribution to the muon anomalous magnetic moment, which in this scenario is of about ∆a µ = 2 ×10 −9 . This is consistent with the experiment value ∆a µ = (2.87 ± 0.8)× 10 −9 [31][32][33][34][35][36][37][38][39]. Smaller values of µ would further enhance the value of ∆a µ , but they will also lead to an enhancement of the BF(b 1 → bχ 0 2 ) and therefore we will not consider them in this analysis.
We performed a collider study of s-bottom pair production using the spectrums shown in Fig 1. We generated the events with Isajet [17], and pass the event to Pythia [18] and PGS [19] for showering and the detector simulation and follow the CMS event selection described in section I. The production cross section was scaled to the Prospino NLO results [20].   Table I.
Although we have not attempted to find the optimal values of the supersymmetric particle masses consistent with the observed signal, we have analyzed the effects of possible variations of these parameters. A s-bottom lighter than 390 GeV will have a larger production rate, but the generation of the kinematic edge becomes more difficult due to the fact that for a BF(b 1 →χ 0 1 b) 1 the experimental bounds on the LSP mass for s-bottoms with masses between 300 GeV and 400 GeV (which will be discussed in more detail in the next section) do not change much with the mass of s-bottoms. That means, for a lighter s-bottom, the allowed mass for the LSP would only be slightly smaller than 260 GeV. Therefore, in order to reproduce the edge the heavier neutralino mass should be kept at approximately the same value and the BF(b 1 → bχ 0 2 ) would be smaller than in the example we discussed above. For instance, for a s-bottom around 385 GeV, the cross section is increased to 0.45 pb while 2 ) is reduced to 0.064. Assuming the kinematic properties do not change in a significant way, the number of events expected would be rescaled by the ratios of the corresponding cross sections and branching ratios, implying about 103 events in the central region. Hence, a small reduction of the signal would be obtained.
If the mass of s-bottom is larger than what we discussed in the scenario A example, the s-bottoms pairs will be produced at a lower rate. For a 400 GeV s-bottom, for instance, the production cross section drops to 0.36 pb. The number of SFOS events may be recovered by increasing BF(b 1 → bχ 0 2 ) (for instance increasing slightly the Higgsino composition ofχ 0 2 or changing the masses ofχ 0 2 and of the LSP), a possibility which is however constrained by the searches in the 4 lepton channel. A more detailed collider study would be needed to estimate the largest BF(b 1 → bχ 0 2 ) allowed by the 4 lepton searches, which is beyond the discussion of this article, butb 1 masses above 400 GeV are significantly constrained by this requirement.
As we explained above, the value of tan β was fixed from the requirement of consistency with Dark Matter and muon anomalous magnetic moment constraints. The predicted Dark Matter relic density in Scenario A, for m A 600 GeV, is Ωh 2 0.11, which is consistent with the cosmological observations Ωh 2 =0.1198 ±0.0026 [40]. The value of tan β may be lower, implying a lower bound on the CP-odd Higgs mass m A . Therefore, we can go to the A-funnel region (resonant annihilation through the CP-odd Higgs) to get the right relic density and µ can be chosen to the value that gives a BF(b 1 →χ 0 1 + b) large enough to contribute about 130 event in the edge and small enough to be consistent with the 4 lepton searches. However, since the main contribution to the muon g − 2 in the MSSM is amplified by tan β, the value of ∆a µ would be smaller than the one obtained in scenario A. In the region where tan β is large, instead, the Higgs to τ τ searches prevents m A to approach the A-Funnel region. At the same time, a large tan β meansχ 0 2 must be very wino-like so that the BF(b 1 → bχ 0 2 ) can be small enough to not let the s-bottom signals show up in the 4 lepton channel. That means µ is also required to be large in this region. Then the LSP is Bino-like, and away from the A-funnel region, so the relic density is larger than the observed value. For instance, for tan β = 50, and m A = 1 TeV, the predicted Dark Matter relic density in Scenario A is Ωh 2 0.8, which is higher than the cosmological observations 3 . In general, for values of tan β significantly larger or smaller than the one chosen in scenario A there will be tension between the requirement of obtaining a value ∆a µ consistent with the observed experimental value and the obtention of the proper relic density.
The spin-independent cross section of the LSP scattering off a proton for Scenario A is σ p SI =3.6×10 −45 cm 2 , which is consistent with LUX [42] and will be probed by Xenon1T and other future experiments [43]. If the sign of µ × M 1 is flipped, but the rest of the parameters are kept as defined in scenario A (with only small variations to obtain the proper relic density) then σ p SI is reduced to about 3 × 10 −47 cm 2 due to the destructive interference between the contribution from the SM-like Higgs and the heavy CP-even Higgs [44][45][46][47].
