Search for supersymmetric partners of electrons and muons in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search for direct production of the supersymmetric (SUSY) partners of electrons or muons is presented in final states with two opposite-charge, same-flavor leptons (electrons and muons), no jets, and large missing transverse momentum. The data sample corresponds to an integrated luminosity of 35.9 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} =$ 13 TeV, collected with the CMS detector at the LHC in 2016. The search uses the $m_{\mathrm{T}2}$ variable, which generalizes the transverse mass for systems with two invisible objects and provides a discrimination against standard model backgrounds containing W bosons. The observed yields are consistent with the expectations from the standard model. The search is interpreted in the context of simplified SUSY models and probes slepton masses up to approximately 290, 400, and 450 GeV, assuming right-handed only, left-handed only, and both right- and left-handed sleptons (mass degenerate selectrons and smuons), and a massless lightest supersymmetric particle. Limits are also set on selectrons and smuons separately. These limits show an improvement on the existing limits of approximately 150 GeV.


Introduction
The standard model (SM) of particle physics provides a description of the fundamental particles and their interactions, and its predictions have been confirmed experimentally with increasing precision over the last several decades. Supersymmetry (SUSY) [1][2][3][4][5][6][7][8], one of the most promising extensions of the SM, addresses several open questions for which the SM has no answer, such as the hierarchy problem and the origin of dark matter. The theory postulates a new fundamental symmetry that assigns to each SM particle a SUSY partner whose spin differs by one half, causing the SUSY partner of an SM fermion (boson) to be a boson (fermion). In addition to stabilizing the Higgs boson (H) mass via cancellations between quantum loop corrections including the top quark and its superpartner, SUSY provides a natural dark matter candidate, if R-parity [9] is conserved, in the form of the lightest SUSY particle (LSP), which is assumed to be massive and stable.
SUSY particles (sparticles) that are colored, the squarks and gluinos, are produced via the strong interaction with significantly larger cross sections than colorless sparticles of equal masses. However, if the squarks and gluinos are too heavy to be produced at the Large Hadron Collider (LHC), the direct production of colorless sparticles, such as the electroweak superpartners (charginos ( χ ± 1 ), neutralinos ( χ 0 2 ), and sleptons ( )), would be the dominant observable SUSY process. Supersymmetric models predict charged sleptons ( e L , µ L , τ L , e R , µ R , τ R ), the superpartners of the charged left-handed and right-handed SM leptons, which can be produced at proton-proton (pp) colliders in direct electroweak pair production. At sufficiently heavy slepton masses, the sleptons undergo a two-body decay into one of the heavier neutralinos or a chargino, while direct decays to a neutralino LSP are favored for light slepton masses. This Letter presents a search for directly produced selectrons and smuons ( e L , µ L , e R , µ R ), under the assumption of direct decays → χ 0 1 with 100% branching ratio, as sketched in Fig. 1. The final state contains little or no hadronic activity and provides a clean signature composed of two oppositecharge (OC), same-flavor (SF) leptons (dielectron or dimuon pairs) and large missing transverse momentum (p miss T ) from the two LSPs that escape detection. The main SM backgrounds resulting in two OC SF leptons and no reconstructed jets are pp → tt (if both jets from the top decays are out of acceptance) and pp → WW → 2 2ν, both of which involve W bosons that decay into an electron or a muon with equal probability, resulting in the same number of dielectron and dimuon events as electron-muon events (different flavor, DF). This flavor symmetry is used in the analysis to predict the number of background SF leptons based on the number of DF leptons in the signal region (SR) in data, after correcting for differences in trigger and lepton reconstruction efficiencies. The Drell-Yan (DY) process would also be a main background in the analysis, but is greatly suppressed by the SR requirements. The pp → ZZ → 2 2ν and pp → WZ → 3 ν processes can also result in two OC SF leptons. These contributions are taken from Monte Carlo (MC) simulation after comparing data and simulation predictions in control regions (CR).
The data set of proton-proton collisions used for this search was collected in 2016 with the CMS detector at a center-of-mass energy of √ s = 13 TeV, and corresponds to an integrated luminosity of 35.9 fb −1 . Interpretations of the search results are given in terms of simplified SUSY model spectra [10,11]. Searches for SUSY in these final states were performed previously by the ATLAS [12] and CMS [13] Collaborations at √ s = 8 TeV.
The gg → ZZ process is generated at LO with MCFM 7.0 [30], and all other diboson production processes [31,32], and tt [33] and the production of single top quark associated with a W boson [34], are generated at NLO with no additional partons with POWHEG v2. Simulated samples of DY processes are generated with MADGRAPH5 aMC@NLO 2.3.3 program [15] to leading order precision with up to four additional partons in the matrix element calculation. Simulated VVV and ttV (V = W, Z) events are simulated with the same generator but at NLO precision. The NNPDF3.0 [35] LO (NLO) parton distribution functions (PDFs) are used for the samples generated at LO (NLO). The matrix element calculations performed with these generators are interfaced with PYTHIA [36], including the CUETP8M1 tune [37,38] for the simulation of parton showering and hadronization. Double counting of partons generated with MADGRAPH5 aMC@NLO and PYTHIA is removed using the MLM [39] and FXFX [40] matching schemes in the LO and NLO samples, respectively. The detector response is simulated with a GEANT4 model [41] of the CMS detector. The simulation of new-physics signals is performed using the MADGRAPH5 aMC@NLO 2.2.2 program at LO precision, with up to two additional partons in the matrix element calculation. Events are then interfaced with PYTHIA for fragmentation and hadronization and simulated using the CMS fast simulation package [42]. The slepton decays are also simulated with PYTHIA. Multiple pp interactions, also known as pileup, are superimposed on the hard collision, and the simulated samples are reweighed in such a way that the number of collisions per bunch crossing accurately reflects the distribution observed in data. Corrections are applied to the simulated samples to account for differences between simulation and data in the trigger and reconstruction efficiencies.

