Search for charged-lepton flavor violation in top quark production and decay in pp collisions at s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s} $$\end{document} = 13 TeV

Results are presented from a search for charged-lepton flavor violating (CLFV) interactions in top quark production and decay in pp collisions at a center-of-mass energy of 13 TeV. The events are required to contain one oppositely charged electron-muon pair in the final state, along with at least one jet identified as originating from a bottom quark. The data correspond to an integrated luminosity of 138 fb−1, collected by the CMS experiment at the LHC. This analysis includes both the production (q → eμt) and decay (t → eμq) modes of the top quark through CLFV interactions, with q referring to a u or c quark. These interactions are parametrized using an effective field theory approach. With no significant excess over the standard model expectation, the results are interpreted in terms of vector-, scalar-, and tensor-like CLFV four-fermion effective interactions. Finally, observed exclusion limits are set at 95% confidence levels on the respective branching fractions of a top quark to an eμ pair and an up (charm) quark of 0.13 × 10−6 (1.31 × 10−6), 0.07 × 10−6 (0.89 × 10−6), and 0.25 × 10−6 (2.59 × 10−6) for vector, scalar, and tensor CLFV interactions, respectively.


JHEP06(2022)082
In the past few years, different measurements of B meson decays that involve leptons have hinted at the presence of possible small violations of lepton universality [14,15]. It has been pointed out [16] that models accommodating such levels of violation of lepton universality generally also lead to observable effects in lepton flavor violation. Moreover, physics models with solutions to the possible anomalies seen in the bottom quark sector predict similar effects in the top quark sector [17]. For example, certain leptoquark models can accommodate the observed deviation in the measurements of the branching fraction ratios of B → D * τ − ν τ relative to B → D * − ν τ (where = e or µ) [18,19]. These models would imply branching fractions of t → c reaching ≈ 10 −6 , with and representing different-flavor charged leptons. Searching for CLFV processes related to the top quark could therefore shed light on anomalies seen in B meson decays.
Assuming the mass scale of new physics responsible for CLFV processes is larger than the energy scale directly accessible at the LHC, CLFV interactions of top quarks are described through an effective Lagrangian consisting of dimension-six operators (O x ) weighted by the Wilson coefficients (C x ) over powers of the new mass scale (Λ), In the Warsaw basis of dimension-six operators, the following operators give rise to top quark CLFV interactions [20]: lequ + h.c, (1.11) where O vector represents the sum of the operators in eqs. (1.3)-(1.6). We probe three Wilson coefficients related to the operators, C vector , C scalar , and C tensor . The operators in eqs. (1.9)-(1.11) can lead to four-fermion interactions involving the top quark, the up or charm quark, and two leptons of different flavor. These four-fermion interactions open new top quark decay modes, e.g., t → q, where and are charged leptons with different flavors, and q is a u or c quark [22]. In addition to top quark decays, CLFV interactions at the LHC contribute to single top quark production in association with a pair of leptons of different flavor. Figure 1 displays representative Feynman diagrams for single top quark production and decay of the top quark in top quark-antiquark pair production (tt) via CLFV interactions.
Final-state signatures are determined by the lepton flavors and decay modes of the W boson from top quark decays. The W boson can decay either leptonically to a charged lepton and a neutrino or to two quarks that develop into jets via quantum chromodynamics (QCD) processes. Final states in which W bosons decay into quarks have cross sections larger than for leptonic decays. This analysis combines first searches for "eµtu" and "eµtc" CLFV interactions in top quark production with decays to the eµ final state at √ s = 13 TeV. We select signal events containing an oppositely charged eµ pair and a top quark that decays fully hadronically. The data used in the analysis correspond to an integrated luminosity of 138 fb −1 , collected by the CMS experiment at the LHC during 2016-2018. The top quark production mode via CLFV interactions plays a leading role in the sensitivity of the search compared to the decay mode. The result is interpreted in terms of limits on vector, scalar, and tensor four-fermion interactions originating from dimension-six operators within the framework of effective field theory.
The paper is organized as follows. Section 2 describes the main features of the CMS detector. Section 3 provides the details of the Monte Carlo (MC) simulations of signal and background. The event reconstruction is outlined in section 4. In section 5, we discuss -3 -