Xenon1T might be able to probe this scenario. In order to keep a positive contribution to

B. Scenario B
An alternative scenario will be that the heavier neutralino decays to aχ 0 1 and an offshell Z, then the Z * decays to a l + l − pair. A spectrum that could be responsible for the CMS kinematic edge is shown in Fig 3. Contrary to what happens in scenario A, since the branching fraction of a Z * → l + l − is about 6 %, (summed over electrons and muons), a sizable BF (b 1 →χ 0 2 b) is needed to get the number of events around 100 without lowering theb 1 mass to the current excluded region. To fulfill that requirement, we haveχ 0 2 andχ 0 3 Higgsino-like, and tan β large to enhance theb 1 Hb coupling. Since the BF(b 1 → bχ 0 1 ) is significantly lower than one, the mass of theb 1 could be lower without leading to a conflict 3 The over-abundance problem can be solved, for instance, by introducing a scalar field φ, which dominates the energy density of the early universe before the nucleosynthesis era [41]. For example, for a number of neutralinos produced per φ decay and per 100 TeV mass of φ, η ≤ 10 −6 , and a reheating temperate of about 1 GeV an observable relic density consistent with experiment may be obtained. In this scenario, the s-bottom pair production will also contribute to the ≥2 jets + ≥2 b-jet channel. There is a potentially large signal in this channel coming from s-bottom pair production, and in the next section we shall discuss the constraints coming from it. Let us only emphasize here that the jets coming from the heavier neutralino decays tend to be soft and there are over-whelming backgrounds associated, for instance, with tt production, so that the scenario B is still consistent with this constraint. In scenario B, the production cross section is σ pp →b 1b1 = 1.14 pb. At the 8 TeV

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that was chosen to be 78 GeV and 76 GeV for the third and second lightest neutralino in this scenario, respectively.
These edges can be seen in the invariant mass distribution presented in Fig 4. At the current luminosity, the mass splitting between the two Higgsinos mχ0 3 − mχ0 2 ∼ 2 GeV is sufficiently small to not be distinguishable in this distribution, and a single edge appears at about 78 GeV, consistent with the CMS data.  Fig. 3 and Table I.
The number of events obtained in the central region in this scenario is lower by about one standard deviation than the central value reported by CMS. This amount may be increased by selecting a larger value of BF(b 1 → bχ 0 2 ,χ 0 3 ) or a largerb 1 production cross section, associated with a lowerb 1 mass. However, any increase on these quantities will also lead to an increase of the number of events in the ≥2 jets, ≥2 b-jets + E miss T channel (as well as more events in the four lepton + E miss T channel). As we shall discuss in section III, there is already a slight tension between the predicted number of events in scenario B and the ones observed by the LHC experiments. Hence, it is in general difficult to obtain a significantly larger number of SFOS dilepton in this scenario.
Moreover, for a lighter s-bottom, the production cross section increases but BF(b 1 → bχ 0 2,3 ) decreases. For instance, for mb 1 =320 GeV, BF(b 1 → bχ 0 2,3 ) ∼ 0.35 and the cross section is 1.37 pb, which rescaling the previous result by the ratio of the corresponding production cross sections and branching ratios leads to about 88 events. However, the bottom quarks coming from theb 1 decay are softer implying that the actual number of events in the edge remains approximately the same as for mb 1 = 330 GeV. This could be improved by lowering the overall neutralino mass scale, but then the constraints from s-bottom direct detection in the 2 b-jets + E miss T channel become stronger, making an increase of events difficult (beyond the problems in the ≥2jets, ≥ 2 b-jets + E miss T channel mentioned above). Similar considerations apply for a heavier s-bottom. Although in such a case the production cross section decreases, a larger BF(b 1 → bχ 0 2,3 ) is expected, together with harder b-jets and missing energy. Therefore, there may be some space with a heavier s-bottom to obtain roughly 100 events in the central region, despite the production cross section being smaller. Again, one of the main constraints in the region with a heavier s-bottom is from the ≥ 2-jet ≥ 2 b-jet channel, with number of events in this channel scaled up by a factor of BF(b 1 → bχ 0 2,3 ) 2 . We will come back to these issues in the next section. This scenario leads to a proper anomalous magnetic moment of the muon for natural values of the s-lepton and Wino masses. In order to accommodate the muon g − 2 result, the s-leptons should not be too heavy. For instance, for ml R = ml L = 500 GeV, M 2 600 GeV and heavy left-handed sleptons ∆a µ = 2.7 ×10 −9 , which is consistent with the experiment value ∆a µ = (2.87 ± 0.8)× 10 −9 .