Object selection
The particle-flow (PF) algorithm [43] reconstructs and identifies particle candidates in the event, referred to as PF objects. To select collision events we require at least one reconstructed vertex, and the one with the largest value of summed physics object p 2 T is taken to be the primary pp interaction vertex. The physics objects used for the primary vertex selection are the objects returned by a jet finding algorithm [44,45] applied to all charged tracks associated with the vertex, plus the corresponding associated p miss T . Its vector p miss T is defined as the projection onto the plane perpendicular to the beam axis of the negative vector sum of the momenta of all reconstructed PF objects in the event, and its magnitude is p miss T . Electrons are reconstructed by associating tracks with ECAL clusters. They are identified using a multivariate approach based on information on ECAL cluster shapes, track reconstruction quality, and the matching between the track and the ECAL cluster [46]. Electrons coming from reconstructed photon conversions are rejected. Muons are reconstructed from tracks in the muon system associated with tracks in the tracker. The identification uses the quality of the track fit and the number of associated hits in the tracking detectors [47]. For both electrons and muons, the impact parameter with respect to the primary vertex is required to be within 0.5 mm in the transverse plane and less than 1 mm along the beam direction. A lepton isolation variable is defined as the scalar p T sum of all PF objects in a cone around the lepton, excluding identified electrons or muons. Additional pp interactions in the same or nearby bunch crossings (pileup) can be mitigated by only considering charged PF objects that are compatible with the primary vertex and the average expected pileup contribution is subtracted from the neutral component of the isolation. The isolation sum is required to be smaller than 10 (20)% of the electron (muon) p T . A shrinking cone-size with increasing p T is chosen that ensures high efficiency for leptons from Lorentz-boosted boson decays [48]. This varying cone size is chosen as the following ∆R = √ (∆φ) 2 + (∆η) 2 = 0.2 for p T < 50 GeV, = 10 GeV/p T for 50 < p T < 200 GeV, and 0.05 for p T > 200 GeV.
Isolated charged particle tracks identified by the PF algorithm are selected with a looser criteria than the leptons defined above, and are used as a veto on the presence of additional charged leptons from vector boson decays. Isolation is evaluated by summing the p T of all charged PF objects within a cone of ∆R = 0.3 and with the longitudinal impact parameter |∆z| < 0.1 cm relative to the primary vertex. PF objects identified as charged hadrons (electrons or muons) are required to have p T > 10 (5) GeV and an isolation value less than 10 (20)% of the object p T .
Jets are clustered from PF objects, excluding charged hadrons not associated with the primary vertex that are assumed to be the result of pileup interactions, using the anti-k T clustering algorithm [44] with a distance parameter of 0.4 as implemented in the FASTJET package [45,49]. Jets are required to have |η| < 2.4 and p T > 35 GeV, where the p T is corrected for nonuniform detector response and pileup effects [50,51]. Jets reconstructed within ∆R < 0.4 of any of the selected leptons are removed from the event. Corrections to the jet energy are propagated to p miss T using the procedure developed in Ref. [50]. At least two such jets are selected for CRs of this analysis, and a veto of jets with p T above 25 GeV is applied in the SR.
Events are selected for the SR by requiring two OC SF leptons (e ± e ∓ or µ ± µ ∓ ) with p T > 50 (20) GeV for the highest (next-to-highest) p T lepton and |η| < 2.4 for both leptons. For the background prediction methods a sample of lepton pairs are selected, with a p T threshold of 25 (20) GeV for the leading (subleading) lepton. The highest minimum p T value is chosen because it efficiently suppresses backgrounds while maintaining signal acceptance efficiency. Any additional leptons, identified with the looser requirement that the isolation sum should be less than 40% of the lepton p T , are vetoed. Leptons must be spatially separated by ∆R > 0.1 to avoid reconstruction efficiency differences between electrons and muons in events with collinear leptons. All leptons in the transition region between the barrel and endcap of the ECAL, 1.4 < |η| < 1.6, are rejected to ensure similar acceptance for electrons and muons. The same lepton selection criteria are used for a control sample of OC DF pairs, e ± µ ∓ . The selection requirements have been chosen in order to maximize the lepton selection efficiency while maintaining a similarity between electron and muon efficiencies.

