Search for supersymmetry in events with at least three electrons or muons, jets, and missing transverse momentum in proton-proton collisions at $\sqrt{s} = $ 13 TeV

A search for new physics is carried out in events with at least three electrons or muons in any combination, jets, and missing transverse momentum. Results are based on the sample of proton-proton collision data produced by the LHC at a center-of-mass energy of 13 TeV and collected by the CMS experiment in 2016. The data sample analyzed corresponds to an integrated luminosity of 35.9 fb$^{-1}$. Events are classified according to the number of b jets, missing transverse momentum, hadronic transverse momentum, and the invariant mass of same-flavor dilepton pairs with opposite charge. No significant excess above the expected standard model background is observed. Exclusion limits at 95% confidence level are computed for four different supersymmetric simplified models with pair production of gluinos or third-generation squarks. In the model with gluino pair production, with subsequent decays into a top quark-antiquark pair and a neutralino, gluinos with masses smaller than 1610 GeV are excluded for a massless lightest supersymmetric particle. In the case of bottom squark pair production, the bottom squark masses are excluded up to 840 GeV for charginos lighter than 200 GeV. For a simplified model of heavy top squark pair production, the $\mathrm{\widetilde{\text{t}}_2}$ mass is excluded up to 720, 780, or 710 GeV for models with an exclusive $\mathrm{\widetilde{\text{t}}_2}\rightarrow\mathrm{\widetilde{\text{t}}_1}\mathrm{H}$ decay, an exclusive $\mathrm{\widetilde{\text{t}}_2}\rightarrow\mathrm{\widetilde{\text{t}}_1}\mathrm{Z}$ decay, or an equally probable mix of those two decays. In order to provide a simplified version of the analysis for easier interpretation, a small set of aggregate signal regions also has been defined, providing a compromise between simplicity and analysis sensitivity.


Introduction
Many different theories beyond the standard model (BSM) predict processes leading to events containing multiple electrons and/or muons [1][2][3][4][5].The background from standard model (SM) processes forging such a final state is small and dominated by multiboson production, which is well understood theoretically [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and well reconstructed experimentally [21][22][23][24][25].The search in this paper is designed to have broad sensitivity to a variety of BSM models by examining the event yields as a function of several kinematic quantities.This paper describes the methods and results of a search for new physics in final states with three or more electrons or muons in any combination accompanied by jets and missing transverse momentum.A sample of proton-proton (pp) collision data, corresponding to an integrated luminosity of 35.9 fb −1 and collected by the CMS detector at the CERN LHC at a centerof-mass energy of 13 TeV throughout 2016, is used.Results of this analysis are interpreted in the context of supersymmetric (SUSY) models [26][27][28][29][30][31][32][33][34].Supersymmetry is an extension of the SM that predicts a SUSY partner for every SM particle by introducing a new symmetry between bosons and fermions.It can potentially provide solutions to questions left open by the SM, such as the hierarchy problem and the nature of dark matter.More specifically, models in which R-parity [31] is conserved, whereby SUSY particles are produced only in pairs, can include a dark matter candidate in the form of a stable and undetectable lightest SUSY particle (LSP).In the models considered in this paper, the LSP is assumed to be the lightest neutralino (a mixture of the superpartners of the Higgs and Z bosons, and of the photon).
The reference models for this analysis are simplified model spectra (SMS) [35].Examples for SUSY processes that can give rise to multilepton final states are shown in Fig. 1.Throughout this paper lepton refers to an electron or a muon.The models under consideration in this analysis feature the pair production of gluinos, g, or third generation squarks, b 1 or t 2 , superpartners of gluons and third generation quarks, respectively, for a wide spectrum of possible masses.A typical process predicted by SUSY models consists of gluino pair production with each gluino decaying to a top quark pair, tt, and an LSP, χ 0 1 (Fig. 1, upper left), or to a pair of quarks and a neutralino, χ 0 2 , or chargino, χ ± 1 .The latter would then decay into a Z or W boson, and an LSP (Fig. 1, upper right).The first model is referred to as T1tttt and the second one as T5qqqqVV throughout this paper.Other models feature bottom squark, b 1 , pair production, with subsequent cascade decays resulting in top quarks, W bosons and LSPs (Fig. 1, lower left) or pair production of the heaviest of the two top squark states, t 2 , with subsequent decays to top quarks, Higgs or Z bosons, and LSPs (Fig. 1, lower right).The latter process allows a challenging scenario to be probed in which the mass difference between the lighter top squark, t 1 , and the neutralino, χ 0 1 , is close to the mass of the top quark [36,37].These two models are denoted as T6ttWW and T6ttHZ, respectively.Through the decays of W, Z or Higgs bosons these processes can result in several leptons.In addition to the presence of multiple leptons, these models predict events with multiple jets and missing transverse momentum, largely induced by the undetected LSPs.The SUSY particles that are not directly included in the diagrams are assumed to be too heavy to be accessible at the LHC.Therefore, the only free parameters in these models are the mass of the produced gluinos or squarks, the masses of the possible intermediate particles in the decay chain, like χ 0 2 or χ ± 1 , and the mass of the χ 0 1 .Similar searches have been carried out by the ATLAS and CMS Collaborations using the 13 TeV dataset.With the data sample collected by the ATLAS experiment and corresponding to an integrated luminosity of 36.1 fb −1 , gluinos with masses up to 1870 GeV can be excluded [38] assuming the model depicted in Fig. 1 (upper left).A comparable search at the same centerof-mass energy with the CMS detector in 2015, based on a data sample corresponding to an Figure 1: Diagrams for models with gluino pair production leading to four top quarks, T1tttt (upper left), or four quarks and two vector bosons, T5qqqqVV (upper right) in the final state, in both cases accompanied by two LSPs.Models of bottom, T6ttWW, and top squark, T6ttHZ, pair production lead to two top quarks, two LSPs and either two W bosons (lower left) or two neutral bosons as SM Higgs (H) and/or Z bosons (lower right).
integrated luminosity of 2.3 fb −1 , excluded gluino masses below 1175 GeV [39].The current analysis improves upon the one performed with the data collected in 2015 with a more advanced strategy that exploits the transverse mass reconstructed with a lepton and the missing transverse momentum vector.Taking into account that approximately 15 times more data were collected in 2016, a new control region dominated by events from the ttZ process and a new interpretation of the results based on a T6ttHZ model also were added.

The CMS detector
The CMS detector features a superconducting solenoid with an internal diameter of 6 m that creates a magnetic field of 3.8 T. Inside the magnet volume are a silicon pixel and strip tracker, an electromagnetic calorimeter (ECAL) made of lead tungstate crystals, and a hadronic calorimeter (HCAL) made of brass and scintillator material, each composed of a barrel and two endcap sections.Forward calorimeters extend the pseudorapidity (η) coverage for the HCAL.
In the barrel section of the ECAL, an energy resolution of about 1% is achieved for unconverted or late-converting photons in the tens of GeV energy range.The remaining barrel photons have a resolution of about 1.3% up to |η| = 1, rising to about 2.5% at |η| = 1.4.In the endcaps, the resolution of unconverted or late-converting photons is about 2.5%, while the remaining endcap photons have a resolution between 3 and 4% [40].When combining information from the entire detector, the jet energy resolution amounts typically to 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV, to be compared to about 40%, 12%, and 5% obtained when the ECAL and HCAL calorimeters alone are used.Muons are measured in the range |η| < 2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers.Matching muons to tracks measured in the silicon tracker results in a relative transverse momentum resolution for muons with 20 < p T < 100 GeV of 1.3-2.0% in the barrel and better than 6% in the endcaps, The p T resolution in the barrel is better than 10% for muons with p T up to 1 TeV [41].The first level of the CMS trigger system [42], composed of specialized hardware processors, uses information from the calorimeters and muon detectors to select the most interesting events in a fixed time interval of less than 4 µs.The high-level trigger (HLT) processor farm further decreases the event rate from approximately 100 kHz to around 1 kHz, before the storage of the data.A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in [43].

Event selection criteria and Monte Carlo simulation
Events are reconstructed using the particle flow, PF, algorithm [44], which reconstructs and identifies each individual particle with an optimized combination of information from the various elements of the CMS detector.The objects identified as particles by this algorithm are commonly referred to as PF candidates.Jets are clustered from PF candidates using the anti-k T algorithm [45,46] with a distance parameter of 0.Here ∆η and ∆φ are the differences in η and azimuthal angle (φ, in radians) between the considered lepton and a given jet.Additional criteria are applied to reject events containing noise and mismeasured jets.Jet energy scale (JES) corrections are applied to correct simulated jets for residual differences with data [47,48].
The combined secondary vertex algorithm CSVv2 [49,50] is used to assess the likelihood that a jet originates from a bottom quark.The tagging efficiency for true b flavor jets is typically 70% and the misidentification probabilities are 10% and 1% for c quark and light-flavor jets, respectively.Jets with p T > 25 GeV and within |η| < 2.4 are considered for b tagging.Another variable related to jets that is used throughout this analysis is the scalar sum of the transverse momenta of all jets, defined as H T = ∑ jets p T , where jets have p T > 30 GeV.The missing transverse momentum p miss T is defined as the magnitude of p miss T , the negative vector sum of the transverse momenta all PF candidates reconstructed in an event [51,52].
Electron candidates are reconstructed using tracking and ECAL information, by combining the clusters of energy deposits in the ECAL with Gaussian sum filter tracks [53].The electron identification is performed using a multivariate discriminant built with shower shape variables, track-cluster matching variables, and track quality variables.The algorithm is optimized to select electrons from the decay of W and Z bosons with a 90% efficiency while rejecting electron candidates originating from jets.To reject electrons originating from photon conversions inside the detector, electrons are required to have all possible measurements in the innermost tracker layers and to be incompatible with any conversion-like secondary vertices.The identification of the muon is performed using the quality of the matching between the measurements of the tracker and the muon system [41].The muon identification efficiency is at least 96%, with some variation depending on p T and η.
The reconstructed vertex with the largest value of summed physics object p 2 T is taken to be the primary pp interaction vertex.The physics objects are the objects returned by a jet finding algorithm [45,46] applied to all charged tracks associated with the vertex, plus the corresponding associated missing transverse momentum.Both muon and electron candidates are required to have a transverse impact parameter smaller than 0.5 mm with respect to the primary vertex and a longitudinal impact parameter smaller than 1 mm.In addition, a selection on the threedimensional impact parameter significance, defined as the value of impact parameter divided by its uncertainty, is applied.This value has to be smaller than 4 for both electrons and muons.
Additional information about the isolation of the lepton is necessary to discriminate between leptons originating from decays of heavy particles such as W and Z bosons ("prompt" leptons) and those produced in hadron decays or jets misidentified as leptons ("nonprompt" leptons).The lepton isolation criterion is constructed using three different variables.
The relative isolation, I rel , is defined as the ratio of the amount of energy measured in a cone around the lepton to the p T of the lepton, p T , with a p T -dependent radius [54]: Requiring I rel below a given threshold ensures that the lepton is locally isolated, even in Lorentzboosted topologies.
The second isolation variable is the ratio of the lepton p T and that of the jet geometrically closest to the lepton: In most cases this is the jet containing the lepton.If no jet is found within a cone defined by ∆R < 0.4, the ratio is set to 1.The use of p ratio T provides a way to identify nonprompt low-p T leptons originating from low-p T b jets, which decay with a larger opening angle than the one used in I rel .
The last variable used in the isolation criteria of leptons is p rel T , defined as the magnitude of the component of the lepton momentum perpendicular to the axis of the closest jet.The jet axis is obtained by subtracting the momentum vector of the lepton from that of the jet.If no matched jet is found around the lepton, the variable is set to 0. This variable allows the recovery of leptons from accidental overlap with jets in Lorentz-boosted topologies.For the calculation of p rel T and the previously mentioned p ratio T , jets with p T > 5 GeV and without any additional identification criteria are considered.
Using those three variables, a lepton is considered isolated if the following condition is fulfilled: The values of I 1 , I 2 , and I 3 depend on the flavor of the lepton; the probability to misidentify a jet as a lepton is higher for electrons than for muons, so tighter isolation values are used for the former.For electrons (muons), the tight selection requirements are I 1 = 0.12 (0.16), I 2 = 0.76 (0.69), and I 3 = 7.2 (6.0) GeV.The isolation requirement for leptons to pass the loose working point of the selection is significantly relaxed, only consisting of I rel < 0.4.
Events used in this analysis are required to pass trigger selection criteria that target dilepton and multilepton events.The following two sets of triggers are used in a logic OR configuration.One set of triggers requires that the two leptons satisfy loose isolation criteria and that the highest-p T (leading) lepton have p T > 23 (17) GeV and the second highest-p T (sub-leading) lepton have p T > 12 (8) GeV for muons (electrons).The second set of triggers places no requirements on the isolation, has a lower p T threshold for both leptons (p T > 8 GeV), and requires the H T reconstructed in the trigger to be greater than 300 GeV.With the thresholds on the p T of the leptons and on the H T applied, the efficiency per event is near 100%.
The selection requires the presence of at least three well-identified leptons in the event.The leptons must satisfy p T thresholds that depend on the lepton flavor and the amount of hadronic activity in the event.For events with low hadronic activity (H T < 400 GeV), the leading electron (muon) must satisfy p T > 25 (20) GeV and sub-leading electrons (muons) must satisfy p T > 15 (10) GeV.In events with high hadronic activity (H T > 400 GeV), the thresholds are relaxed to 15 (10) GeV for the leading electrons (muons).The lowest-p T (trailing) lepton must have p T > 10 GeV in all cases.Opposite-charge same-flavor lepton pairs are required to have an invariant mass (m ) greater than 12 GeV to suppress Drell-Yan and quarkonium processes.
In order to estimate the contribution from SM processes with prompt leptons in the signal regions and to calculate the predicted yields from new physics models, Monte Carlo (MC) simulations are used.The MADGRAPH5 aMC@NLO v2.2.2 or v2.3.3 generator [55] was used to simulate events for the tt, Wγ * and tWZ processes, at leading order (LO), and for ttZ, ttW, tZq, tHq, tHW, WWZ, WZZ, ZZZ, ttγ, and Zγ * final states, at next-to-leading order (NLO) in perturbative quantum chromodynamics.The NLO POWHEG v2 [56] generator is exploited for the ttH [57] and diboson [58,59] production.The NNPDF3.0LO [60] parton distribution functions (PDFs) are used for the simulated samples generated at LO and the NNPDF3.0NLO[60] PDFs for those generated at NLO. Parton showering and hadronization are simulated using the PYTHIA v8.212 generator [61] with the CUETP8M1 tune [62,63].A double-counting of the partons generated with MADGRAPH5 aMC@NLO and those with PYTHIA is removed using the MLM [64] and the FXFX [65] matching schemes, in the LO and NLO samples, respectively.The CMS detector response is modeled using a GEANT4-based model [66].The simulated samples include additional simultaneous interactions per bunch crossing (pileup), with distributions that are weighted to match the observed data.
Monte Carlo simulation of signal events used for interpretation of the final results is done with the MADGRAPH5 aMC@NLO program at LO precision, allowing for up to two additional partons in the calculation of the matrix elements.The SUSY particle decays, parton showering, and hadronization are simulated with PYTHIA v8.212.The detector response for signal events is simulated using a CMS fast-simulation package [67] that is validated with respect to the GEANT4-based model.All simulated events are processed with the same reconstruction procedure as data.Cross sections for SUSY signal processes, calculated at NLO with nextto-leading-logarithmic (NLL) resummation, were provided by the LHC SUSY Cross Section Working Group [68][69][70][71][72][73].

Search strategy
A baseline selection is applied to the dataset containing events of interest: three or more electrons or muons, at least two jets (N jets ≥ 2), p miss T ≥ 50 GeV, and m ≥ 12 GeV for all oppositecharge, same-flavor lepton pairs.All these requirements are listed in Table 1.Two different regions are defined, based on whether or not an event contains an opposite-charge, same-flavor lepton pair with an invariant mass within the 15 GeV window around the Z boson mass [74].If such a lepton pair is found the event is categorized as "on-Z", otherwise "off-Z".Events are further categorized into signal regions, which are defined according to several event observables: N b jets , H T , p miss T , m , as well as the transverse mass reconstructed with a lepton and the missing transverse momentum vector, ( If the event is categorized as on-Z, the M T is calculated with the lepton that is not involved in the Z boson mass reconstruction, otherwise the lepton yielding the lowest M T value (M min T ) is used in the computation of this variable.
The classification of selected events based on the number of b jets creates signal regions with high signal-to-background ratios for events from different signal models.For example, the T1tttt model features several b jets, which would be categorized into signal regions that are almost free of the leptonic WZ background owing to the b jet requirements.Including the 0 b jet signal regions keeps the analysis sensitive to signatures without b jets, such as T5qqqqVV model.Additionally, a categorization in H T and p miss T is useful to distinguish between compressed and noncompressed SUSY spectra, i.e. models with small or large mass differences between the SUSY particles in the decay chain.
Table 2 shows the definition of the signal regions (SRs) into which the events passing the baseline selection are subdivided.There are 16 separate off-Z and 16 on-Z SRs.Each category is split, depending on the number of b jets (0, 1 and 2), the value of H T (greater or lower than 400 GeV), and p miss T (greater or lower than 150 GeV).These SRs are denoted as SR 1-12.Motivated by the low expected yield of events with high b jet multiplicities, one inclusive SR with p miss T < 300 GeV and H T < 600 GeV has been defined for ≥3 b jets (SR 13), and additionally to this three SRs with significant amounts of H T (>600 GeV, SRs 14, 15) or p miss T (>300 GeV, SR 16) have been introduced, since various noncompressed SUSY models yield very high values for these variables.These latter three regions are inclusive in the number of b jets.All of the 0 b jet regions, as well as three regions with high H T and p miss T values, are further split depending whether M T is smaller (designated with the letter "a" after the region number) or greater (designated with "b") than 120 GeV, leading to a total of 23 regions for each of the off-Z and on-Z categories.In the on-Z regions with 0 or 1 b jet and 60 < H T < 400 GeV, the p miss T lower bound is raised to 70 GeV to completely suppress the contribution from the Drell-Yan process.
Table 2: Summary of the signal region definitions.The minimum p miss T requirement is raised from 50 to 70 GeV only for the on-Z SR1 and SR5.Signal regions that are further subdivided at M T = 120 GeV are indicated with †.The search regions are mirrored for on-and off-Z categories.
In order to provide a simplified version of the analysis for easier interpretation, a small set of aggregate signal regions has been defined, providing a compromise between simplicity and analysis sensitivity.The definition of these so-called super signal regions (SSR) is given in Table 3.The additional requirement M T greater than 120 GeV was added to the SSRs with respect to the relevant SRs.

Background estimation
All backgrounds leading to the multilepton final states targeted by this analysis can be subdivided into the categories listed below.
Table 3: Definition of the aggregate super signal regions (SSRs).This simpler classification is proposed for reinterpretations, depending on the presence of a Z boson candidate and the number of b jets, along with additional simultaneous requirements on M T , p miss T , and H T .
Nonprompt leptons are leptons from heavy-flavor decays, misidentified hadrons, muons from light-meson decays in flight, or electrons from unidentified photon conversions.In this analysis tt events can enter the signal regions if nonprompt leptons are present in addition to the prompt leptons from the W boson decays.Top quark pair production gives the largest contribution for regions with low H T and p miss T values, and therefore predominately populates signal regions 1 and 5, with 0 and 1 b jet, respectively.Apart from tt, Drell-Yan events can enter the baseline selection.However, they are largely suppressed by the p miss T > 50 GeV selection, and additional rejection is achieved by increasing the p miss T requirement to 70 GeV for on-Z regions with low H T and low p miss T .Processes that yield only one prompt lepton in addition to nonprompt ones, such as W+jets and various single top quark channels, are effectively suppressed by the three-lepton requirement because of the low probability that two nonprompt leptons satisfy the tight identification and isolation requirements.Albeit small, this contribution is nevertheless accounted for in our method to estimate the background due to nonprompt leptons (see below).
Diboson production can yield multilepton final states with up to three prompt leptons (WZ or Wγ * ) and up to four prompt leptons (ZZ or Zγ * ), rendering irreducible backgrounds for this analysis.For simplicity, in the following we refer to these backgrounds as WZ and ZZ, respectively.The WZ production has a sizable contribution in the on-Z events, especially in the SRs without b jets.The yields of these backgrounds in the various SRs are estimated by means of MC simulation, with the normalization factors derived from control regions in data.
Other rare SM processes that can yield three or more leptons are ttW, ttZ, and triboson production.We also include the contribution from the SM Higgs boson produced in association with a vector boson or a pair of top quarks in this category of backgrounds, as well as processes that produce additional leptons from internal conversions, which are events that contain a virtual photon that decays to leptons.The internal conversion background components, X+γ, are strongly suppressed by the p miss T > 50 GeV and N jets ≥ 2 requirements.The background events containing top quark(s) in association with a W, Z or Higgs boson or another pair of top quarks are denoted as ttX, except for ttZ which is separately delineated.For the estimation of the latter process, the same strategy as for the WZ is used.All other processes are grouped into one category that is denoted as rare SM processes.The contribution from these processes as well as ttX are estimated from MC simulation.
The background contribution from nonprompt leptons is estimated using the tight-to-loose ratio method [54].In this method, the yield is estimated in an application region that is similar to the signal region but which contains at least one lepton that fails the tight identification and isolation requirements but satisfies the loose requirements.The events in this region are weighted by f /(1 − f ), where the tight-to-loose ratio f is the probability that a loosely identified lepton also satisfies the full set of requirements.This ratio is measured as a function of lepton p T and η in a control sample of multijet events that is enriched in nonprompt leptons (measurement region).In this region, we require exactly one lepton, satisfying the loose object selection, and one recoiling jet with ∆R(jet, ) > 1.0 and p T > 30 GeV in the event.To suppress processes that can contribute prompt leptons from a W or Z boson decay, such as W(+jets), DY or tt, we additionally require both p miss T and M T to be below 20 GeV.The remaining contribution from these processes within the measurement region is estimated from MC simulation and subsequently subtracted from the data.
In order to reduce the dependence of the tight-to-loose ratio on the flavor composition of the jets from which the nonprompt leptons originate, this ratio is parameterized as a function of a variable that correlates more strongly with the mother parton p T than with the lepton p T .This variable is calculated by correcting the lepton p T as a function of the energy in the isolation cone around it.This definition leaves the p T of the leptons satisfying the tight isolation criteria unchanged and modifies the p T of those failing these criteria so that it is a better proxy for the mother parton p T and results in a smaller variation as a function of the mother parton p T .The flavor dependence, which is much more important for the case of electrons, is further reduced by adjusting the loose electron selection to obtain similar f values for nonprompt electrons that originate from light-or heavy-flavor jets.As a result, the tight-to-loose ratio measured in a multijet sample leads to a good description of nonprompt background originating from tt events, which in most of the SR are dominant in this category of background.
The tight-to-loose ratio method for estimating the nonprompt background is validated both in a closure test in simulation and in a data control region orthogonal to the baseline selection with minimal signal contamination.This region is defined by the requirement of three leptons that satisfy the nominal identification, isolation, and p T selection, one or two jets, 30 < p miss T < 50 GeV, and no dilepton pair with an invariant mass compatible with a Z boson.With these selection criteria a purity in tt of 80% can be achieved.We find an agreement of the order of 20-30% between the predicted and observed yields in this control region.
The WZ process is one of the main backgrounds in the regions with 0 b jets, while ttZ gives a significant contribution in categories enriched in b jets.As mentioned earlier, the contribution of these backgrounds is estimated from simulation, but their normalizations are obtained from a simultaneous fit using two control regions, designed so that each is highly enriched in one of the processes.The WZ control region is defined by the requirement of three leptons satisfying the nominal identification and isolation selections.Two leptons have to form an opposite charge, same flavor pair with |m − m Z | < 15 GeV, the number of jets and b jets has to be ≤1 and 0, respectively.The p miss T has to be in the range 30 < p miss T < 100 GeV, and M T is required to be at least 50 GeV to suppress contamination from the Drell-Yan process.The purity of the WZ control region is 80%.The orthogonal control region for ttZ is defined similarly to that for WZ, except for a requirement on the number of jets: three leptons satisfying the nominal identification and isolation selection are to be found, two of them forming an opposite charge, same flavor pair with |m − m Z | < 15 GeV, at least 3 jets, and 30 < p miss T < 50 GeV.Events are classified by the number of b jets, and three bins are formed for the ttZ CR: the 0 b jet category, where the background is dominated by the WZ and tt processes, and the 1 and ≥2 b jet categories, enriched in ttZ.The overall purity of the ttZ process is 20%, increasing to 50% in the bins with at least one b jet.These three bins, together with the WZ control region are used in a simultaneous fit to obtain the scale factors for the normalization of the simulated samples.In the fit to data, the normalization and relative population across all four bins of all the components are allowed to vary according to experimental and theoretical uncertainties.For the WZ process the obtained scale factor is compatible with unity, 1.01 ± 0.07, and no correction is applied to the simulation, while for the ttZ it is found to be 1.14 ± 0.28.Therefore the yields from the MC ttZ sample obtained in the baseline region are scaled by a factor of 1.14.

Systematic uncertainties
The uncertainties in the expected SM backgrounds and signal yields are categorized as experimental, such as those related to the JES or the b tagging efficiency description in the simulation; theoretical, such as the uncertainties in the considered cross sections; statistical, related to the observed yield in control regions in data; and as uncertainties in the background estimation methods relying on control regions in data.These uncertainties and their effect on the predicted yields are described below and summarized in Table 4.
One of the major experimental sources of uncertainty is the knowledge of the JES.This uncertainty affects all simulated background and signal events.For the data set used in this analysis, the uncertainties in the jet energy scale vary from 1% to 8%, depending on the transverse momentum and pseudorapidity of the jet.The impact of these uncertainties is assessed by shifting the jet energy correction factors for each jet up and down by one standard deviation and recalculating all kinematic quantities.The systematic uncertainties related to JES corrections are also propagated to the p miss T calculation.The propagation of the variation of the JES results in a variation of 1-10% in the predicted event yields in the various signal regions of this analysis.
A similar approach is used for the uncertainties associated with the corrections for the b tagging efficiencies for light, charm and bottom flavor jets, which are parameterized as a function of p T and η.The variation of the scale factor correcting for the differences between data and simulation is at a maximum of the order of 10% per jet, and leads to an overall effect in the range of 1-10% depending on the signal region and on the topology of the event.The inaccuracy of the inelastic cross section value that affects the pile up rate gives up to a 5% effect.The sources of uncertainties explained here were also studied for the signal samples, and their impact on the predicted signal yields in every search region has been estimated following the same procedures.p T and η.They are applied to correct for residual differences in lepton selection efficiencies between data and simulation.The corresponding uncertainties are estimated to be about 3% per lepton for both flavors, and additionally 2% per lepton is assigned to the signal leptons due to the detector fast simulation.Assuming 100% correlation between the uncertainties on the corrections for the different leptons, a flat uncertainty of 9% is taken into account for the background, while 15% is considered for the signal.The uncertainty related to the HLT trigger efficiency is evaluated to amount to 3%.

Lepton identification and isolation scale factors have been measured as a function of lepton
For the nonprompt and misidentified lepton background, several systematic uncertainties are considered.The statistical uncertainty from the application region, which is used to estimate this background contribution, ranges from 10 to 100%.The regions where these uncertainties are large are generally regions where the overall contribution from this background is small.The uncertainty arising from the electroweak background subtraction in the measurement region for the tight-to-loose ratio is propagated from the uncertainty on the scale factor obtained from the fit to the control regions.In the case where no events are observed in the application region, an upper limit of the background expectation is used as determined from the upper limit at 68% confidence level (CL) multiplied by the most likely tight-to-loose ratio value.
The systematic uncertainty related to the extrapolation from the control regions to the signal regions for the nonprompt lepton background is estimated to be 30%.This value has been extracted from closure tests performed by applying the method described in Section 5 to simulated samples containing nonprompt leptons.From the simultaneous fit in the control regions, the uncertainty in the normalization of the WZ process is estimated to be 10%, while a value of 25% is found for ttZ background.
The limited size of the generated MC samples represents an additional source of uncertainty.
For the backgrounds that are estimated from simulation, such as ttW, ttZ and ttH, as well as for all the signal processes, this statistical uncertainty is computed from the number of MC events entering the signal regions and varies widely across the SRs.
For signal efficiency calculations additional uncertainties in the description of the initial-state radiation (ISR) are taken into account.The modeling of ISR by the version of the MAD-GRAPH5 aMC@NLO generator used for signal events was compared against a data sample of tt events in the dilepton final state.The corresponding corrections range from 0.51 to 0.92, depending on the jet multiplicity.These corrections are then applied on simulated SUSY events based on the number of ISR jets to improve upon the MADGRAPH5 aMC@NLO modeling of the multiplicity of additional jets from ISR.Half the magnitude of these ISR corrections is assigned as an additional systematic uncertainty, which can be as large as 10%.
The uncertainty in potential differences between the modeling of p miss T in data and the fast simulation arising from unclustered energy in the CMS detector is evaluated by comparing the reconstructed p miss T with the p miss T obtained using generator-level information.This uncertainty ranges up to 20%.
Theoretical uncertainties include the uncertainty in the renormalization (µ R ) and factorization (µ F ) scales, and in the knowledge of the PDFs.These uncertainties are evaluated for several processes, namely ttW, ttZ, and ttH, which are dominant backgrounds in several signal regions.Both the changes in the acceptance and cross sections related to these effects are taken into account and propagated to the final uncertainties.
For the study of the renormalization and factorization uncertainties, variations up and down by a factor of two with respect to the nominal values of µ F and µ R are evaluated.The maximum difference in the yields with respect to the nominal case is observed when both scales are varied up and down simultaneously.The effect on the overall cross section is found to be ∼13% for ttW and ∼11% for ttH backgrounds.The effect of the variations of µ F and µ R on the acceptance is taken as additional, uncorrelated uncertainty on the acceptance corresponding to different signal regions.This effect is found to vary between 3% and 18% depending on the SR and the process.
The uncertainty related to the PDFs is estimated from the 100 NNPDF 3.0 replicas, computing the deviation with respect to the nominal yield for each of them in every signal region (the cross section and acceptance effect are considered together) [60].The root-mean-square of the variations is taken as the value of the systematic uncertainty.Since no significant differences between signal regions have been found, a flat uncertainty of 3% (2%) is considered for ttW (ttZ and ttH) backgrounds.This value also includes the effect of the strong coupling constant variation, α S (M Z ), which is added in quadrature.An extra, conservative, flat uncertainty of 50% is assigned to the yield of the remaining rare processes, which are not well measured.

Results
Comparisons between data and the predicted background of the distributions of the four event observables used for signal region categorization, namely H T , p miss T , M T and N b jets , as well as the lepton p T spectra, the lepton flavor composition, and the event jet multiplicity are shown in Fig. 2 (Fig. 3) for events satisfying the selection criteria of the off-Z (on-Z).Figure 4 graphically presents a summary of the predicted background and observed event yields in the individual SR bins.The same information is also presented in Tables 5 and 6 for the off-Z and on-Z regions, respectively.Table 7 represents the yields in the SSRs.
The number of events observed in data is found to be consistent with the predicted background yields in all 46 SRs.The results of the search are interpreted by setting limits on superpartner masses using simplified models.For each mass point, the observations, background predictions, and expected signal yields from all on-Z and off-Z search regions are combined to extract the minimum cross section that can be excluded at a 95% CL using the CL s method [75][76][77], in which asymptotic approximations for the distribution of the test-statistic, which is a ratio of profiled likelihoods, are used [78].Log-normal nuisance parameters are used to describe the uncertainties listed in Section 6.
The limits are shown in Fig. 5 for the T1tttt model (left) and for the T5qqqqVV model (right).In the T5qqqqVV model each gluino decays to a pair of light quarks and a neutralino ( χ 0 2 ) or chargino ( χ ± 1 ), followed by the decay of that neutralino or chargino to a W or Z boson, respectively, and an LSP (Fig. 1, top right).The probability for the decay to proceed via the χ + 1 , χ − 1 , or χ 0 2 is taken to be 1/3 for each case.In this scenario, the second neutralino χ 0 2 and chargino are assumed to be mass-degenerate, with masses equal to 0.5(m g + m χ 0 1 ).
The limits on the bottom squark pair production cross section are shown in Fig. 6.In this model, the mass of the LSP is set to 50 GeV.Finally, the limits on the t 2 pair production cross section are shown in Fig. 7.In this scenario, the mass difference between the t 1 and the LSP is set to 175 GeV, the t 1 decays via a top quark to LSP, and the t 2 decays via a Z or Higgs boson to t 1 .We consider the reference values B( t 2 → t 1 Z) = 0, 50, and 100%; the sensitivity is diminished for the t 1 H final state because of the additional branching factors for Higgs cascade decays to electrons or muons via gauge bosons or tau leptons.
Search regions providing the best sensitivity to new physics scenarios depend on the considered models and their parameters.In the non-compressed scenario of the T1tttt model, the most sensitive region is off-Z SR16b (high p miss T and M T region).When considering the compressed scenario, the contribution from SR16b region remains the largest, up to the most compressed cases where the SR12 off-Z region (2 b jets, medium p miss T and high H T ) starts to contribute significantly.For the T5qqqqVV model in the non-compressed scenario, the most sensitive regions are on-Z SR16b and SR15b (high and medium p miss T , high H T and high M T values).When moving towards more compressed scenarios, the most significant contributions come from the SR16b and SR15b on-Z regions, until reaching the compressed scenario where the most sensitive region is SR4b (medium p miss T , high H T and high M T ).The exclusion limit for T6ttWW model is dominated by both off-Z SR16 regions (high p miss T region).For the T6ttHZ model with B( t 2 → t 1 Z) = 0%, the limits in the non-compressed scenario are driven by the off-Z SR15a (high H T , medium p miss T , low M T ), while for compressed case by off-Z SR13 (high N b jets , low and medium H T and p miss T ).For B( t 2 → t 1 Z) = 50% in the non-compressed scenario, the on-Z SR16b region dominates the the exclusion limit, while in the compressed scenario the on-Z SR13 (high N b jets ) and SR15b (high H T , medium p miss T , high M T ) give the highest contribution.Finally, for B( t 2 → t 1 Z) = 100% the on-Z SR16b plays the leading role in both compressed and non-compressed scenarios.T , the lepton p T spectra and the event yields by flavor category are shown.The background events containing top quark(s) in association with a W, Z or Higgs boson, except ttZ, or another pair of top quarks are denoted as ttX.The last bin includes the overflow events, and the hatched area represents the statistical and combined systematic uncertainties in the prediction.The lower panels show the ratio of the observed and predicted yields in each bin.For illustration the yields, multiplied by a factor 10, for two signal mass points in the T6ttHZ model, where the B( t 2 → t 1 H) = 100%, are displayed for non-compressed (m( t 2 ) = 700 GeV and m( t 1 ) = 175 GeV) and compressed (m( t 2 ) = 600 GeV and m( t 1 ) = 425 GeV) scenarios.T , the lepton p T spectra and the event yields by flavor category are shown.The background events containing top quark(s) in association with a W, Z or Higgs boson, except ttZ, or another pair of top quarks are denoted as ttX.The last bin includes the overflow events, and the hatched area represents the combined statistical and systematic uncertainties in the prediction.The lower panels show the ratio of the observed and predicted yields in each bin.For illustration the yields, multiplied by a factor 10, for two signal mass points in the T6ttHZ model, where the B( t 2 → t 1 Z) = 100%, are displayed for non-compressed (m( t 2 ) = 700 GeV and m( t 1 ) = 175 GeV) and compressed (m( t 2 ) = 600 GeV and m( t 1 ) = 550 GeV) scenarios.).The excluded regions are to the left and below the observed and expected limit curves.The color scale indicates the excluded cross section at a given point in the mass plane.plane for T6ttWW simplified model.The mass of the neutralino is set to 50 GeV.The descriptions of the excluded regions and color scale are the same as in Fig. 5.

Conclusions
A search for physics beyond the standard model in final states with at least three electrons or muons in any combination, jets, and missing transverse momentum has been presented using data collected by the CMS detector in 2016 at √ s = 13 TeV, corresponding to an integrated luminosity of 35.9 fb −1 .The analysis makes use of control regions in data to estimate reducible backgrounds and to validate simulations used to estimate irreducible background processes.To maximize sensitivity to a broad range of possible signal models, 46 exclusive signal regions are defined.No significant deviation from the expected standard model background is observed in any of these signal regions.
The results are interpreted using a simplified gluino-pair production model that features cascade decays producing four top quarks and two neutralinos.In this model, gluinos with a mass up to 1610 GeV are excluded in the case of a massless LSP.The maximum excluded LSP mass is 900 GeV.This represents an improvement of approximately 435 and 250 GeV, respectively, compared to the exclusion limit set in a similar search based on data collected with the CMS detector in 2015, corresponding to an integrated luminosity of 2.3 fb −1 [39].
For the simplified model of gluino-gluino production with decay to light-flavor quark jets, two vector bosons and neutralinos, gluino masses up to 1160 GeV and neutralino masses up to 680 GeV can be excluded.The limit on gluino and neutralino masses extends the corresponding limit from the previous analysis by about 335 and 180 GeV, respectively.
For a simplified model of bottom squark pair production decaying to top quarks, W bosons and neutralinos, bottom squark masses up to 840 GeV are excluded for a low mass chargino, while chargino masses are excluded up to 750 GeV.These extend the previous limits by 380 GeV for each particle.
Finally, for a simplified heavy top squark pair production model with further decays to two top quarks, Higgs or Z bosons, and neutralinos, the t 2 mass is excluded up to 720, 780, and 710 GeV for models with an exclusive t 2 → t 1 H decay, an exclusive t 2 → t 1 Z decay, and an equally probable mix of those two decays, while the t 1 mass is excluded up to 430, 540, and 450 GeV for the same branching fractions.This significantly improves the results obtained with the 8 TeV dataset [36].

Figure 2 :
Figure 2: Background prediction and the observed event yields in the key observables for the off-Z baseline selection: the number of jets and b jets, H T , M T , p missT , the lepton p T spectra and the event yields by flavor category are shown.The background events containing top quark(s) in association with a W, Z or Higgs boson, except ttZ, or another pair of top quarks are denoted as ttX.The last bin includes the overflow events, and the hatched area represents the statistical and combined systematic uncertainties in the prediction.The lower panels show the ratio of the observed and predicted yields in each bin.For illustration the yields, multiplied by a factor 10, for two signal mass points in the T6ttHZ model, where the B( t 2 → t 1 H) = 100%, are displayed for non-compressed (m( t 2 ) = 700 GeV and m( t 1 ) = 175 GeV) and compressed (m( t 2 ) = 600 GeV and m( t 1 ) = 425 GeV) scenarios.

Figure 3 :
Figure 3: Background prediction and the observed event yields in the key observables of the on-Z baseline selection: the number of jets and b jets, H T , M T , p missT , the lepton p T spectra and the event yields by flavor category are shown.The background events containing top quark(s) in association with a W, Z or Higgs boson, except ttZ, or another pair of top quarks are denoted as ttX.The last bin includes the overflow events, and the hatched area represents the combined statistical and systematic uncertainties in the prediction.The lower panels show the ratio of the observed and predicted yields in each bin.For illustration the yields, multiplied by a factor 10, for two signal mass points in the T6ttHZ model, where the B( t 2 → t 1 Z) = 100%, are displayed for non-compressed (m( t 2 ) = 700 GeV and m( t 1 ) = 175 GeV) and compressed (m( t 2 ) = 600 GeV and m( t 1 ) = 550 GeV) scenarios.

Figure 4 :
Figure4: Background prediction and observed event yields in the 23 off-Z (left) and the 23 on-Z (right) signal regions.The background events containing top quark(s) in association with a W, Z or Higgs boson, except ttZ, or another pair of top quarks are denoted as ttX.The hatched area represents the statistical and systematic uncertainties on the prediction.The lower panels show the ratio of the observed and predicted yields in each bin.For illustration the yields, multiplied by a factor 10, for t 2 → t 1 H (left) and t 2 → t 1 Z (right) decays are displayed for two signal mass points in the T6ttHZ model to represent compressed and non-compressed scenarios.

Figure 5 : 1 = m χ 0 2 =
Figure 5: Cross section upper limits at 95% CL in the m χ 0 1 versus m g plane for T1tttt (left) and T5qqqqVV (right) simplified models.For the latter model the branching fraction of gluino decay to neutralino or chargino is equal to 1/3 and m χ ± 1 = m χ 0 2 = 0.5(m g + m χ 0 1 limit on cross section[pb]

Figure 6 : 1 versus m b 1
Figure 6: Cross section upper limits at 95% CL in the m χ ± 1 versus m b 1 plane for T6ttWW simplified model.The mass of the neutralino is set to 50 GeV.The descriptions of the excluded regions and color scale are the same as in Fig. 5.
limit on cross section[pb]

Figure 7 :
Figure7: Cross section upper limits at 95% CL in the m t 1 versus m t 2 plane for T6ttHZ simplified model.Different branching fractions of the decay t 2 → t 1 Z are considered: 0% (top left), 50% (top right), and 100% (bottom).The mass difference between the lighter top squark ( t 1 ) and a neutralino is close to the mass of the top quark.The descriptions of the excluded regions and color scale are the same as in Fig.5.

Table 1 :
Summary of all requirements used in baseline selection criteria.

Table 4 :
The effect of the systematic uncertainties on the event yields of the backgrounds and signal processes.

Table 5 :
Expected and observed yields in the off-Z search regions.The first uncertainty states the statistical uncertainty, while the second represents the systematic uncertainty.

Table 6 :
Expected and observed yields in the on-Z search regions.The first uncertainty states the statistical uncertainty, while the second represents the systematic uncertainty.