Searches for pair production of charginos and top squarks in final states with two oppositely charged leptons in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search for pair production of supersymmetric particles in events with two oppositely charged leptons (electrons or muons) and missing transverse momentum is reported. 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 during the 2016 data taking period at the LHC. No significant deviation is observed from the predicted standard model background. The results are interpreted in terms of several simplified models for chargino and top squark pair production, assuming $R$-parity conservation and with the neutralino as the lightest supersymmetric particle. When the chargino is assumed to undergo a cascade decay through sleptons, with a slepton mass equal to the average of the chargino and neutralino masses, exclusion limits at 95% confidence level are set on the masses of the chargino and neutralino up to 800 and 320 GeV, respectively. For the top squark pair production, the search focuses on models with a small mass difference between the top squark and the lightest neutralino. When the top squark decays into an off-shell top quark and a neutralino, the limits extend up to 420 and 360 GeV for the top squark and neutralino masses, respectively.


Introduction
The standard model (SM) of particle physics has so far been able to describe a wide variety of phenomena with outstanding precision. However, the SM does not address the hierarchy problem between the Higgs boson mass and the Planck scale [1,2], and does not contain a dark matter candidate to explain cosmological observations [3][4][5]. Supersymmetry [6][7][8][9][10][11][12][13][14] is an extension of the SM that assigns a fermion (boson) superpartner to every SM boson (fermion). This theory can solve the hierarchy problem since the large quantum loop corrections to the Higgs boson mass, due mainly to the top quark, can be largely canceled by the analogous corrections from the top quark superpartner [15][16][17]. Moreover, if R-parity [18] is conserved, the lightest supersymmetric particle (LSP) is stable and, if massive, provides a good candidate for dark matter. This paper presents a search for supersymmetric particle production in final states with two oppositely charged (OC) leptons ( ) and missing transverse momentum stemming from the two LSPs. Only electrons (e) and muons (µ) are considered. The search targets two specific signal scenarios with chargino ( χ ± 1 ) and top squark ( t 1 ) pair production, using data from protonproton (pp) collisions at √ s = 13 TeV collected by the CMS experiment [19] at the CERN LHC in 2016, and corresponding to an integrated luminosity of 35.9 fb −1 .
The results are interpreted in terms of simplified supersymmetric model spectra (SMS) [20][21][22] scenarios. The search for chargino pair production considers, as a reference, a model ( Fig. 1, left) where the charginos decay into a lepton, a neutrino (ν), and the lightest neutralino ( χ 0 1 ) via an intermediate charged slepton ( χ ± 1 → ν → ν χ 0 1 ) or sneutrino ( χ ± 1 → ν → ν χ 0 1 ). The three generations of sleptons are assumed to be degenerate, with a mass equal to the average of the chargino and neutralino masses. The branching fractions (B's) of the chargino decays into charged sleptons or sneutrinos are assumed to be equal. Results are also interpreted in terms of a second model (Fig. 1, right), where each chargino decays into the lightest neutralino and a W boson. Searches for chargino pair production have been previously published by the CMS Collaboration in the context of the former scenario using 8 TeV collision data [23] and by the ATLAS Collaboration in the context of both scenarios using 8 TeV [24-26] and 13 TeV [27-29] collision data. The search for top squark pair production focuses on an SMS in which the top squark decays into a top quark and the lightest neutralino as shown in Fig. 2 (left). The analysis strategy is optimized for a compressed spectrum scenario where the mass difference (∆m) between the top squark and the lightest neutralino lies between the top quark and W boson masses m W < ∆m m t . In this regime, the top quarks are produced off-shell, giving rise to final states with low-momentum bottom quarks which often fail to be identified. Further interpretations of the results are given in terms of an additional model, where each of the pair-produced top squarks decays into a bottom quark and a chargino, which in turn decays into a W boson and the lightest neutralino, as shown in Fig. 2 (right). In this model, the mass of the chargino is assumed to be equal to the average of the top squark and neutralino masses. This work is complementary to another OC dilepton search published by the CMS Collaboration [30], aimed at testing models where ∆m > m t , which result in signatures with on-shell top quarks and higher momentum particles. With respect to that analysis, this search gains sensitivity in the compressed mass region by loosening the requirements on the jets from bottom quark hadronization and optimizing the signal event selection for the lower momentum carried by the neutralino LSPs. The CMS Collaboration has also published other searches targeting the same signal models in the final states with exactly one lepton [31] and with no leptons [32], with the latter also covering the four-body-decay of the top squark in the region ∆m < 80 GeV. The ATLAS Collaboration published several searches addressing these signal models using all three final states [33][34][35].  Figure 2: Simplified-models diagrams of the top squark pair production with two benchmark decay modes of the top squark: the left plot shows decays into a top quark and the lightest neutralino, while the right one displays prompt decays into a bottom quark and a chargino, further decaying into a neutralino and a W boson.