Search strategy
The slepton SRs are designed to suppress expected backgrounds from SM processes, while maintaining sensitivity to different assumptions on the masses of the and χ 0 1 . To suppress backgrounds due to low-mass resonances and Z boson production, the dilepton invariant mass is required to be above 20 GeV, and to be either below 76 or above 106 GeV. Little or no hadronic activity is expected in the direct production of sleptons at pp colliders when assuming a 100% branching ratio for → χ 0 1 . As a result, events are rejected if they contain jets with p T above 25 GeV. Furthermore, events with two leptons and an additional isolated and charged PF candidate passing the selections described in Section 4 are vetoed since signal events would not include additional isolated charged particles.
The kinematic variable M T2 [52,53] is used to reduce backgrounds from tt and WW processes. This variable was first introduced to measure the mass of pair-produced particles, each decaying to the same final state, consisting of a visible and an invisible particle. It is defined as: where p miss T (i) (i = 1, 2) are trial vectors obtained by decomposing p miss T . The transverse masses are obtained by pairing either of these trial vectors with one of the two leptons.
The ∆φ is the angle between the p T of the lepton (noted as p vis T ) and p miss T (i) . The minimization is performed over all trial momenta satisfying the p miss T constraint. When building M T2 from the two selected leptons and p miss T , denoted as M T2 ( ), its distribution exhibits a sharp decrease above the mass of the W boson for tt and WW events and is therefore well suited to suppress these backgrounds. For this reason a requirement of M T2 ( ) > 90 GeV is imposed in this search.
The SR is divided into four bins of p miss T : 100-150, 150-225, 225-300, and ≥300 GeV. The selection results in a signal selection efficiency that ranges from 20 to 30% assuming a massless LSP. In addition to results including both flavors of SF lepton pairs, results separated in dielectron and dimuon pairs are presented, as the simplified models do not assume that smuon and selectron masses should be the same.