Simulation of background and signal
Monte Carlo events are used to estimate the SM backgrounds and samples are simulated through independent events generated for the years 2016, 2017, and 2018 so as to match the different data-taking conditions. The SM tt, single top quark production in association with a W boson (tW), and diboson events (including WW, WZ, and ZZ) are simulated at next-to-leading order (NLO) using the powheg v2 event generator [26][27][28][29]. All other background processes, including Drell-Yan processes produced with additional jets, a W boson with additional jets (W+jets), and W or Z bosons produced in association with tt (tt+Z/W) are simulated using the MadGraph5_amc@nlo v2.4.2 (v2.2.2 for 2016) generator [30].
The cross sections are calculated at the highest orders of perturbative QCD currently available. This corresponds to next-to-NLO (NNLO) for Drell-Yan and W+jets [31], approximate NNLO for single top quark in the tW channel [32], and NLO calculations for diboson [33] and tt+Z/W [34]. The SM tt events are normalized to their NNLO cross sections (832 +20 −29 (scale) ± 35 (PDF + α S ) pb) calculated with the Top++2.0 program [35], where PDF is the parton distribution function and α S is the strong coupling constant, assuming a top quark mass of 172.5 GeV. To improve the modeling of the transverse momentum (p T ) spectrum of the top quark in powheg, simulated SM tt events are weighted as a function of the p T of the top quark to match the expectations at NNLO QCD accuracy, including electroweak corrections [36].   [37,38], and then used in the Mad-Graph5_amc@nlo generator for the cross section calculation and event generation at leading order. The top quark CLFV signal has two components: (i) events from the production of SM tt followed by a CLFV decay of one of the top quarks, and (ii) single top quark production in association with an eµ pair via CLFV interactions, as shown in figure 1. Due to the fact that single top quark production via eµtu CLFV interactions is initiated by a u quark, and u quarks are mostly proton valence quarks with a very different Bjorken-x spectrum relative to sea quarks, the production rate and kinematic distributions of final-state particles are different than when a sea quark is involved in the interaction, as is the case for single top quark production via eµtc CLFV. Each component of signal is therefore generated independently for the eµtu and eµtc CLFV interactions. Events from the "eτtq" and "µτtq" CLFV interactions are not included in the signal samples. Since there is no interference between the SM and the signal processes, signal events are generated separately from the SM background. The new mass scale and the Wilson coefficients are arbitrarily chosen to be Λ = 1 TeV and C eµtq x = 1 for event generation. For SM tt production with top quark CLFV decay, the cross section is calculated using the SM tt cross section at NNLO times the branching fraction B(t → eµq), assuming Λ = 1 TeV and C eµtq x = 1 for both the u and c quarks [39]. Theoretical cross sections, for single top quark production and top quark decays via the vector, scalar, and tensor CLFV interactions are shown in For SM tt production, the CP5 tune is also used for 2016 data. Simulated minimum-bias events are added to the MC simulations to model the impact of additional pp interactions within the same or adjacent bunch crossing (pileup). Simulated events are then reweighted to reproduce the pileup distribution observed in data. All generated events undergo a full simulation of the detector response using Geant4 [45].

Event selection
Signal events contain an oppositely charged eµ pair together with multiple jets, one of which is expected to stem from the hadronization of a bottom quark that originates from the t → bW decay. The data for this analysis are collected using a combination of triggers designed to record events containing a single muon, a single electron, or an eµ pair passing isolation and identification criteria. For the single-electron (muon) trigger, at least one electron (muon) with p T larger than 27, 35, and 32 (24, 27, and 24) GeV is required for 2016, 2017, and 2018 data, respectively. The eµ trigger selects events having an electron with p T > 12 GeV and a muon with p T > 23 GeV, or an electron with p T > 23 GeV and a muon with p T > 8 GeV, in all years. The trigger efficiency within the detector acceptance is measured in data to be greater than 96% for events with at least an eµ pair. Events selected at the trigger level are reconstructed offline using the particle-flow (PF) algorithm [46], which identifies and reconstructs each individual particle in an event through an optimized combination of information from the various components of the CMS detector. The candidate 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 the jet finding algorithm (anti-k T ) [47, 48] with the tracks assigned to candidate vertices as inputs, and the associated missing transverse momentum, taken as the negative vector sum of the p T of those jets. Electron candidates are reconstructed from a combination of a track in the tracker and associated energy deposition in the ECAL [49]. They are required to have p T > 20 GeV and to lie within |η| < 2.4, except that candidates in the transition region between barrel and endcap calorimeters (1.44 < |η| < 1.57) are removed. A relative isolation requirement I rel < 0.05 is imposed where I rel is the scalar-p T sum of all neutral and charged hadron, and photon candidates within a distance of ∆R = (∆η) 2 + (∆φ) 2 < 0.3 from the axis of the electron candidate, divided by the p T of the electron candidate. In addition, stringent electron identification requirements are applied to reject misidentified electron candidates and candidates originating from photon conversions in the detector materials [49]. Muon candidates are reconstructed by associating tracks found in the muon system with tracks in the inner tracking systems [50]. They are required to have p T > 20 GeV and |η| < 2.4. The relative isolation requirement I rel < 0.15 is applied where I rel is calculated for all particles within a cone of radius ∆R < 0.4 from the muon trajectory. A correction to suppress a residual effect of the pileup is included [50]. Muon candidates must pass identification requirements [50]. In addition, some dedicated muon identification requirements are applied to reject misidentified muon candidates of large p T [51]. Electrons and muons are selected if they are compatible with originating from the primary vertex.
The PF candidates are clustered into jets using the anti-k T algorithm with a distance parameter R = 0.4. The charged hadron subtraction procedure [52] mitigates event by event the effect of tracks coming from pileup on the transverse energy of the jet. Jets are calibrated in simulation and separately in data, accounting for energy depositions from pileup and from imprecise detector response [53]. Jets with p T > 30 GeV and |η| < 2.4 are selected for further study. To prevent overlap between selected jets and selected leptons, jets that are found within a cone of ∆R < 0.4 around any of the selected leptons are -6 -removed from the selected set of jets. Jets originating from the hadronization of bottom quarks are identified ("b tagged") using deep machine learning algorithms [54] with an efficiency of 68% and a 1% misidentification rate for gluon and light-flavor quark jets. The missing transverse momentum vector p miss T is computed as the negative vector p T sum of all the PF candidates in an event, and its magnitude is denoted as p miss Events with an oppositely charged eµ pair and at least one jet are selected. The leading lepton must have p T > 25 GeV. Events are rejected if the invariant mass of the eµ pair is less than 20 GeV [56]. Since the top quark CLFV signal has one b quark, events are required to have at least one b tagged jet.

