Search for pair production of second-generation leptoquarks at √s = 13 TeV

A search for pair production of second-generation leptoquarks is performed using proton-proton collision data collected at $\sqrt {s} = 13$ TeV in 2016 with the CMS detector at the CERN LHC, corresponding to an integrated luminosity of 35.9 $fb^{−1}$. Final states with two muons and two jets, or with one muon, two jets, and missing transverse momentum are considered. Second-generation scalar leptoquarks with masses less than 1530(1285) GeV are excluded for β=1.0(0.5), where β is the branching fraction for the decay of a leptoquark to a charged lepton and a quark. The results of the search are also interpreted as limits on the pair production of long-lived top squarks in an R-parity violating supersymmetry model that has a final state with two muons and two jets. These limits represent the most stringent limits to date on these models.

A search for pair production of second-generation leptoquarks is performed using proton-proton collision data collected at ffiffi ffi s p ¼ 13 TeV in 2016 with the CMS detector at the CERN LHC, corresponding to an integrated luminosity of 35.9 fb −1 . Final states with two muons and two jets, or with one muon, two jets, and missing transverse momentum are considered. Second-generation scalar leptoquarks with masses less than 1530(1285) GeV are excluded for β ¼ 1.0ð0.5Þ, where β is the branching fraction for the decay of a leptoquark to a charged lepton and a quark. The results of the search are also interpreted as limits on the pair production of long-lived top squarks in an R-parity violating supersymmetry model that has a final state with two muons and two jets. These limits represent the most stringent limits to date on these models. DOI: 10.1103/PhysRevD.99.032014

I. INTRODUCTION
The standard model (SM) of particle physics displays a symmetry between the quark and lepton families. Leptoquarks (LQs) are new bosons that would manifest a fundamental connection between quarks and leptons and are predicted by numerous extensions of the SM, such as grand unified theories [1][2][3][4][5][6][7][8], composite models with lepton and quark substructure [9], technicolor models [10][11][12], and superstring-inspired models [13]. LQs are color-triplet scalar or vector bosons carrying both lepton and baryon numbers, and they decay either to a charged lepton and a quark or to a neutrino and a quark. Interpretations of direct searches for LQs are typically based on a general model where LQ-lepton-quark interactions are added to the Lagrangian [14]. Recently, interest in LQs has increased as they may provide an explanation for the observation of anomalies in the decays of B mesons by the Belle [15][16][17], BABAR [18,19], and LHCb [20][21][22][23] collaborations.
At hadron colliders, LQs can be produced singly or in pairs. This analysis concentrates on pair production of scalar LQs. The dominant leading-order (LO) processes for pair production of LQs at the LHC involve gluon-gluon fusion and quark-antiquark annihilation, shown in Fig. 1.