Standard model background predictions
The backgrounds from the SM processes are divided into four categories. Flavor-symmetric (FS) background processes are those processes that result in DF pairs (e ± µ ∓ ) as often as SF pairs (µ ± µ ∓ , e ± e ∓ ). The dominant contributions to this category are due to top quark pair production and WW production.
The subleading background contribution arises from diboson production, ZZ and WZ, and is estimated from simulation. The ZZ process can result a final state with two leptons originating from one Z boson decay and two neutrinos from the other Z boson decay. The WZ process can give rise to a final state with three leptons and p miss T , which can satisfy the signal selection criteria if one of the leptons fails the identification or acceptance requirements.
The contribution from DY is small but not negligible in the SR due to the large p miss T requirement. The contribution is estimated using simulated events after relaxing the Z boson veto and a transfer factor r out/in that gives the contribution of DY+jets events outside of the Z boson mass window of 76-106 GeV. The transfer factor r out/in is measured in a DY enriched CR as the ratio of events outside of the Z boson mass over the events compatible with the Z boson mass. A systematic uncertainty of 50% is assumed to result from this method.
Finally, a very minor background, referred to in the following as Rare backgrounds, originates from triboson production, or processes resulting in non-FS leptons, such as ttZ, tZq and tWZ. The simulation is also used to estimate this contribution, with a conservative systematic uncertainty of 50% assigned in place of QCD scale and PDF variations.

Flavor-symmetric backgrounds
The data-driven prediction of SM SF backgrounds is obtained using event counts in the DF sample, multiplied by a translation factor, R SF/DF , correcting for flavor dependent reconstruction, identification and trigger efficiencies which can be different for electrons and muons, as described in Ref. [54]. The translation factor is estimated with two independent methods.
The first method estimates directly the translation factor in a data CR enriched in enriched in tt events, requiring exactly two jets, 100 < p miss T < 150 GeV and excluding the dilepton invariant mass range 70 < m < 110 GeV to reduce contributions from DY production. Here, R SF/DF is computed using the observed yield of the SF and DF events, R SF/DF = N SF /N DF . Data and simulation agree to within 2% in this region. A 4% systematic uncertainty on the translation factor is assigned from simulation studies, as the maximal magnitude of the systematic needed to cover discrepancies in the translation factor as a function of some SR variables.
The second method utilizes a factorized approach. The ratio of muon to electron reconstruction and identification efficiencies, r µ/e , is measured in a CR enriched in DY events by requiring at least two jets, p miss T < 50 GeV, and 60 < m < 120 GeV. This results in a large sample of e ± e ∓ and µ ± µ ∓ events with similar kinematic distributions to those of the SR. Assuming factorization for the efficiencies of the two leptons, the ratio of efficiencies for muons and electrons is measured as This ratio depends on the lepton p T due to the trigger and reconstruction efficiency differences, especially at low lepton p T , and a parametrization as a function of the p T of the less energetic lepton is used: Here r µ/e,c and α are constants that are determined from a fit to data and cross-checked using simulation. These fit parameters are determined to be r µ/e,c = 1.140 ± 0.005 and α = 5.20 ± 0.16 GeV. In addition to the fit uncertainty, a 10% systematic uncertainty is assigned to account for remaining variations observed when studying the dependence of r µ/e on p miss T and on the p T of the more energetic lepton.
The trigger efficiencies for the three flavor combinations are used to define the factor R T = √ T µ ± µ ∓ T e ± e ∓ / T e ± µ ∓ , which takes into account the difference between SF and DF channels. The efficiencies, T µ ± µ ∓ , T e ± e ∓ and T e ± µ ∓ , are calculated as the fraction of events collected with PF HT triggers, that also passes the dimuon, dielectron and eµ triggers respectively. The measured efficiencies range between 90-96%, yielding a final value of R T = 1.052 ± 0.043. The translation factor in the factorized approach is thus R SF/DF = 0.5(r µ/e + r −1 µ/e )R T where the factor of 0.5 is due to the assumption that the number of produced DF events is twice the number of produced events in each SF sample (ee and µµ). Since r µ/e depends on the lepton kinematic variables, this translation factor is calculated on an event-by-event basis. A separate translation factor is determined for each SR and is combined with the translation factor from the direct measurement using a weighted average.