Contrary to what happens in scenario A, the presence of light Higgsinos and Binos in the spectrum makes it possible to obtain a large enough Dark Matter annihilation cross section to ensure consistency with the observed relic density without the need of any fine tuning of parameters. The predicted Dark Matter relic density for Scenario B is Ωh 2 0.11, assuming the CP-odd Higgs is heavy, m A 1.5 TeV, which is consistent with experiments. The spinindependent cross section of the LSP scattering off a proton is σ p SI =2.7×10 −44 cm 2 , which is consistent with LUX [42] and will be probed by Xenon1T and other future experiments [43].
As discussed above, if the sign of µ × M 1 is flipped, then due to the destructive interference between the light and heavy CP-even Higgs bosons, σ p SI is reduced to ∼ 1 × 10 −46 cm 2 and Xenon1T may be able to probe this scenario. Provided the sign of µ × M 2 remains positive, the contribution to ∆a µ is reduced by about 10% in this case.

SEARCHES
As we discussed in the previous section, there are several constraints on the presence of light s-bottoms and neutralinos coming from both ATLAS and CMS. The constraints from direct searches for s-bottoms decaying into bottom quarks and missing energy [21,22] apply here. For scenario A, the direct limit for s-bottoms shows that, for a mass of the LSP of about 260 GeV, and a BF(b 1 → bχ 0 1 ) = 1, s-bottoms with masses from 390 GeV to 620 GeV are excluded by ATLAS, while CMS has a weaker limit. Due to the smaller BF(b 1 → bχ 0 1 ), these bounds are weakened for this scenario. In particular, as we stressed in the previous section, since we chose masses close to the ATLAS limit for a BF(b 1 → bχ 0 1 ) = 1, the mass parameters in scenario A are beyond the current ATLAS limit.  [24]. For loose cuts the number of observed events is consistent with the ones associated with s-bottom production. For tight cuts, the number of observed events is small but it falls short of the ones expected in the SM. Therefore, there is a small tension with the numbers predicted from s-bottom production in scenario B, which however are still much smaller than background. Therefore, if the edge is confirmed, we expect this channel to provide a relevant test of scenario B at the next run of the LHC.
Also, the limits from chargino and neutralino searches should be taken into consideration [25,26]. The limits are quite weak for a LSP as heavy as 200 GeV, and our choice of parameters in section II is well allowed by both experiments. Both scenarios contribute to the single lepton channel, but both experiments require more than 3 hard jets in the single lepton search [27][28][29][30] and therefore do not set any constraints in our scenarios from this channel. Scenario A also gets constrained by direct s-lepton searches, but the current limits from direct s-lepton searches do not cover the LSP mass larger than 100 GeV [25,26] assuming the lighter s-lepton is right-handed.

IV. CONCLUSIONS
To summarize, we have shown two possible scenarios with s-bottoms with masses around 300 to 400 GeV to explain the recent CMS excess of events in the SFOS dilepton and missing energy channel, leading to an edge with a dilepton invariant mass m ll 78 GeV.
In both scenarios, one of the pair produced s-bottoms decays to a b-jet and the LSP, and the other decays to a b-jet and a heavier neutralino, which further decays to the LSP and a pair of SFOS lepton through an on-shell s-lepton or an off-shell Z, respectively. Both For simplicity, we have assumed s-taus to be heavy in both scenarios. It would be natural to expect the presence of light s-taus in scenario A. In the presence of a light s-tau, we would expect 2b-jets+2 taus + E miss T as well as a small amount of 2-bjets + 2 taus + SFOS leptons +E miss T and 2 b-jets, 4 taus and E miss T events at the LHC. While we don't expect that currently these channels set any additional constraint on this scenario, they must be studied and in the presence of light s-taus they may provide additional ways of testing this scenario at the LHC. A light s-tau would also induce a new Dark Matter annihilation channel and, depending on its mass, could change the discussion we had on this issue, but the discussion on muon anomalous magnetic moment would stay the same (for a recent study on light stau contributions to Dark Matter annihilation, see for instance Ref. [48]).
These scenarios should be probed by a similar analysis of the 8 TeV LHC data from ATLAS. If the existence of the edge is confirmed, further analyses in the 2 b-jets plus E miss T channel, the 4 lepton plus E miss T channel, and the ≥ 2-bjets ≥ 2jets E miss T channel in the next run of the LHC will be able to further probe these scenarios.