Signal extraction
The contributions from the SM are estimated using the simulated events introduced in section 3 normalized to the integrated luminosity of the data. After requiring at least one b tagged jet, the dominant source of background originates from SM tt events, which contribute ≈90% of the total background. To control this background, events are subdivided according to the number of b tagged jets, irrespective of the number of untagged jets. The signal region includes events with one b tagged jet while events with at least two such jets are assigned to the tt control region. The numbers of events with one and greater than one b tagged jets are shown in table 2, together with the expected number of background events in the combined Run-2 data. The overall number of events is well described by the expectations in both regions. In table 2, we give the expected number of events for single top quark production and top quark decay in the signal channels (cf. figure 1), assuming C x /Λ 2 = 1 TeV −2 . Signal channels are further categorized by the CLFV interaction (vector, scalar, or tensor) and the u or c quark flavor.
The background in the signal region consists mostly of SM tt events where both W bosons decay leptonically. Several differences between the signal and the SM tt events are used to construct a discriminating observable. For example, the sources of p miss T in signal events are due to detector resolutions, while SM tt events have genuine p miss T produced by neutrinos from the W boson decays. Leptons in SM tt events arise from the decay of W bosons and have different angular separations and energy spectra relative to signal dilepton events. Furthermore, signal events have a larger number of light-flavor quark jets because of the multijet top quark decays in signal events. To maximize the sensitivity of the search, a boosted decision tree (BDT) that combines several discriminating variables is defined in the toolkit for multivariate analysis [57] and used to distinguish signal from SM tt events.
The BDT uses 5 variables: the p T of the leading lepton (p 1 T where refers to e or µ), the p T of the leading jet, the distance between the electron and muon [∆R(e, µ) = (η e − η µ ) 2 + (φ e − φ µ ) 2 ], p miss T , and the number of jets. Figures 2 and 3 provide distributions of the BDT input variables in data and simulations for signal and tt control regions. A good description of the data is observed for the background model. The leading lepton distribution is somewhat softer in data, although it is within the estimated systematic uncertainties after p T reweighting of simulated SM tt events to the most precise cross section available (cf. section 3) [56].      The CLFV single top quark production and top quark decay events, weighted according to their cross sections, are compared against the SM tt events in the BDT training. The BDT is trained and tested on independent samples with no evidence of overtraining or bias. As shown in table 2, the CLFV single top quark production channel has higher yields than the CLFV top quark decay channel in all signal samples. In addition, events from the CLFV single top quark production channel result in higher p T on average for the final-state particles when compared to the CLFV decay channel. Therefore, events from the CLFV single top quark production channel play a leading role in the BDT discrimination. The vector, scalar, and tensor CLFV samples show similar distributions in the selected BDT input variables. A single BDT is therefore trained using all signal samples in the region with one b tagged jet, and is used to probe all of the CLFV Wilson coefficients. To control the background uncertainties in the fit, the trained BDT in the signal region is used in the tt control region.  The three mentioned sources of modeling uncertainties are considered for both signal and SM tt processes. In addition, uncertainties originating from the scheme used to match the ME-level calculation to the parton-shower (PS) simulation, the modeling of the underlying event defined in pythia tunes (UE tune), and the models of color reconnection for the SM tt process according to what is described in ref. [ Table 3. Summary of representative systematic uncertainties in selection efficiency for the SM tt process and for single top quark production and decays via vector eµtu CLFV interactions in the signal plus tt control regions.
The systematic uncertainties in signal and SM tt selection efficiencies are summarized in table 3. The largest uncertainty is from the b tagging SF since we have used SFs that are measured in inclusive multijet samples instead of dilepton tt events to reduce a potential bias. Although only a representative signal sample is shown in table 3, all signal samples have similar uncertainties. Except the uncertainties in total integrated luminosities and background normalizations, all other uncertainties affect both the background rate and the shape of the BDT distributions.

Results
The final BDT discriminant distributions for the three data-taking years and two data regions (signal region and tt control region) are jointly used to test for the presence of signal events. A binned likelihood function L(µ, θ) constructed as a product of Poisson probability terms over all bins is used for the statistical analysis where µ is the signal-strength parameter and θ is a set of nuisance parameters. The parameter of interest, µ, changes the cross sections of both signal channels, top quark CLFV production and decay, by exactly the same scale. The cross sections of both signal channels depend quadratically on the CLFV Wilson coefficients. Since our signal samples are normalized to the cross sections at Post-fit Data/Pred.  The BDT output distributions for data (points) and backgrounds (histograms) with the ratio of data to the total background yield, before (middle panel) and after (lower panel) the fit. Events in the signal region (one b tagged jet) and tt control region (more than one b tagged jets) are shown in the left and right column, respectively. The hatched bands indicate the total uncertainty (statistical and systematic taken in quadrature) for the SM background predictions (cf. section 6). Examples of the predicted signal contribution for the vector type CLFV interactions via eµtu and eµtc vertices are shown, assuming C x /Λ 2 = 1 TeV −2 . The signal production-and decay-mode contributions are summed. The eµtc signal cross section is scaled up by a factor of 10 for improved visualization.
√ µ and C x /Λ 2 are equivalent parameters. All the systematic uncertainties defined in section 6 are treated as nuisance parameters θ, assuming a log normal prior for normalization parameters, and Gaussian priors for BDT shape uncertainties. The uncertainties due to the limited number of simulated events used for signal and background expectations are taken into account using "the Barlow-Beeston lite" method [66]. The data are found to be consistent with expectations of the SM in the absence of signal. The observed distributions of the BDT discriminant, together with the SM background expectations, before and after a fit to signal plus background hypothesis are shown in figure 4.
Upper limits on the production cross section for signal are set at 95% confidence level (CL) using the modified frequentist CL s method [67, 68], with a likelihood ratio as a test statistic. The limit setting procedure is performed for a given individual Wilson coefficient (C vector , C scalar , or C tensor ) while the other Wilson coefficients are set to zero. Consequently, upper limits on the Wilson coefficients are translated to limits on the related top quark CLFV branching fractions [39]. Limits obtained for vector-, scalar-and tensor-like interactions are summarized in table 4. The measured one-dimensional exclusion limits are also interpreted for the scenario of the non-vanishing eµtu and eµtc CLFV couplings via a linear interpolation.  The limit obtained on the tensor CLFV Wilson coefficient is more stringent than those on scalar and vector coefficients because of its larger relative production cross section, as presented in table 2. Tabulated results are provided in HEPDATA [69]. When translated into limits on the branching fractions to CLFV final states, the relative contributions of the tensor and scalar operators to the decay translate into more stringent limits on the scalar operators [39].

JHEP06(2022)082 8 Summary
A search is reported for charged-lepton flavor violation in top quark production and decay. The analysis is based on pp collisions collected by the CMS detector at the LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb −1 . Events are selected if they contain an oppositely charged electron-muon pair and at least one b tagged jet. An effective field theory approach is used for parametrizing top quark lepton flavor violating interactions. The production and decay modes of the top quark through these effective interactions are included in this analysis.
A boosted decision tree is used to distinguish signal from background. No significant excess is observed over the expectations from the standard model. Upper limits are set on the strength of the individual vector-, scalar-, and tensor-like four-fermion effective operators. These are converted to limits on the branching fractions of the top quark B(t → eµq), q = u (c) quark, <0.13 × 10 −6 (1.31 × 10 −6 ), 0.07 × 10 −6 (0.89 × 10 −6 ), and 0.25 × 10 −6 (2.59 × 10 −6 ) for vector, scalar, and tensor CLFV interactions, respectively. The resulting limits are the most restrictive bounds to date.  -20 -