Diboson backgrounds
Although a Z boson veto is applied, the ZZ process can still enter the SR through an off-shell Z boson. This contribution is estimated from simulated events, validated in a data CR with four identified leptons. The selections for the CR and SR are exclusive, and the physics process in the CR (ZZ where both Z bosons decay to charged leptons) has similar kinematics as the process it is designed to validate. In order for the CR to accurately reflect the kinematics in the SR, the same jet veto as in the SR is applied in the CR. In addition, for the CR the Z boson candidate with the invariant mass best (next best) compatible with the Z boson mass is required to have 76 < m < 106 GeV (50 < m < 130 GeV). A generator-level p T dependent NNLO/NLO K factor taking into account missing electroweak corrections [55][56][57] is applied to the qq → ZZ process cross-sections. The smaller contribution from the gg → ZZ process is normalized to the NLO calculation [19]. After subtracting contributions to the CR from other processes, as determined by simulation, a simulation-to-data scale factor of 0.94 ± 0.07 is obtained. This scale factor is used to correct the ZZ background prediction from simulation in the SR, where one Z boson decays to charged leptons, and the other Z boson decays to neutrinos. A systematic uncertainty of 7% results from the limited statistics in the CR.
A difference in the p miss T and M T2 ( ) distributions is observed after applying the qq → ZZ NNLO/NLO K factor as a function of different generator level kinematic variables. An uncertainty is then assigned to the method based on the difference in the p miss T shape for MC events in the SR before and after the application of the K factor. Additional systematic uncertainties are considered in the background prediction, originating from the jet energy scale, the variation of the renormalization and factorization scales, the PDF choice, and the uncertainties in the lepton reconstruction and isolation efficiencies, and in the trigger modelling.
The WZ process result in SF events when one of the three leptons is not reconstructed (lost). The two detected leptons are of the SF when the lepton from W decay is lost, but they can be either SF or DF, with equal probability, when the lost lepton is from the Z boson decay. In the first case the background contribution is estimated from simulation, whereas in the second case it is covered by the data-driven FS prediction method.
Just as for the ZZ background, the prediction from simulation is validated in a CR enriched in WZ events. We select events with three leptons, with an additional jet veto and a requirement of p miss T > 70 GeV. The invariant mass of two SF leptons must be within 76 < m < 106 GeV. To reduce contributions from the DY process, events are required to have M T > 50 GeV, where M T is calculated from p miss T and the lepton from the W boson. After subtracting contributions from other processes, a simulation-to-data scale factor of 1.06 is obtained and applied to the prediction from simulation in SR A systematic uncertainty of 6% results from the limited statistics in the CR.
An additional uncertainty of 5% is added (in quadrature) to cover possible differences in the identification and isolation efficiencies at low lepton p T . Finally, uncertainties due to the jet energy scale, the lepton efficiencies, the trigger modeling, the PDF choice, and the renormalization and factorization scales are taken into account when computing the expected WZ yields in the SR.

Results
The observed number of events in data in the SR are compared with the stacked SM background estimates as shown in Fig. 2 (SF events), and in Fig. 3 (dielectron and dimuon events separately). The SM background and data yields are summarized in Table 1 for SF events and in Table 2 for dielectron and dimuon events.
At high p miss T values, the uncertainties in the background prediction are driven by the statistical uncertainty in the number of events in the DF sample used to derive the FS background. There is agreement between observation and SM expectation given the systematic and statistical uncertainties.

Interpretation
The results are interpreted in terms of the simplified model described in Section 1. Upper limits on the cross section, assuming branching ratios of 100%, have been calculated at 95% confidence level (CL) using the CL s criterion and an asymptotic formulation [58][59][60][61], taking into account the statistical and systematic uncertainties in the signal yields and the background predictions. All systematic uncertainties are of the type log-normal in the limit determination, except the gamma function nuisance which is used for the FS statistical uncertainty.