The interactions of scalar LQs with SM particles are completely determined by three parameters [14]: the LQ mass m LQ , the Yukawa coupling at the LQ-lepton-quark vertex λ LQ , and the branching fraction β of the LQ decay to a charged lepton and a quark. The decay of a LQ to a neutrino and a quark is complementary to the decay to a charged lepton and a quark and has a branching fraction of 1 − β. Vector LQs are further dependent on two couplings which relate to the anomalous magnetic and electric quadrupole moments of the vector LQ [24].
As can be seen in Fig. 1, the dominant pair production processes have no LQ-lepton-quark vertices, and thus the production cross sections do not depend on λ LQ . The mean lifetime of the LQ is dependent on λ LQ .F o rλ LQ ≳ 10 −6.5 [14], TeV-scale LQs will have decay lengths that are less than the resolution of the impact parameter measurement of the CMS detector [25]. As is customary, the value of λ LQ has been set such that λ 2 LQ =ð4πÞ¼α em , where α em is the electromagnetic coupling. Therefore the LQs considered in this analysis always decay very close to the point of production and are referred to as prompt. As a consequence, the limits set on the pair production cross sections can be considered independent of λ LQ for λ LQ ≳ 10 −6.5 .
Pair production of LQs is characterized by final states with two leptons and two jets with large transverse momentum p T . This analysis assumes no flavor mixing between generations, to be consistent with experimental constraints on lepton flavor violation and flavor-changing neutral currents [26,27]. In this scenario, second-generation LQs will always decay to either a muon and a charm quark or to a neutrino and a strange quark. Values of 1.0 and 0.5 are considered for β, corresponding to maximal production of the two final states μμjj and μνjj. Previous limits on second-generation scalar LQ pair production have been published by the CMS and ATLAS collaborations [28,29]. The CMS result excludes LQs with m LQ < 1080ð760Þ GeV for β ¼ 1.0ð0.5Þ, in proton-proton (pp) collisions at 8 TeV, and ATLAS excludes LQs with m LQ < 1160 GeV for β ¼ 1.0, at 13 TeV. The most stringent limits on vector LQs have been reported by CMS [28].
Other models of physics beyond the SM, such as R-parity violating (RPV) supersymmetry (SUSY) [30], can lead to the same final states as LQ production. Supersymmetry postulates a symmetry between fermions and bosons, which gives rise to superpartner particles for all known SM particles. In some SUSY scenarios, one of the two top quark superpartners (top squark,t) is the lightest SUSY particle and when R-parity is violated can decay to a bottom (b) quark and a charged lepton. Fort pair production and directt decays to a charged lepton + b quark, limits can be extracted directly from the LQ results. If the couplings of the RPV operators are sufficiently small, however, the superpartners will have long lifetimes and will travel through part or all of the detector before decaying. In this scenario, referred to in this paper as displaced SUSY [31],thet has a finite but nonzero lifetime and decays to a charged lepton of any flavor and a bottom quark within a distance, cτ, between 0.1 and 100 cm, where τ is thet mean lifetime. We assume thet decays with equal probability to electrons, muons, and tau leptons. This analysis is sensitive to the low-lifetime, high-mass region of phase space where dedicated searches for displaced SUSY lose sensitivity [32].

II. 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. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter, each composed of a barrel and two end cap sections. Forward calorimeters extend the pseudorapidity coverage provided by the barrel and end cap detectors. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. 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 Ref. [33].
Events of interest are selected using a two-tiered trigger system [34]. The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a time interval of less than 4 μs. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing and reduces the event rate to around 1 kHz before data storage.

III. DATA AND SIMULATED SAMPLES
The dataset used in this paper was collected by CMS during the 2016 pp LHC run at ffiffi ffi s p ¼ 13 TeV and corresponds to an integrated luminosity of 35.9 AE 0.9 fb −1 [35]. Events are selected using triggers that require at least one muon with p T > 50 GeV, with no isolation requirements. These triggers supply the data for the μμjj and μνjj channels, as well as for the eμ sample used in the tt þ jets background estimate for the μμjj channel. Signal samples are produced in 50 GeV steps for scalar m LQ between 200 and 2000 GeV using an effective theory based on Ref. [14] at LO with PYTHIA 8.212 [36]. These samples are used to study the acceptance of the signal. The production cross sections, calculated using next-to-leadingorder (NLO) QCD corrections [37] with the CTEQ6L1 [38] LO and CTEQ6.6 [39] NLO parton distribution function (PDF) sets, are used for comparison with data in the limit setting procedure. The search limits are independent of λ LQ for sufficiently large values of λ LQ , as discussed in Sec. I. Displaced SUSY samples are produced with PYTHIA 8.212 using the Snowmass "Points and Slopes point 1a" parameter set [40] fort masses from 200 to 1200 GeV, in 100 GeV steps, and for cτ ¼ 0.1, 1, 10, and 100 cm. The lighter, left-handed top squark is the lightest A. M. SIRUNYAN et al. PHYS. REV. D 99, 032014 (2019) supersymmetric particle (LSP) in this model, while the heavier right-handed top squark has a mass beyond the relevant kinematic regime. Production cross sections fort are calculated at NLOþ next-to-leading logarithmic (NLL) precision with PROSPINO version 2 [41] and NLL-fast programs version 3.0 [42,43], using the CTEQ6L1 PDF set. Standard model backgrounds considered include Z=γ Ã þ jets, tt þ jets, W þ jets, single top quark production, and diboson ðWW=WZ=ZZÞþjets. The Z=γ Ã þ jets, W þ jets, and diboson samples are generated at NLO using MADGRAPH5_aMC@NLO version 2.3.3 [44,45]. Single top quark and tt þ jets samples are generated at NLO using POWHEG v2 [46][47][48][49] and MADGRAPH5_aMC@NLO [50]. All backgrounds use PYTHIA 8.212 for fragmentation and hadronization.
Signal and background events are generated using the NNPDF3.0 PDF sets [63], with the full CMS detector geometry and response simulated using GEANT4 [64,65]. All samples use the CUETP8M1 underlying event tune [66], with additional pp interactions (the pileup distribution) overlaid and corrected to match the distribution measured in data.
The simulated samples are corrected so that the detector response and resolution for both leptons and jets and the triggering efficiency match those measured in data.

IV. EVENT RECONSTRUCTION AND SELECTION
The CMS particle-flow event algorithm [67] aims to reconstruct and identify each individual particle in an event, with an optimized combination of information from the various elements of the detector. 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 in this context are jets clustered using the jet finding algorithm with all tracks assigned to the vertex as inputs, and the associated missing transverse momentum ⃗p miss T , taken as the negative vector sum of the p T of those jets. The magnitude of the ⃗p miss T is referred to as p miss T . Hadronic jets are reconstructed using the anti-k T algorithm [68,69] with a size parameter of 0.4. Jet momentum is determined as the vectorial sum of all particle momenta in the jet, and it is found from simulation to be within 5% to 10% of the true momentum over the whole p T spectrum and detector acceptance. Additional pp interactions within the same or nearby bunch crossings can contribute additional tracks and calorimetric energy depositions, increasing the apparent jet momentum. To mitigate this effect, tracks identified to be originating from pileup vertices are discarded, and an offset correction is applied to correct for remaining contributions. 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 dijet, photon þ jet, Z þ jet, and multijet events are used to determine any residual differences between the jet energy scale in data and in simulation and appropriate corrections are made [70]. These jet energy corrections are propagated to the p miss T . Additional selection criteria are applied to each jet to remove jets potentially dominated by instrumental effects or reconstruction failures. Jets are required to have pseudorapidity jηj < 2.4, p T > 50 GeV and to be separated from all selected muons by ΔR>0.5, where ΔR ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðΔηÞ 2 þðΔϕÞ 2 p and ϕ is the azimuthal angle in radians. At least two jets are required for both the μμjj and μνjj channels, with no jet flavor requirement. Jets originating from b quarks are used to estimate backgrounds in data control regions, and they are identified using the combined secondary vertex algorithm [71]. Jets are considered as b-tagged if they pass the "loose" working point, with an 80% b jet identification efficiency and a 10% rate of erroneous b jet identification. Simulated samples are corrected on a jet-by-jet basis using correction factors to agree with b-tagged distributions measured in data.
Muons are measured in the pseudorapidity range jηj < 2.4 in concentric stations with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers. Hits in the muon tracking system are combined into hit segments. Muons are reconstructed as tracks by combining these hit segments with hits in the silicon tracker, with a reconstruction optimized for high p T muons. Matching muons to tracks measured in the silicon tracker results in a relative p T resolution for muons with p T < 100 GeV of 1% in the barrel and 3% in the end caps. The p T resolution in the barrel and end caps is better than 10% for muons with p T up to 1 TeV [72]. Muons are required to have p T > 53 GeV and jηj < 2.4 to be fully efficient with respect to the trigger, and they are required to satisfy a set of identification criteria optimized for high p T . Segments in at least two muon stations are required to be geometrically matched to a track in the silicon tracker, with at least one hit from a muon chamber in each station included in the muon track fit. In order to suppress muons from hadron decays and to allow for a more precise p T measurement, at least five strip tracker layers with hits associated with the muon are required, and at least one hit in the pixel detector. To reject muons from cosmic rays, the transverse impact parameter of the muon track with respect to the primary vertex is required to be less than 2 mm, and the longitudinal distance of the track with respect to the SEARCH FOR PAIR PRODUCTION OF SECOND-… PHYS. REV. D 99, 032014 (2019) primary vertex is required to be less than 5 mm. An isolation requirement is imposed, as the signal produces isolated muons. The p T sum of all tracks from the primary vertex (excluding the muon track itself) in a cone of ΔR ¼ 0.3 around the muon track, divided by the muon p T ,i s required to be less than 0.1. This relative isolation is shown to be independent of pileup [72]. In the μμjj channel at least two muons are required, with no charge requirement. In the μνjj channel exactly one muon is required. Electrons are measured in the pseudorapidity range jηj < 2.5. The electron momentum is estimated by combining the energy measurement in the ECAL with the momentum measurement in the tracker. The momentum resolution for electrons with p T ≈ 45 GeV from Z → ee decays ranges from 1.7% to 4.5% [73]. In this analysis electrons are used as a control data sample for a tt þ jets background estimate in the μμjj channel, and electrons with p T > 53 GeV are vetoed in the μνjj channel to avoid overlap with this control region. With this high veto threshold the selection is kept as inclusive as possible for signal. The tt þ jets background is small in the mass region of interest, which is above 1 TeV.
The LQ candidates are reconstructed using the pairing where the two reconstructed masses are closest. In the μμjj channel the two highest p T muons and two highest p T jets that pass the selection criteria above are considered. Each muon is paired with a jet in the configuration that minimizes the LQ-LQ invariant mass difference. In the μνjj channel the two highest p T jets are considered together with the required single muon. The muon and ⃗p miss T are each paired with a jet in a similar manner to the μμjj channel, using instead the LQ transverse masses of the muon-jet and ⃗p miss T -jet systems, where in this case l represents the muon or neutrino in the decay. This method correctly matches the decay products of the two LQs in 50% to 70% of signal events, increasing with m LQ .

V. ESTIMATION OF STANDARD MODEL BACKGROUNDS
A. The μμjj channel The main backgrounds that can mimic the LQ signal in the μμjj channel are Z=γ Ã þ jets and tt þ jets events.
Backgrounds are estimated and validated using a selection dominated by background events, referred to as the preselection. The preselection applies criteria that are looser than any final selection. This preselection requires at least two muons with p T > 53 GeV and at least two jets with p T > 50 GeV. The muons are required to be separated from one another by ΔR>0.3. The invariant mass of the dimuon system (m μμ ) is required to be greater than 50 GeV, and the S μμjj T of the event is required to be greater than 300 GeV, where S μμjj T is defined as the scalar sum of the p T of the two jets and two muons in the event.
The Z=γ Ã þ jets background is estimated with events that satisfy the preselection, in a data control region around the Z peak that is not in the search region. The background shape is taken from simulation, which shows good shape agreement with the data in the control region. For normalization, the simulation is compared to data in a window 80 <M μμ < 100 GeV around the Z peak, and a measured data normalization scale factor of 0.98 AE 0.01ðstatÞAE 0.09ðsystÞ is applied to simulated events passing the final selection criteria. The systematic uncertainty is assigned to account for the dependence of the scale factor on event kinematic properties. All final selections require M μμ > 100 GeV, to reduce the Z=γ Ã background, and to maintain the separation of the control region from the search region.
The tt þ jets background is estimated using an independent eμ data sample. Events are selected that contain one electron and one muon, and must satisfy all requirements of the μμjj preselection, other than the normal two muon requirement. No charge requirement is placed on the electron and muon. This sample is corrected for differences between the μμ and eμ selection, such as those based on identification and isolation, as well as on trigger efficiency. The kinematic distributions of this sample are found to be in good agreement with the tt þ jets simulation, and use of the eμ control sample in data reduces the systematic uncertainties associated with this background.
Background contributions from single top quark, W þ jets, and diboson events are estimated from simulation. Background from QCD multijets is shown to be negligible using data control regions.
Background predictions are validated at the preselection level by comparing them with data. Good agreement is seen in all relevant kinematic distributions. Three kinematic variables are identified that have strong discrimination power between signal and background. In the μμjj channel, these variables are S μμjj T , m μμ , and m min μj , where m min μj is defined as the smaller of the two muon-jet invariant masses that represent the LQ and LQ candidates. A comparison of these main kinematic variables is shown in Fig. 2 at the preselection level.
B. The μνjj channel As in the μμjj channel, a background-dominated preselection is used to calculate and validate the SM background estimates. This preselection requires exactly one muon with p T > 53 GeV and at least two jets with p T > 50 GeV. The direction of the muon in the event is required to be separated from ⃗p miss T by Δϕ > 0.8, and the momentum vector of the highest-p T jet to be separated where S μνjj T is defined as the scalar sum of the p T of the two jets matched to leptons (l ¼ μ, ν), the muon, and the p miss T in the event. The main backgrounds that can mimic the LQ signal in the μνjj channel are W þ jets and tt þ jets events. Both backgrounds are calculated using simulated samples normalized to the number of events in two separated data control regions. They are estimated with events that, in addition to satisfying the μνjj preselection, also satisfy 70 <M μν T < 110 GeV. The events are then separated into two control regions, further enriched in their respective background processes, using b tagging. The W þ jets background control region requires no b-tagged jets, while the tt þ jets control sample requires at least one b-tagged jet. The W þ jets data normalization scale factor is found to be 0.93 AE 0.01ðstatÞ, and the tt þ jets data normalization scale factor is found to be 0.98 AE 0.01ðstatÞ. As the scale factors do not depend on the kinematic distributions, no further systematic uncertainty is applied. These data normalization scale factors are then applied to simulated events passing the final selections.
Backgrounds from single top quark, Z=γ Ã þ jets, and diboson events are estimated from simulation. Background from QCD multijets is shown to be negligible using data control regions.
After preselection, discriminating variables are identified, as with the μμjj channel. In the μνjj channel, these variables are S μνjj T , m μν T , and m μj , where m μν T and m μj are defined as the muon-⃗p miss T transverse mass and the muon-jet invariant mass for the combination that minimizes the LQ-LQ transverse mass difference. Distributions for these variables in events satisfying the preselection are shown in Fig. 3.

A. Final selection optimization
For both the μμjj and μνjj channels, the previously described kinematic variables identified as having strong discrimination power between signal and background are used to define a final selection for each m LQ . The signal-tobackground separation is optimized with a full threedimensional optimization using the Punzi significance [74] for a discovery potential of 5 standard deviations at 95% confidence level (C.L.). This method is optimal for both making a discovery and for setting limits, and it is valid in cases with low background event counts. In the μμjj channel, the m μμ is required to be greater than 100 GeV to exclude the background control region. In the μνjj channel, the m μν T is required to be greater than 110 GeV for the same reason. The lower bounds of the final selection criteria for the three variables are shown as a function of scalar m LQ in Fig. 4. The behavior of the different variable responses to the optimization can be attributed to the shapes of the signal distributions of the different variables, as seen in Figs. 2 and 3.

B. Systematic uncertainties
Systematic uncertainties in the LQ signal production cross sections vary from 14% to 50% across the full LQ mass range. They are estimated by varying the PDF eigenvectors within their uncertainties and the renormalization and factorization scales by factors of one-half and two.
Systematic uncertainties in the background yields and in the signal acceptance for both the μμjj and μνjj channels are calculated for each final selection by running the full analysis with separately varied detector quantities, particle momenta, or scale factors. These yields are compared to those for the nominal analysis, and the differences are propagated as log-normal nuisance parameters in the limit setting. The effects of these systematic uncertainties in signal acceptance and total background yield are shown for the μμjj and μνjj channels in Tables I  and II, respectively. Systematic uncertainties in the jet energy resolution and muon energy resolution are measured by smearing the jet and muon momenta, including high-p T specific corrections for muons [75]. Uncertainties due to the jet energy scale and the muon energy scale are estimated by propagating jet and muon energy corrections.
Uncertainties in the shapes of the main backgrounds are estimated by varying the factorization and normalization scales in the simulation by factors of 1=2 and 2. These uncertainties, which include the uncertainty in the extrapolation of the distributions of the final selection variables from the control to signal regions, are estimated for the Z=γ Ã þ jets, tt þ jets, W þ jets, and diboson backgrounds. In the μμjj channel the uncertainty in the Z=γ Ã þ jets background normalization is estimated by varying the normalization scale factor described in Sec. VA up and down by its statistical and systematic uncertainties added in quadrature. The uncertainty in the tt þ jets normalization is estimated by varying the μμ=eμ correction factor up and down by its statistical uncertainty. In the μνjj channel the uncertainties in the W þ jets and tt þ jets normalizations are estimated by varying the normalization scale factors described in Sec. VB up and down by their statistical uncertainties.
Other sources of systematic uncertainty considered are the luminosity measurement [35], muon identification and isolation [72], pileup [76], trigger efficiency, and track reconstruction efficiency. The uncertainty from the PDF prediction is estimated by varying the NNPDF3.0 eigenvectors within their uncertainties, following the PDF4LHC prescription [77,78]. A further uncertainty in the b tagging efficiency is applied only in the μνjj channel [71], where the control region is defined via b tagging. For most values of m LQ the systematic uncertainties are at the lower end of the range. The maximum values given in Tables I and II are only relevant for large values of m LQ , where the total uncertainty is dominated by the statistical uncertainty in the simulated background samples.

VII. RESULTS
A. Data comparison with background after final selection The data are compared to background predictions after the final selections have been applied. Comparisons of the kinematic distributions, after the final selection, for data and simulation for two m LQ hypotheses are shown in Fig. 5. No significant excess above the predicted background is seen for any m LQ , within uncertainties. The largest difference between data and the background estimate is a roughly two standard deviation excess in the μνjj channel for m LQ ¼ 950 GeV. Kinematic distributions of the small excess of events in this region do not look like signal events, lacking the characteristic mass peak expected of LQs. There is one high-S μμjj T event that can be seen in Fig. 5 (upper left) that merits mention. The background estimate for high-mass final selections for S μμjj T > 3000 GeV is 0.0 þ0.1 −0.0 .However,thiseventisunlike a signal event. In particular, the invariant masses of the two LQ candidates in this event are not compatible with LQ pair production.
Comparisons of background, data, and signal for each set of final selections can be seen in Figs. 6 and 7. The y axis shows the final selection event yields for each of the individual m LQ hypotheses shown on the x axis. All the bins are correlated in these plots, as the events selected for each m LQ are a strict subset of the events selected for the lower mass LQ. The product of acceptance and efficiency of the signal for all final selections, as well as detailed tables of the event counts in data, background, and signal, are shown in the Appendix.    Table I. All the bins are correlated, as the events selected for each m LQ are a strict subset of the events selected for the lower mass LQ. The hashed band represents the combined statistical and systematic uncertainty in the full background estimate.  Table II. All the bins are correlated, as the events selected for each m LQ are a strict subset of the events selected for the lower mass LQ. The hashed band represents the combined statistical and systematic uncertainty in the full background estimate.

B. Limit setting
Limits are set on the LQ pair production cross section σ as a function of scalar m LQ , using the asymptotic approximation [79] of the modified frequentist CL s approach [80,81], utilizing the ratio of the confidences in the signal+background to background hypotheses. The systematic uncertainties listed above are introduced as nuisance parameters in the limit setting procedure using log-normal probability functions. Uncertainties of a statistical nature are described by Γ distributions with widths determined by the number of events in simulated samples or observed in data control regions. These limits have been compared to the so-called "LHC-style" fully frequentist CL s limits [82] and are found to be in good agreement with the expected and observed limits for all final selections, but with slightly more conservative systematic uncertainties in the low background regime.
The 95% C.L. upper limits on σβ 2 or σ2βð1 − βÞ as a function of scalar m LQ are shown, together with the NLO predictions for the scalar LQ pair production cross section, in Fig. 8. Systematic uncertainties in the LQ signal production cross sections are shown as a band around the signal production cross section. By comparing the observed upper limit with the theoretical cross section values, second-generation scalar LQs with masses less than 1530 (1150) GeV are excluded under the assumption that β ¼ 1.0 ð0.5Þ, compared to the median expected limits of 1515(1260) GeV.
Limits are also set at 95% C.L. for β values from 0 to 1 for both the μμjj and μνjj channels, as well as for the combination of both channels. In the combination, all systematic uncertainties are treated as fully correlated and all statistical uncertainties are treated as fully uncorrelated. The resulting two-dimensional limit plot is shown in Fig. 9. The combination of the two channels improves the mass exclusion, particularly for low values of β. Using the combined channels, second-generation scalar LQs with masses less than 1285 GeV can be excluded for β ¼ 0.5, compared with an expected limit of 1365 GeV.
The results in the μμjj channel are also interpreted in the context of the displaced SUSY model described in Sec. I. Studies in both simulation and data have shown that tracking efficiency remains at ∼100% for the lifetimes and corresponding impact parameters considered [32], which allows interpretation of the results for a displaced signal to be made with the same final selections and systematic uncertainties as previously used for a prompt signal. The 95% C.L. expected and observed limits on the displaced SUSYt pair production cross section are shown in Fig. 10. The limits are presented in two dimensions as a function oft mass and lifetime. The expected and observed limits have been extrapolated to cτ ¼ 0 cm using the prompt LQ limits, taking into account the assumedt branching ratio,t → bμ ¼ 1=3. This extrapolation connects these results to the prompt kinematic range and is motivated by the fact that prompt top squark pair production is kinematically very similar to that for LQs. The observed exclusion limits are 1150, 940, and 305 GeV for cτ ¼ 0.1, 1.0, and 10.0 cm. Following the formulation in Ref. [83] these limits can be translated into lower bounds on the coupling strength of the RPV term in the SUSY Lagrangian, in this case λ 0 233 cosðθÞ, where cosðθÞ represents the mixing on the product of the scalar LQ pair production cross section and the branching fractions β 2 or 2βð1 − βÞ as a function of the second-generation m LQ obtained with the μμjj (upper) or μνjj (lower) analysis. The solid lines represent the observed limits, the dashed lines represent the median expected limits, and the inner dark green and outer light yellow bands represent the 68% and 95% confidence intervals. The σ theory curves and their blue bands represent the theoretical scalar LQ pair production cross sections and the uncertainties on the cross sections due to the PDF prediction and renormalization and factorization scales, respectively.

VIII. SUMMARY
A search has been presented for pair production of second-generation leptoquarks using proton-proton collision data collected at ffiffi ffi s p ¼ 13 TeV in 2016 with the CMS detector at the LHC, corresponding to an integrated luminosity of 35.9 fb −1 . Limits are set at 95% confidence level on the product of the scalar leptoquark pair production cross section and β 2 (2β½1 − β)i n the μμjj (μνjj) channels, as a function of the leptoquark mass m LQ . Second-generation leptoquarks with masses less than 1530(1285) GeV are excluded for β ¼ 1.0 ð0.5Þ,a n improvement of 370 (525) GeV compared to previously published results. Two-dimensional limits are set in the β-m LQ plane. The results in the μμjj search are interpreted in the context of an R-parity violating supersymmetry model with long-lived top squarks. These limits represent the most stringent limits to date on these models.

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 ( No. 123842, No. 123959, No. 124845, No. 124850 and No. 125105 (Hungary)

APPENDIX: EFFICIENCIES AND EVENT YIELDS
The product of signal acceptance and efficiency for optimized final selections as a function of m LQ in the μμjj (left) and μνjj (right) channels is shown in Fig. 11. Event yields at final selection level for the μμjj and μνjj analyses are shown in Tables III and IV, respectively.   [76] CMS Collaboration, Measurement of the inelastic protonproton cross section at ffiffi ffi s p ¼ 13 TeV, J. High Energy Phys.