The paper is organized as follows: Section 2 introduces the experimental apparatus; Sections 3 and 4 describe the data and simulated event samples used in this search and the details on the reconstruction of the physics objects, respectively; Section 5 presents the general strategy of the analysis; Section 6 discusses the estimates of the contributions from SM processes to the selected events; Section 7 details the sources of systematic uncertainties for signal and background processes; Section 8 reports the results and their interpretation in terms of the considered SMS; and finally Section 9 summarizes the results of the search.

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. In the inner part of the solenoid volume is a silicon pixel and strip tracker, which reconstructs the trajectories of the charged particles up to a pseudorapidity |η| < 2.5. Outside the tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL) and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections, measure the energy of the particles in the region |η| < 3. Forward calorimeters extend coverage provided by the barrel and endcap detectors up to |η| < 5. The information from the tracker and calorimeter systems is merged to reconstruct electrons and hadronic jets. Muons are detected in gas-ionization chambers embedded in the steel flux-return The detector response to the generated events is simulated using a realistic model of the CMS detector based on GEANT4 [67] for SM processes, while for signal events a fast simulation (FASTSIM) [68] of the detector based on a parametrization of the average response to particles is used. Simulated events are subsequently reconstructed using the same algorithms as applied to data.
In order to model the effect of multiple interactions per bunch crossing (pileup), simulated events are mixed with minimum-bias events simulated with PYTHIA, and are reweighted in order to match the observed rate of multiple interactions.
The modeling and normalization of the main background processes are studied in data, as discussed in Section 6. The modeling of tt, tW, and WW production is studied in data control regions (CRs), and their normalization is determined via a maximum likelihood (ML) fit to data. The normalization of the yields of events from ttZ, WZ, ZZ, and Drell-Yan production is taken from simulation and corrected by the event rates measured in dedicated CRs.
To improve the modeling of jets from initial-state radiation (ISR) in simulated signal events, reweighting factors are applied, which make the distributions of observables for related SM processes in simulation agree with control samples in data. For chargino pair production, mediated by the electroweak interaction, the reweighting procedure is based on studies of p T balance in inclusive Z boson production events [69]. Events are then reweighted according to the total transverse momentum (p ISR T ) of the system of supersymmetric particles. The reweighting factors range between 1.18 at p ISR T ≈ 125 GeV and 0.78 for p ISR T > 600 GeV. A global reweighting is further applied in order not to alter the signal production cross section. As the top squark pair production occurs via strong interactions, a different set of reweighting factors is derived as a function of the multiplicity of ISR jets (N ISR jet ) in a sample of tt events selected by requiring an OC electron-muon pair and two jets identified as coming from bottom quark hadronization. The measured reweighting factors vary between 0.92 and 0.51 for N ISR jet between 1 and 6, with an additional scale factor applied to keep the total event yields invariant.

Event reconstruction
The particle-flow algorithm [70] aims to reconstruct and identify each individual particle in an event, with an optimized combination of information from the various elements of the CMS detector. The energy of photons is directly obtained from the ECAL measurement, corrected for zero-suppression effects. The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. The momentum of muons is obtained from the curvature of the corresponding track. The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for zero-suppression effects and for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energy.
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 jets, clustered using a jet finding algorithm [71,72] with the tracks assigned to the vertex as inputs, and the associated momentum imbalance in the transverse plane, taken as the negative vector p T sum of those jets.
The identification of the muons used in the analysis is based on the number of reconstructed energy deposits in the tracker and in the muon system, and on the fit quality of the muon track [73]. Electron identification relies on quality criteria of the electron track, matching between the electron trajectory and the associated cluster in the calorimeter, and shape observables of the electromagnetic shower observed in the ECAL [74]. The efficiency for the reconstruction and selection of the muons (electrons) is found to be 70-95 (30-75)% depending on their p T and η.
The lepton selection is further optimized to select leptons from the decays of W or Z bosons. The leptons are required to be isolated by measuring their relative isolation (I rel ), as the ratio of the scalar p T sum of the photons and of the neutral and charged hadrons within a cone of radius R = √ (∆φ) 2 + (∆η) 2 = 0.3 around the candidate lepton, and the p T of the lepton itself. The contribution of particles produced in pileup interactions is reduced by considering only charged hadrons consistent with originating from the primary vertex of the event, and correcting for the expected contribution of neutral hadrons from the pileup [73,74]. Leptons are considered to be isolated if their relative isolation I rel is found to be smaller than 0.12. A looser requirement of I rel < 0.4 is used to define a veto lepton selection. Candidate lepton trajectories are further required to be compatible with the primary interaction vertex by imposing constraints on their transverse (d 0 ) and longitudinal (d z ) impact parameters, and on the three-dimensional impact parameter significance (S d 3D ), computed as the ratio of the threedimensional impact parameter and its uncertainty. Both electrons and muons are required to satisfy the conditions |d 0 | < 0.05 cm, |d z | < 0.10 cm, and S d 3D < 4. Finally, electrons originating from photon conversions are rejected by requiring that the electron track not have missing hits in the innermost layers of the tracker, and not form a conversion vertex with any other candidate electron in the event [74].
For each event, hadronic jets are clustered from the PF reconstructed particles using the infrared and collinear-safe anti-k T algorithm [71,72] with a distance parameter of 0.4. The jet momentum is determined as the vectorial sum of all particle momenta in the jet, and is found in the simulation to be within 5 to 10% of its true value over the whole p T spectrum and detector acceptance. Jet energy corrections are derived from simulation to bring the measured response of jets to that of particle level jets on average. In situ measurements of the momentum balance in the dijet, multijet, photon+jet, and leptonically decaying Z+jet events are used to account for any residual difference in jet energy scale in data and simulation [75]. Additional quality criteria are applied to reject spurious jets from detector noise. Finally, the jets overlapping with any selected lepton within a cone of radius R < 0.4 are removed.
Jets originating from the hadronization of bottom quarks (b jets) are identified by the combined secondary vertex v2 b-tagging algorithm, using the medium operating point [76]. This requirement provides an efficiency for identifying b jets that increases from 50 to 70% for jets with p T from 20 to 100 GeV. The misidentification rate for jets originating from light quarks and gluons is about 1% in the same p T range.
The momentum imbalance of the event in the transverse plane is referred to as missing transverse momentum ( p miss T ) and it is defined as the negative vectorial p T sum of all PF candidates in the event, taking into account the energy corrections applied to the jets [77]. The magnitude of p miss T is denoted as p miss T . Differences have been observed in the modeling of the p miss T resolution in events simulated with FASTSIM and with the full detector simulation. To account for this effect, the acceptance for signal events is computed both using the p miss T at the generator level and after the event reconstruction. The average value of the two acceptances in each analysis bin is taken as the central value for the acceptance.
Simulated events are reweighted to account for differences with respect to data in the efficiencies of the lepton reconstruction, identification, and isolation requirements, and in the performance of b-jet identification. The values of the data-to-simulation scale factors differ from unity by less than 10% with typical efficiency corrections of 2-3 (5)% for the identification of leptons (b jets) with p T > 20 GeV and |η| < 2.4.

Search strategy
The search strategy is developed for two signal hypotheses: the chargino pair and top squark pair productions. The first signal hypothesis is studied along the whole (m χ ± 1 , m χ 0 1 ) mass plane, while for the second one the analysis is optimized on the compressed scenario, where the mass difference of the top squark and the lightest neutralino is in between the top quark and W boson masses. The searches involve the same techniques for the background estimation and the signal extraction, while they differ slightly in the signal region (SR) selection in order to improve their respective sensitivity.
The signal models are characterized by a common final state with two OC leptons and two lightest neutralinos contributing to large p miss T . Based on this, a general high-acceptance baseline selection is defined, requiring two OC isolated leptons with |η| < 2.4 and p T ≥ 25 (20) GeV for the leading (trailing) lepton. Events with τ leptons decaying into electrons or muons that satisfy the selection requirements are taken into account. To reduce the contributions from lowmass resonances, Z → ττ production, and nonprompt leptons from hadronic jets, the invariant mass m of the lepton pair is required to be greater than 20 GeV, and if both leptons have the same flavor (SF), m is further required to satisfy |m − m Z | > 15 GeV, where m Z is the Z boson mass. High p miss T (≥140 GeV) is required. Events are further rejected if they contain a third lepton with p T > 15 GeV, |η| < 2.4, and satisfying the veto lepton selection (as detailed in Section 4). A summary of the baseline selection is found in Table 1.

≥140 GeV
The SM processes that contribute most after the baseline selection are tt, tW, and WW production. For all these backgrounds, the lepton pair and p miss T come from a W boson pair. Consequently, we construct the variable m T2 [78], which generalizes the transverse mass (m T ) for a system with two invisible particles, by using the two leptons as the two visible systems, This observable reaches a kinematic endpoint at the m W for the considered backgrounds. Signal events, instead, present m T2 ( ) spectra without such an endpoint because of the additional contribution to the p miss T given by the neutralinos. The sensitivity of the analysis is further enhanced by dividing the SR in bins of p miss T . This allows the analysis not only to exploit the larger tails in the p miss T distribution of the signal events, but also to optimize the sensitivity to signals with different mass separation between the produced supersymmetric particle and the LSP. Each p miss T bin is in turn divided into events with SF and different flavor (DF) leptons to exploit the smaller contamination from WZ, ZZ, and Drell-Yan production of the latter.
The SRs are further subdivided based on the specific characteristics of each signal model. A veto on b-tagged jets is applied to reject tt, tW, and ttZ events in the chargino search. Selected events in the p miss T bins below 300 GeV are then split into two different subregions, depending on the presence of a jet with p T > 20 GeV and |η| < 2.4. This allows for a better discrimination between signal events and top quark background, which still contaminates the SRs after applying the b-tagged jet veto. Events with b-tagged jets are kept as a CR for the normalization of the background from tt and tW production (discussed in Section 6).
The final states produced in the top squark decays are characterized by the presence of two bottom quarks. When the difference in the mass of the top squark and the neutralino is close to the edge of the compressed region, ∆m m W , the bottom quarks are soft and give rise to jets with relatively low momentum that have a lower probability to be tagged. In this case, the top squark final states are similar to those from chargino pair production, and requiring a veto on b-tagged jets is again an effective strategy to define SRs with reduced contamination from tt, tW, and ttZ backgrounds. For signal scenarios with larger ∆m, instead, the b jets have higher momentum and the final states are more tt-like. Consequently, sensitivity to top squark production is enhanced by requiring a b-tagged jet to reduce the background from diboson and Drell-Yan events.
Another useful means to discriminate the top squark production from SM processes is given by the presence of high-p T jets from ISR in the events. The invisible particles (neutrinos and neutralinos) produced in the decay chain of the top squark in the compressed scenario are expected to be soft; events with harder neutralinos, however, can arise when the top squark pair system recoils against a high-p T ISR jet. In this hard ISR regime, background is still constrained by the kinematic m W endpoint in m T2 ( ), and can be effectively separated from the signal. Hard ISR events are selected by requiring that the leading jet satisfies p T > 150 GeV and is not b tagged. In order to favor the topology in which the jet recoils against the rest of the system, the ∆φ between the jet and the p miss T is required to be larger than 2.5 rad. This requirement is found to be effective in discriminating the top squark production from background events at high p miss T , and is therefore applied only for events with p miss T > 300 GeV.
A summary of the SRs for the chargino and top squark searches is given in Tables 2 and 3, respectively, indicating the p miss T range, the selection on the multiplicity of jets (N jets ) and b jets (N b jets ) in the event, and the ISR jet requirement. The observed distributions of some observables used to define the SRs are compared to SM expectations in Fig. 3. Tables 2 and 3 is further divided into seven m T2 ( ) bins of 20 GeV width, starting from 0 GeV and with the last bin collecting all events with m T2 ( ) > 120 GeV. A simultaneous ML fit to the m T2 ( ) distribution in all the SRs is then performed to extract the signal (as described in Section 8). Since the first m T2 ( ) bins have a low signal contribution, we exploit them to constrain the contributions of the dominant backgrounds in the SRs with one b-tagged jet (dominated by tt and tW production) and without b-tagged jets (where WW production becomes relevant) through the fit.     and the leading jet (required not to be b-tagged and with p T > 150 GeV, events missing this requirements are shown in the first bin), and multiplicity of b-tagged jets in the event. The last bin includes the overflow entries. In the bottom panel, the ratio of observed and expected yields is shown. The hatched band represents the total uncertainty in the background expectation, as described in Section 7. Table 2: Definition of the SRs for the chargino search as a function of the p miss T value, the bjet multiplicity and jet multiplicity. Also shown are the CRs with b-tagged jets used for the normalization of the tt and tW backgrounds. Each of the regions is further divided in seven m T2 ( ) bins as described in the last row.

Background estimation
The main contributions from SM processes to the SRs comes from tt, tW, and WW production. The normalization of these backgrounds is determined by the ML fit, as mentioned in Section 5. Their m T2 ( ) shape has a natural endpoint at the m W , and events enter into the relevant region for signal extraction (m T2 ( ) > 80 GeV) mainly due to detector resolution effects, whose contributions are not easy to model. For this reason, we study the modeling of the m T2 ( ) distribution for these processes in dedicated CRs in data described in Section 6.1. The contributions of the subleading ttZ, WZ, ZZ, and Drell-Yan backgrounds are also tested in CRs, where correction factors for their normalizations are extracted, as discussed in Section 6.2. Events from ttW, triboson, and H → WW production give minor contributions in the SRs, and the estimates for these processes are taken directly from simulation. Background contributions from rest of the SM processes are found to be negligible. The contribution of signal to any of the CRs used is found to be negligible compared to SM processes.

Modeling of m T2 ( ) in tt, tW, and WW events
The simulated m T2 ( ) distributions for tt, tW, and WW backgrounds are validated in two CRs.
To construct the first one, the baseline selection is modified by requiring 100 < p miss T < 140 GeV. The events in this CR are further separated according to their b-jet multiplicity to define two sub-regions with different content in top quark (tt and tW) and WW backgrounds. In order to reject events from Drell-Yan production, only DF events are considered. The second CR aims at validating the modeling of the m T2 ( ) distributions in events with p miss T > 140 GeV. For this purpose, we select events from WZ → 3 1ν production and emulate the m T2 ( ) shape of WW and top quark events. We take the lepton from the Z boson with the same charge as the lepton from the W boson, and we add its p T vectorially to p miss T , effectively treating it like a neutrino. These events are selected by requiring three leptons and vetoing the presence of a fourth lep-ton passing the lepton veto requirements. A veto is applied to events with b-tagged jets to remove residual tt events. Among the three leptons, a pair of OC SF leptons with an invariant mass within 10 GeV of the Z boson mass is required to identify the Z boson. The simulation is found to describe the data well in the CRs. Based on the statistical precision of these CRs, a conservative uncertainty of 5, 10, 20, and 30% is taken for the bins 60 ≤ m T2 ( ) < 80 GeV, 80 ≤ m T2 ( ) < 100 GeV, 100 ≤ m T2 ( ) < 120 GeV, and m T2 ( ) ≥ 120 GeV, respectively. These uncertainties are applied to top quark and WW production, and treated as uncorrelated between the two types of backgrounds.
Another potential source of mismodeling in the tails of the m T2 ( ) distributions arises from nonprompt leptons originating, for instance, from semileptonic decays of B hadrons in b jets or from hadronic jets accidentally passing the lepton selection. The value of m T2 ( ) in tt, tW, and WW events with one nonprompt lepton replacing a prompt one failing the selection requirements will not be bound by the m W endpoint. The contribution of these events is found to be less than 1% of the expected background across the different SRs. It becomes more relevant only at large values of m T2 ( ) and p miss T , where it constitutes up to 20% of the tt background. We study the modeling of the rate of nonprompt leptons in simulation by selecting events with two leptons with the same charge and at least one b-tagged jet. The dominant contribution to this sample comes from tt events with a nonprompt lepton. Based on the observed agreement with data, a correction factor of 1.08 ± 0.21 is derived for the nonprompt lepton rate in simulation.

Normalization of ttZ, WZ, ZZ, and Drell-Yan backgrounds
The production of ttZ events where the two W bosons decay leptonically and the Z boson decays into neutrinos leads to final states with the same experimental signature as the signal events and with no natural endpoint for the reconstructed m T2 ( ) distribution, due to the additional contribution of the neutrinos from the Z boson decay to the p miss T . The normalization of this background is validated in events with three leptons, p miss T > 140 GeV, and at least two jets with p T > 20 GeV, of which at least one is tagged as b jet. At least one pair of OC SF leptons with an invariant mass not further than 10 GeV from the Z boson mass is also required. A normalization scale factor of 1.44 ± 0.36 for ttZ production is measured comparing the observed and predicted numbers of events.
Events from WZ production enter the signal event selection when both bosons decay leptonically and one of the three decay leptons fails the veto lepton requirements. We test the modeling of this source of background in a CR with three leptons, p miss T > 140 GeV, and no b-tagged jets, and derive a normalization scale factor of 0.97 ± 0.09 for the simulated WZ background.
The ZZ background is dominated by events with one boson decaying into charged leptons and the other one decaying into neutrinos. This contribution is studied by mimicking the ZZ → 2 2ν production via ZZ → 4 events, where the p T of one of the reconstructed Z bosons (randomly chosen between the ones satisfying the |m − m Z | < 15 GeV condition) is added to the p miss T . Events are selected by requiring four leptons, with one lepton allowed to pass the looser veto lepton requirement in order to increase the acceptance for ZZ production. The events are retained if the four leptons can be arranged into two pairs of OC SF leptons, both with an invariant mass within 30 GeV of the Z boson mass, and at least one within 15 GeV. A scale factor for the ZZ background normalization is derived in events with p miss T > 140 GeV and with no b-tagged jets. Since the chargino search uses separate SRs for events with or without jets, two corresponding scale factors are also measured, which suggest a higher jet multiplicity in data than in ZZ simulated events.
A summary of the scale factors derived in this section is given in Table 4. For all the quoted scale factors, uncertainties include the statistical uncertainties on data and simulated events, and the systematic uncertainties on the purity of the CRs.
Drell-Yan events can pass the baseline selection because of mismeasurements in p miss T . We study the modeling of this background in events with two OC SF leptons with |m − m Z | < 15 GeV, no additional leptons, and no b-tagged jets (Z boson events). The events with 100 < p miss T < 140 GeV are dominated by Drell-Yan production, and are used to derive a m T2 ( ) shape correction, which is subsequently tested in Z boson events with p miss T > 140 GeV. The correction ranges from a few percent at low m T2 ( ) to about 50% for m T2 ( ) > 100 GeV. An overall normalization uncertainty of 32% is also established by the observed disagreement between data and simulated events with 100 < p miss T < 140 GeV. Finally, the predictions for Drell-Yan events with no jets are tested in Z boson events with no jets and p miss T > 140 GeV: a conservative uncertainty of 100% in this contribution is applied. The Drell-Yan production is a subdominant background in the SRs with no jets and this uncertainty has a negligible impact on the expected sensitivity for signal production. Table 4: Summary of the normalization scale factors for ttZ, WZ, and ZZ backgrounds in the SRs used for the chargino (a) and top squark (b) searches. Uncertainties include the statistical uncertainties of data and simulated event samples, and the systematic uncertainties in the purity of the CRs.

Process
Scale factors

Systematic uncertainties
Several sources of systematic uncertainty that affect both the normalizations and the m T2 ( ) shapes of the background and signal events are considered in the analysis.
• The overall uncertainty in the integrated luminosity is estimated to be 2.5% [79].
• The uncertainty on the measured trigger efficiency is 2%.
• Lepton identification and isolation efficiencies are corrected by data-to-simulation scale factors measured in Z → events. The corresponding uncertainties are typically smaller than 3% per lepton.
• The jet energy scale is varied by its uncertainty [75], and the changes are propagated to all the related observables in the event.
• The energy scale of the low-p T particles that are not clustered in jets is varied by its uncertainty, and the changes are propagated to the p miss T .
• The efficiencies and misidentification rates of the b-jet identification algorithms are also corrected by data-to-simulation scale factors measured in inclusive jet and tt events [76]. The respective uncertainties range between 1 and 6%, depending on the p T and η of the jets.
• The effect of the simulated data sample sizes on the modeling of the m T2 ( ) distributions is taken into account by treating the statistical uncertainty in each bin for each process as an additional uncorrelated uncertainty.
• Uncertainties in the renormalization and factorization scales, and PDFs are propagated by taking the largest changes in the acceptance when independently doubling and halving the renormalization and factorization scales, and when varying the choice of PDFs between the NNPDF3.0 replicas. The PDF uncertainties are not considered for signal models as they are found to be redundant, once the uncertainty in the ISR modeling is included.
The estimates of the SM backgrounds are also affected by specific uncertainties in the modeling of the different processes.
• A background normalization uncertainty is applied for each background separately. The normalizations of the tt, tW, and WW processes are determined by the ML fit, as described in Section 8. We assign a common normalization parameter for tt and tW events and another for WW production. No explicit normalization uncertainty is defined for tt and WW events, while a 10% uncertainty is set for the tW process to take into account its relative normalization with respect to the tt production. The uncertainties applied to ttZ (25%), WZ (9%), and ZZ (26%) in the SRs with 0 jets, 14% in the SRs with at least 1 jet, and 11% in the rest of the SRs) correspond to the scale factor uncertainties obtained in Section 6.2. Minor backgrounds (ttW, H → WW, triboson production) are assigned a conservative uncertainty of 50%. Finally, Drell-Yan events have a 100% normalization uncertainty in the SR with no jets and 32% in all other SRs.
• The modeling of the yields of events with no jets has been explicitly studied in Section 6.2 for ZZ and Drell-Yan production. For the other SM processes, we introduce a related uncertainty by adding two free parameters in the ML fit, scaling respectively the rate of events with no jets for diboson and b-enriched (tt, tW, ttZ, and ttW) backgrounds. The total number of expected events without b-tagged jets is constrained to remain invariant, so that only a migration of events between the SRs with and without jets is allowed.
• The modeling of the m T2 ( ) shapes in events with an endpoint at the m W (tt, tW, and WW) has been studied in Section 6.1: an uncertainty of 5, 10, 20, and 30% is assigned for the last four m T2 ( ) bins. • The choice of the set of NNLO/NLO K factors applied to the qq → ZZ events affects the modeling of the m T2 ( ) shape for the ZZ background (as described in Section 3). Relative variations range from 16% for m T2 ( ) < 20 GeV to about 2% for m T2 ( ) > 120 GeV and are taken as the uncertainties.
• The m T2 ( ) distribution in Drell-Yan events has been corrected by scale factors derived in bins of m T2 ( ) in the validation region 100 < p miss T < 140 GeV, as discussed in Section 6.2. The full size of the correction in each bin is taken as an uncertainty.
• The weight of events with nonprompt leptons in simulated samples is varied by the ±19% uncertainty in the correction factor derived in events with two same-charge leptons, as described in Section 6.1.
• The spectrum of top quark p T in tt events has been observed to be softer in data than in simulated events [80][81][82]. An uncertainty is derived from the observed variations when reweighting the tt events to the p T distribution observed in data.
Finally, additional uncertainties in the modeling of signal events are taken into account, mostly related to the performance of the event reconstruction in FASTSIM.
• The uncertainty in the lepton identification efficiency in events simulated with FAST-• The analogous uncertainty in the b-tagging efficiency in FASTSIM samples ranges between 0.2-0.5%.
• The p miss T modeling in FASTSIM events is studied by comparing the acceptances computed using the p miss T at the generator level and after the event reconstruction. Since the average of the two is taken as central value for the acceptance, half of their difference is taken as an uncertainty, fully correlated among bins.
• An uncertainty in the modeling of pileup events in FASTSIM signal samples is derived by studying the dependence of the acceptance on the multiplicity of primary vertices reconstructed in the event. This uncertainty varies from 0 to 10% across the SRs and m T2 ( ) bins. • Simulated signal events are reweighted to improve the modeling of the ISR, as described in Section 3. Uncertainties on the reweighting procedure are derived from closure tests. For chargino models, the deviation from unity is taken as the systematic uncertainty in the p ISR T reweighting factors. For top squark models, half of the deviation from unity in the N ISR jet factors is taken. Tables 5 and 6 summarize the systematic uncertainties in the predicted yields for SM processes and for two reference signals, respectively. Table 5: Sizes of systematic uncertainties in the predicted yields for SM processes. The first column shows the range of the uncertainties in the global background normalization across the different SRs. The second column quantifies the effect on the m T2 ( ) shape. This is computed by taking the maximum variation across the m T2 ( ) bins (after renormalizing for the global change of all the distribution) in each SR. The range of this variation across the SRs is given.   Table 5 for two representative signal points, one for chargino pair production and one for top squark pair production.

Source of uncertainty SM processes
Source of uncertainty   Tables 7-8 for all dilepton final states and all SRs. No excess over SM prediction is observed in data. The asymptotic approximation of the CL s criterion [83][84][85] is used to set upper limits at 95% confidence level (CL) on the production cross sections for the different signal models considered.

Results and interpretation
The 95% CL upper limits on the chargino pair production cross sections with the chargino decaying into sleptons are shown in Fig. 8 (left). The χ ± 1 → ν → ν χ 0 1 and χ ± 1 → ν → ν χ 0 1 decay chains are given a B of 50% each, and the sleptons are assumed to be degenerate, with a mass equal to the average of the chargino and neutralino masses. By comparing the upper limits with pp → χ + 1 χ − 1 production cross sections, observed and expected exclusion regions in the (m χ ± 1 , m χ 0 1 ) plane are also determined. Masses are excluded up to values of about 800 and 320 GeV for the chargino and the neutralino, respectively. Limited sensitivity is found when the chargino is assumed to decay into a W boson and the lightest neutralino, due to the relatively small B for the leptonic decay of the W boson. For this scenario, we derive upper limits on the chargino pair production cross section assuming a lightest neutralino mass of 1 GeV. Observed and expected upper limits as a function of the chargino mass are compared to theoretical cross sections in Fig. 8 (right).      < 300 GeV (middle), or p miss T > 300 GeV (lower), for DF events with b-tagged jets (left plots) and without b-tagged jets (right plots). The solid magenta histogram shows the expected m T2 ( ) distribution for top squark pair production with m t 1 = 350 GeV and m χ 0 1 = 225 GeV. Expected total SM contributions before the fit (dark blue dashed line) and after a background+signal fit (dark red dotted line) are also shown. The last bin includes the overflow entries. In the bottom panel, the ratio of data and SM expectations is shown for the expected total SM contribution after the fit using the background-only hypothesis (black dots) and before any fit (dark blue dashed line). The hatched band represents the total uncertainty after the fit.     cross section for the two SMS considered. While the search strategy has been optimized for a compressed scenario, the results are presented on the whole (m t 1 , m χ 0 1 ) plane for completeness. Also shown are the expected and observed exclusion regions when assuming NLO+NLL top squark pair production cross sections. When assuming the top squark to decay into a top quark and a neutralino, top squark (neutralino) masses are excluded up to about 420 (360) GeV in the compressed mass region where ∆m lies between the top quark and W boson masses. For the t 1 → b χ ± 1 → bW χ 0 1 decay mode, a lower bound ∆m ≈ 2 m W is set by the assumption that m χ ± 1 = (m t 1 + m χ 0 1 )/2. For ∆m ≈ 2 m W , top squark masses are excluded in the range 225-325 GeV. The uncovered region around a top squark mass of 200 GeV in Fig. 9 (right) corresponds to a signal phase space similar to that of tt events, with little contribution from the neutralinos to p miss T . In this situation, the uncertainty in the modeling of p miss T in FASTSIM events becomes too large to provide any signal sensitivity.

Summary
A search has been presented for pair production of supersymmetric particles in events with two oppositely charged isolated leptons and missing transverse momentum. The data used consist of a sample of proton-proton collisions collected with the CMS detector during the 2016 LHC run at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb −1 . No evidence for a deviation with respect to standard model predictions was observed in data. The results have been interpreted as upper limits on the cross sections of supersymmetric particle production for several simplified model spectra.   Chargino pair production has been investigated in two possible decay modes. If the chargino is assumed to undergo a cascade decay through sleptons, an exclusion region in the (m χ ± 1 , m χ 0 1 ) plane can be derived, extending to chargino masses of 800 GeV and neutralino masses of 320 GeV. These are the most stringent limits on this model to date. For chargino decays into a neutralino and a W boson, limits on the production cross section have been derived assuming a neutralino mass of 1 GeV, and chargino masses in the range 170-200 GeV have been excluded.
Top squark pair production was also tested, with a focus on compressed decay modes. A model with the top squark decaying into a top quark and a neutralino was considered. In the region where m W < m t 1 − m χ 0 1 m t , limits extend up to 420 and 360 GeV for the top squark and neutralino masses, respectively. An alternative model has also been considered, where the top squark decays into a chargino and a bottom quark, with the chargino subsequently decaying into a W boson and the lightest neutralino. The mass of the chargino is assumed to be average between the top squark and neutralino masses, which gives a lower bound to the mass difference (∆m) between the top squark and the neutralino of ∆m ≈ 2 m W . This search reduces by about 50 GeV the minimum ∆m excluded in the previous result with two leptons in the final state [30] from the CMS Collaboration, excluding top squark masses in the range 225-325 GeV for ∆m ≈ 2 m W .
In summary, by exploiting the full data set collected by the CMS experiment in 2016, this search extends the existing exclusion limits on the pair production of charginos decaying via sleptons [29], improving by about 70 GeV the limit on the chargino mass for a massless neutralino. Exclusion limits on the top squark pair production extend the results obtained by the CMS Collaboration in final states with two oppositely charged leptons [30] to the compressed region, where they are competitive with the results obtained by the ATLAS Collaboration in the same decay channel [35].

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: BMWFW and FWF (Aus [27] ATLAS Collaboration, "Search for the direct production of charginos and neutralinos in final states with tau leptons in √ s = 13 TeV pp collisions with the ATLAS detector", Eur. Phys. J. C 78 (2018) 154, doi:10.1140/epjc/s10052-018-5583-9, arXiv:1708.07875.
[29] ATLAS Collaboration, "Search for electroweak production of supersymmetric particles in final states with two or three leptons at √ s = 13 TeV with the ATLAS detector", (2018). arXiv:1803.02762. Submitted to Eur. Phys. J. C. [34] ATLAS Collaboration, "Search for top-squark pair production in final states with one lepton, jets, and missing transverse momentum using 36 fb −1 of √ s = 13 TeV pp collision data with the ATLAS detector", (2017). arXiv:1711.11520. Submitted to JHEP.