Systematic uncertainty in the signal yield
The systematic uncertainties associated with the signal are shown in Table 3, and described below. The uncertainty in the measurement of the integrated luminosity is 2.5% [62]. A flat uncertainty of 5% is associated to the lepton identification and isolation efficiency in the signal acceptance and an uncertainty of 4% in the lepton efficiency of the signal using fast simulation. The uncertainty on the trigger efficiency is measured to be 3%. The uncertainty in the jet en-   ergy scale is assessed by shifting the jet energy correction factors for each jet by one standard deviation up and down and recalculating the kinematic quantities. The result varies between 1 and 16% depending on the signal kinematics. Determining the signal acceptance in high-and low-pileup regimes separately yields an uncertainty of 0.5-7%. The uncertainty in the p miss T modeling is assessed by comparing the reconstructed p miss T to the generator-level p miss T in fast simulation and amounts to 0.5-20%. Varying the unclustered energy, and the electron and muon scales, results in systematic uncertainties of 0.5-8%, 0.5-4%, and 0.5-20% respectively. The large variation associated to the muon energy scale is due to the poor muon momentum resolution at high p T , and the quoted value is driven by one signal scenario containing such a high p T muon event. The theoretical uncertainties are those related to the uncertainty on the QCD renormalization (µ R ) and factorization (µ F ) scales, and of the PDF. The systematic uncertainties associated with the µ R and µ F scales are evaluated using weights derived from the SysCalc code applied to simulated signal events [63]. For renormalization and factorization scales the Stewart-Tackmann prescription [64] is followed, that treats the theory uncertainties in analyses with a jet selection. This procedure results in an uncertainty of 1-11%. Finally the statistical uncertainty in the number of simulated events is also considered and found to be in the range 0.5-20%, depending on the signal scenario.

Interpretations using simplified models
Upper limits on the direct slepton pair production cross section are displayed in Fig. 4 for three scenarios: assuming the existence of both flavor mass degenerate left-and right-handed sleptons, for only left-handed sleptons, and for only right-handed sleptons. Similarly, the limits on direct selectron and smuon production are displayed in Figs. 5 and 6, respectively. The Figs. 4-6 also show the 95% CL exclusion contours, as a function of the and χ 0 1 masses. Note that the cross section at a given mass for right-handed sleptons is expected to be about one third of that for left-handed sleptons. The analysis probes slepton masses up to approximately 450, 400, or 290 GeV, assuming both left-and right-handed, left-handed only, or right-handed sleptons, and a massless LSP. In the case of selectrons (smuons), the limits corresponding to these 3 scenarios are 350, 310 and 250 GeV (310, 280, and 210 GeV). Since the dimuon data yield in the highest p miss T bin is somewhat higher than predicted, the observed limits in this channel are weaker than expected in the absence of signal. These results improve the previous 8 TeV exclusion limits by 100-150 GeV in the slepton mass [13].

Summary
A search for direct slepton (selectron or smuon) production, in events with opposite-charge, same-flavor leptons, no jets, and missing transverse momentum has been presented. The data comprise a sample of proton-proton collisions collected with the CMS detector in 2016 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb −1 . Observations are in agreement with Standard Model expectations within the statistical and systematic uncertainties. Exclusion limits are provided assuming right-handed only, left-handed only and right-and left-handed two flavor slepton production scenarios (mass degenerate selectrons and smuons). Slepton masses up to 290, 400 and 450 GeV respectively are excluded at 95% confidence level. Exclusion limits are also provided assuming right-handed only, lefthanded only and right-and left-handed single flavor production scenarios, excluding selectron (smuon) masses up to 250, 310 and 350 GeV (210, 280 and 310 GeV), respectively. These results improve the previous exclusion limits measured by the CMS experiment at a centerofmass energy of 8 TeV by 100-150 GeV in slepton masses.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: