Search for singly and pair-produced leptoquarks coupling to third-generation fermions in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search for leptoquarks produced singly and in pairs in proton-proton collisions is presented. We consider the leptoquark (LQ) to be a scalar particle of charge -1/3$e$ coupling to a top quark plus a tau lepton ($\mathrm{t}\tau$) or a bottom quark plus a neutrino ($\mathrm{b}\nu$), or a vector particle of charge +2/3$e$, coupling to $\mathrm{t}\nu$ or $\mathrm{b}\tau$. These choices are motivated by models that can explain a series of anomalies observed in the measurement of B meson decays. In this analysis the signatures $\mathrm{t}\tau\nu\mathrm{b}$ and $\mathrm{t}\tau\nu$ are probed, using data recorded by the CMS experiment at the CERN LHC at $\sqrt{s} =$ 13 TeV and that correspond to an integrated luminosity of 137 fb$^{-1}$. These signatures have not been previously explored in a dedicated search. The data are found to be in agreement with the standard model prediction. Lower limits at 95% confidence level are set on the LQ mass in the range 0.98-1.73 TeV, depending on the LQ spin and its coupling $\lambda$ to a lepton and a quark, and assuming equal branching fractions for the two LQ decay modes considered. These are the most stringent constraints to date on the existence of leptoquarks in this scenario.


Introduction
Experimental evidence has promoted the standard model (SM) to the role of a reference theory of the physics of elementary particles. Despite the theory's successes, there are several fundamental aspects of observed particle physics that lack a complete explanation. One of these is the symmetry between the quark and lepton families. Possible explanations have been offered by several models that extend the SM, such as grand unified theories [1][2][3][4], technicolor models [5][6][7][8], compositeness scenarios [9,10], and R-parity violating supersymmetry [11][12][13][14][15][16][17][18][19][20]. These theories foresee a new particle that carries both lepton number L and baryon number B, and is generically referred to as a "leptoquark" (LQ).
A leptoquark has a fractional electric charge, and can be either a scalar particle (LQ S , with a spin of 0), or a vector particle (LQ V , with a spin of 1), with 3B + L equal to either 2 or 0. At hadron colliders, leptoquarks can be produced in pairs, or singly in association with a lepton [21,22], as illustrated by the Feynman diagrams in Fig. 1. For LQ S pair production, the cross section depends only on the LQ S mass for the range of LQ mass and λ values investigated in this search, while for LQ V it may depend on additional parameters [23], to comply with constraints imposed by unitarity at high energy scales. For singly produced leptoquarks, the cross section further depends on the couplings of the LQ to the quark and the lepton, and on the quark flavor.
Leptoquarks have recently gained enhanced interest, as they may provide an explanation for a series of anomalies observed in the measurement of B meson decays in charged-current b → c ν [24][25][26][27][28][29][30][31][32][33] and neutral-current b → s [34-41] processes. The solutions proposed to explain these anomalies favor effective couplings to third-generation SM fermions at the TeV scale, leading to processes that may be accessible at the CERN LHC. In particular, the model of Ref.
[42] predicts a charge -1/3e LQ S , with 3B + L = 2, decaying to a top quark and a τ lepton (tτ), or a bottom quark and a neutrino (bν τ ), while the model presented in Ref.
[43] contains a charge +2/3e LQ V , with 3B + L = 0, decaying to a top quark and an antineutrino (tν τ ) or a bottom quark and an anti-τ lepton (bτ + ). Each model includes a charge-conjugate leptoquark and prefers a region of parameter space that gives equal branching fractions for the two allowed decays, rendering the tτνb signature as the most frequent for pair-produced leptoquarks.
The analysis described in this Letter investigates the existence of leptoquarks produced in pairs with decays leading to the tbτν signature, or singly with the decay leading to tτν. The models of Refs. [42,43] are considered in this analysis, relying on the implementations described in Refs. [44,45]. In these models, the parameters of interest for determining the cross section are: the LQ mass; for LQ V , a dimensionless coupling k, set to 1 (Yang-Mills case) or 0 (minimal coupling case) [23]; and the LQ coupling (λ) to the lepton and quark, which affects the cross section for single LQ production. We note that the analysis is designed to be agnostic to the charge of the LQ, and is thus sensitive also to models with up-type scalar LQ and down-type vector LQ, which are not directly considered below.
Differently from previous searches that have separately considered single or pair LQ production, the present analysis strategy is devised to search for both production mechanisms simultaneously. The tτν(b) signatures are analyzed for the first time considering the inclusive hadronic decay channels of the top quark and τ lepton. We include a dedicated selection for the case of a large LQ-t mass splitting giving rise to a Lorentz-boosted top quark, whose decay Figure 1: Feynman diagrams for dominant leptoquark production modes at leading order: pairwise (left), and in combination with a lepton (right). In the scenarios considered the LQ S may couple to tτ or bν, while the LQ V may couple to tν or bτ.
products may not be resolved as individual jets.
The search is based on a data sample of proton-proton (pp) collisions at a center-of-mass energy of 13 TeV recorded by the CMS experiment at the CERN LHC in the years 2016-18, corresponding to an integrated luminosity of 137 fb −1 .

The CMS detector
The central feature of the CMS detector is a 3.8 T superconducting solenoid magnet with an inner diameter of 6 m. Within the magnet volume are the following subdetectors: a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. In addition, two steel and quartz-fiber hadron forward calorimeters extend the detection coverage to regions close to the beam pipe. 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. [58]. Events of interest are selected using a two-tiered trigger system [59]. The first level, 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 fixed time interval of about 4 µs. The second level, known as the high-level trigger, 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.

Simulated data samples
Monte Carlo (MC) event generators are used to simulate the SM background processes and the signal. These simulations are used to guide the design of the analysis, to estimate minor backgrounds, and to interpret the results.
Signal samples are generated at LO using MADGRAPH5 AMC@NLO [72]) parton distribution function (PDF) set is utilized with the tune CUETP8M1 [68] (CP2 [70]) for the signal events used with the 2016 (2017-18) data. The LQ mass range studied is between 0.5 and 2.3 TeV, with samples produced in steps of 0.3 TeV. We consider LQ S (LQ V ) decaying as LQ → tτ (tν) or LQ → bν (bτ). Samples of pair-produced leptoquarks are generated considering both gluon-initiated and quark-initiated mechanisms. We consider equal values of λ for leptoquarks coupled to (tτ, bν) and (tν, bτ). Samples of singly produced LQ are generated with λ values 0.1, 0.5, 1, 1.5, 2, and 2.5. In the MC simulation, the kinematic distributions of singly produced leptoquarks are independent of λ below λ = 0.5 (1) in the case of LQ S (LQ V ), and in both cases are independent of k. The dependence on λ above these values is ascribed to the contributions of virtual LQ states in the quark-gluon fusion amplitude ( Fig. 1 right) that become more and more relevant compared to the resonant LQ production for increasing values of LQ mass and λ, and are manifest as off-shell events that tend to populate the low-mass tail.
Additional pp interactions within the same or nearby bunch crossings (pileup) are taken into account by superimposing simulated minimum bias interactions onto the hard scattering process, with a number distribution matching that observed in data. Simulated events are propagated through the full GEANT4 based simulation [73] of the CMS detector.

Particle reconstruction and identification
A particle-flow (PF) algorithm [74] is used to identify and reconstruct individual particles in the event (electrons, muons, photons, neutral and charged hadrons) through a combination of the information from the entire detector. These PF objects are used to reconstruct higher-level objects such as hadronically decaying τ leptons (τ h ), jets, and missing transverse momentum ( p miss T ), taken as the negative vector sum of the transverse momenta ( p T ) of all reconstructed particles in an event. The magnitudes of p T and p miss T are referred to as p T and p miss T , respectively.
Jet candidates are reconstructed from PF candidates using the anti-k T clustering algorithm [75] with a distance parameter of 0.8 ("AK8 jet") or 0.4 ("AK4 jet"), and are selected requiring p T > 30 GeV and |η| < 2.4. The jet energy scale (JES) is calibrated through correction factors dependent on the p T , pseudorapidity (η), energy density, and the area of the jet. The jet energy resolution (JER) for the simulated jets is corrected to reproduce the resolution observed in data [76].
The AK8 jet candidates are required to have p T > 180 GeV, |η| < 2.4, and to be separated by ∆R > 0.8 from an identified τ h , where ∆R ≡ √ (∆η) 2 + (∆φ) 2 and φ is the azimuthal angle. They are selected if they are identified as originating from a W boson decaying to qq (denoted as "W jets") by using a pruning algorithm [77] or from a top quark decaying fully hadronically ("t jets"). The mass of the pruned AK8 W jet is required to be within the range 65-105 GeV to select candidates consistent with W bosons and to reject quark and gluon jets. The discrimination between W jets and quark and gluon jets is further improved by requiring the ratio τ 21 to be less than 0.35 or 0.45, depending on the year of data taking, where τ 21 ≡ τ 2 /τ 1 and the N-subjettiness τ n has the property that it attains a smaller value the more nearly the jet resembles a collection of n subjets [78]. In a similar way, an AK8 jet may be identified as arising from the fully hadronic decay of a top quark. These t jets are required to have p T > 400 GeV, mass of the jet reconstructed through the modified mass drop tagger algorithm [79, 80] between 105 and 220 GeV, and τ 32 ≡ τ 3 /τ 2 less than 0.81.
The τ h candidates are reconstructed with the hadron-plus-strips algorithm [81], which is seeded with AK4 jets. This algorithm reconstructs τ h candidates in the one-prong, one-prong plus π 0 (s), and three-prong decay modes. A discriminator based on a multivariate analysis, including isolation [81] as well as lifetime information, is used to reduce the frequency of jets being misidentified as τ h candidates. The typical working point used in this analysis has an efficiency of ≈60% for a genuine τ h , with a misidentification rate for quark and gluon jets of ≈0.1% [81]. Electrons and muons misidentified as τ h candidates are suppressed using criteria based on the consistency among the measurements in the tracker, the calorimeters, and the muon detectors. The τ h candidates are required to have a minimum p T of 20 GeV and |η| < 2.3.
Jets arising from a bottom quark ("b jets") are identified among AK4 jets using the combined secondary vertex algorithm [82]. We choose a "loose" working point that has an efficiency of 85% for genuine b jets and a rejection of 90% of light-flavor jets. The b jets are considered regardless of whether they are contained in top quark candidates.
Further requirements are imposed on the AK4 jets used in the construction of top and bottom quark candidates. These are required to have p T > 30 GeV and |η| < 2.4, and to be separated by ∆R > 0.4 (0.8) from an identified τ h (W jet).
A hadronically decaying top quark candidate is reconstructed considering three cases: an AK8 jet identified as a t jet, a pair comprising an AK4 jet and a W jet and having combined mass closest to the top quark mass among such pairs, and the triplet of AK4 jets having a mass closest to the top quark mass. The b tagging information is not used in any of these three reconstruction processes. These cases correspond to the three possible topologies of hadronic top quark decay and are referred to as "fully merged", "partially merged", and "resolved", respectively. The reconstruction considers these cases in the order just described, removing the objects contained in a candidate from further consideration to ensure that the categories are exclusive. The efficiency for identifying W, b, and t jets in simulation is corrected to match the results found in data [82,83].
To select events from processes with fully hadronic states, a veto on electrons and muons is applied. Electron candidates are reconstructed by combining the information from the ECAL and the silicon tracker, and are identified if they satisfy quality requirements and isolation as specified in [84]; they are selected if they have p T > 20 GeV and |η| < 2.5. Muon candidates are reconstructed by combining the information from the muon system and the silicon tracker, and are identified if they pass additional identification criteria and isolation as specified in [85]; they are selected if they have p T > 20 GeV and |η| < 2.4.

Event selection
Selected events must satisfy a trigger that requires both p miss T and H miss T greater than 120 GeV, H miss T being the magnitude of the negative summed p T of all the AK4 jets reconstructed with the PF algorithm.
Offline, we consider events in which both p miss T and H miss T ≥ 200 GeV, and H T ≥ 300 GeV, where H T is the scalar sum of the p T of all AK4 jets. Events entering this region are further required to contain exactly one top quark candidate, one τ h candidate, no elec-trons or muons, and at least one b jet. Finally, the transverse mass m T (τ h , p miss ] has to exceed 300 GeV, where p T (τ h ) is the transverse momentum vector of the τ h candidate.
From simulation we find that the total selection efficiency, accounting for both the LQ decay branching fraction and the event selection, varies between about 2 and 9% for an LQ mass in the range 0.5-2.3 TeV for pair-produced leptoquarks. For singly produced leptoquarks, taking λ = 1.5, the signal efficiency is about 0.7% for an LQ S with a mass of 1.1 TeV; the corresponding number for an LQ V is 2.4 (3.1)% for k = 0 (1) for a mass of 1.4 TeV. The efficiency decreases for higher λ and LQ mass values. This is because of the increased impact of the virtual leptoquarks leading to the nonresonant process in which the events tend to populate the low-mass tail, as described in Section 3. The efficiency values for all the different leptoquark hypotheses and parameters investigated in this search can be found in the HEPData database [86]. The search is less sensitive to single LQ production than to pair production because of the smaller signal efficiency for higher λ and LQ mass values and the similarity of the kinematic properties to those of the expected SM background. These effects outweigh the higher relative LQ S (LQ V k = 0, LQ V k = 1) cross section for mass values of 0.5 and 0.7 TeV (0.6 and 1.2 TeV, 1.2 and 2 TeV) at values of λ of 2 and 1.5.
The events that pass the above selection are categorized according to the number of b jets (N b-jet = 1 or ≥ 2) and to whether the top quark candidate is selected through the fully or partially merged topology ("boosted"), or the resolved topology ("resolved"). For each of these four categories of events a distribution-based analysis is performed, searching for evidence of a signal by considering the distribution of S T , which is the scalar sum of the p T of the top quark candidate, the selected τ h , and the p miss T . Figure 2 shows the S T distributions for the events passing the signal selection in the four categories of the analysis, while Table 1 gives the yields from the background estimation and the expected signal. Table 1: Yields from the SM background estimation, data, and expected signal, for the selected events, with total (statistical+systematic) uncertainties.

Background estimation
Several SM processes contribute as backgrounds in the signal region. We treat separately the two cases in which a genuine τ lepton is present or not in the event.
The irreducible background with a real τ lepton that decays hadronically is estimated from simulated samples, and normalized to data in a control region where we expect negligible   Figure 2: Distribution of the variable S T for events passing the signal selection for the SM background estimation (stacked filled histograms), data (black points), and different hypotheses of LQ signals (lines). Upper left: boosted top quark candidate (hadronically decaying top quark reconstructed in the fully or partially merged topology) and exactly one b jet; lower left: boosted top quark candidate and at least two b jets; upper right: resolved top quark candidate (hadronically decaying top quark reconstructed in the resolved topology) and exactly one b jet; lower-right: resolved top quark candidate and at least two b jets. The cross-hatched band in the upper panels represents the total uncertainty (statistical+systematic). The lower panel of each distribution shows the ratio, and its uncertainty, between the observation and the SM expectation.
contribution from the signal to account for residual differences between data and simulation. Processes with at least one top quark (e.g. tt or tt + W) account for most of this irreducible background, and a control region is defined by applying the requirements used for the signal region, except with m T (τ h , p miss T ) < 80 GeV and N b-jet ≥ 2. The dominant source of contamination is the reducible background, which comprises all of the processes (mainly events composed uniquely of jets produced through the strong interac-tion, W + jets, and tt) that pass the signal region selection and in which a jet is misidentified as a τ h candidate. We estimate this background entirely from data by applying misidentification weights w to the yields of events selected with the same requirements as the signal region, except that the τ h must pass a looser identification requirement and fail the nominal one. We refer to this sample as the application region. An estimate from simulation of the number of events entering the application region while having a genuine τ h is subtracted from the application region yields. The weight w of each event depends on the probability f that a misidentified τ h candidate passing the relaxed criteria also passes the nominal criteria, and is given by f /(1 − f ). The probability f is parameterized as a function of the p T and |η| of the jet associated with the selected τ h candidate, within ∆R(jet, τ h ) < 0.4. It is measured in a large data sample with a high fraction of jets misidentified as τ h . To select this sample the signal region requirements are modified by removing the thresholds on p miss T and H miss T and requiring instead the presence of a muon with p T greater than 60 GeV. The requirement N b-jet ≥ 1 is replaced by N b-jet = 0, to suppress tt events with genuine τ h , and the requirement on m T (τ h , p miss T ) is replaced by m T (τ h , µ) > 120 GeV, to suppress Drell-Yan events. In the resultant sample, more than 90% of the events have jets misidentified as τ h , with W+jets contributing 60% and the rest consisting of a mixture of top, diboson, and multijet events. This estimation method has been validated in a region that passes the signal region selection, except for the modified requirement 120 < m T (τ h , p miss T ) < 300 GeV. This region is verified to have a composition of background processes similar to that of the signal region but is dominated by events with a misidentified τ h candidate, as determined from MC simulation. We find good agreement between the data and the estimated background in this region, as well as in a larger one with the N b-jet requirement released. The observed difference does not exceed 12%, and this value is therefore assigned as the systematic uncertainty in the background estimated using this method.

Systematic uncertainties
Systematic uncertainties from various sources are propagated to both the shape and normalization of the distributions in the discriminating variable S T . The systematic uncertainties affect both the signal and the background, particularly the minor backgrounds (t production or "Others") that are derived relying on the MC simulation, while the main background (τ misidentification) is estimated from data.
The shape uncertainties vary according to the background process, S T bin, and year of data taking. Thus in the following, we quote a range of values, reflecting the minimum and maximum uncertainties observed under the various conditions. The effect of the uncertainty on the simulation of pileup is estimated by varying the inelastic cross section [87] used in the simulation by 5%. This results in an uncertainty associated with the background of between 1 and 6%, and of 1% associated with the signal. The uncertainty in the acceptance associated with the PDFs is evaluated in accordance with the PDF4LHC recommendations [88], using the PDF4LHC15 Hessian PDF set with 100 eigenvectors, and is found to be less than 5% for the signal. The uncertainty related to the trigger is between 1 and 2%, for both the background and the signal. The jet four-momenta are varied within the JES and the JER uncertainties [76], resulting in an effect that ranges between 1 and 35% for the background and up to 2.5% for the signal. The above uncertainties are correlated across the years, while those discussed below are treated as uncorrelated, as they are dominated by statistical uncertainties. Corrections related to the b tagging are varied by the uncertainties that are measured with control samples in data and simulation [82], giving a systematic uncertainty in the yields in the range 3-10% for the background and 8-10% (13-23%) for single (pair) LQ production. Analogously, we take into account the uncertainty in the τ h energy scale and identification [81], which amounts to 1-5% (less than 1%) and 5-13 (13-20)% for the background (signal). The W and t jet tagging uncertainty amounts to 2-11 (1-4)% and 3-15 (7-14)% for the background (signal). For all of the background processes, the statistical uncertainty in the samples used is included in the systematic uncertainty.
The sources of systematic uncertainty that affect only the normalization are the uncertainties in the cross sections of the backgrounds estimated from simulation (5% for top quark production and 30% for the remaining backgrounds), the uncertainty in the misidentified τ h contribution, whose value of 12% is assigned from the consistency test discussed in Section 6, and the uncertainty in the integrated luminosity. The integrated luminosities of the 2016-18 data-taking periods are individually known with uncertainties in the 2.3-2.5% range [89-91], while the total Run 2 (2016-18) integrated luminosity has an uncertainty of 1.8%, the improvement in precision reflecting the (uncorrelated) time evolution of some systematic effects. Figure 2 and Table 1 show that the data are in agreement with the background expectations from the SM in all of the event categories investigated. We proceed with setting upper limits at 95% confidence level (CL) on the cross sections for the production of leptoquarks in pairs, σ(pp → LQLQ), and singly, σ(pp → LQ), for LQ S ( = ν), and LQ V ( = τ). We use the CL s criterion [92,93] with binned templates of both background and signal as given by the distributions of Fig. 2. For each category and each bin of S T , the observed number of events is fitted by a Poisson distribution, whose mean is the sum of the total SM expectation, determined as described in Section 6, and a potential signal contribution determined from simulation. The systematic uncertainties described in Section 7 are considered as nuisance parameters, with a lognormal distribution for the normalization parameters and a Gaussian distribution for systematic uncertainties affecting the shape.

Results
The observed and expected upper limits on σ(pp → LQLQ), σ(pp → LQ), and the case where both pair and single production mechanisms are considered simultaneously, σ(pp → LQLQ) + σ(pp → LQ), as a function of the mass of the leptoquarks are shown in Figs. 3-5, where the leptoquarks are LQ S , LQ V k = 0, and LQ V k = 1, respectively. The uncertainty in the production cross section shown in these figures is given by the sum in quadrature of contributions arising from the PDFs and the renormalization and factorization scales. To estimate the latter, we consider the effects of multiplying these scales by factors of 0.5 and 2 [94][95][96]. For single LQ production, the limits are shown for fixed values of λ = 1.5 and 2.5. Only values of λ less than 2.5 are considered, since higher values are excluded by constraints from electroweak precision measurements [97]. The bands represent the one-and two-standard deviation variations of the expected limit. The solid blue curve indicates the theoretical prediction of σ(pp → LQLQ) and σ(pp → LQ), calculated at LO except for the pair production of LQ S , computed using NLO quantum chromodynamics corrections [98] and the model implementation in Ref. [45]. The intersection of the blue and the solid (dotted) black lines determines the observed (expected) lower limit on the LQ mass. Table 2 summarizes the observed and expected lower limits on the LQ mass inferred from Figs. 3-5 for the three cases, LQ S , LQ V k = 0, and LQ V k = 1. The observed limits are, respectively, 0.98-1.02, 1.34-1.41, and 1.69-1. 73 TeV for values of λ between 1.5 and 2.5, based on the simultaneous search for single and pair production. The table also reports exclusion limits for the separate searches for single and pair production. Table 2: Lower limits on the mass in TeV of the leptoquarks LQ S , LQ V k = 0, and LQ V k = 1, based on the pair-and single-production mechanisms taken either separately or together. These lower limits are derived from the intersection of the observed 95% CL upper limits on the signal cross section and the signal cross section in Figs. 3-5. The results of the searches that depend on the λ parameter are given for values of 1.5 and 2.5. The expected limits are given in parentheses. The combination of the two production mechanisms extends the exclusion on the LQ mass by 30-120 GeV depending on the type of LQ. These exclusions represent the most stringent limits to date on the existence of LQ S (LQ V ) coupled to tτ, bν (tν, bτ) under the assumption of equal couplings to the lepton-quark pairs. Comparing the cases of λ = 1.5 and 2.5 in Figs. 3-5, one can see how the upper limits on the cross section increase at higher LQ masses and λ values, as a result of an increasing relative contribution of virtual LQ states in single LQ production, as discussed in Section 3, which degrades the sensitivity of the search. Figure 6 gives the observed and expected exclusion on the existence of leptoquarks in the λ − m LQ plane, for the single and pair production mechanisms and their combination. For LQ V , the gray area shows the 95% CL band preferred by the B physics anomalies [43], which is given by λ = Cm LQ , where C = √ 0.7 ± 0.2 TeV −1 and m LQ is expressed in TeV. A relevant portion of this parameter space is excluded.

Summary
A search for leptoquarks coupled to third-generation fermions, and produced in pairs and singly in association with a lepton, has been presented. The leptoquark (LQ) may couple to a top quark and a τ lepton (tτ) or a bottom quark and a neutrino (bν, scalar LQ) or else to tν and bτ (vector LQ), resulting in the tτνb and tτν signatures. The channel in which both the top quark and the τ lepton decay hadronically is investigated, including the case of a large LQt mass splitting giving rise to a Lorentz-boosted top quark, whose decay daughters may not be resolved as individual jets. This particular signature has not been previously examined in searches for physics beyond the standard model. The data used corresponds to an integrated luminosity of 137 fb −1 collected with the CMS detector at the CERN LHC in proton-proton collisions at √ s = 13 TeV. The observations are found to be in agreement with the standard model predictions. Exclusion limits are given in the plane of the LQ-lepton-quark vertex coupling λ and the LQ mass for scalar and vector leptoquarks. The range of lower limits on the LQ mass, at 95% confidence level, is 0.98-1.73 TeV, depending on λ and the leptoquark spin. These results represent the most stringent limits to date on the existence of such leptoquarks for the case of equal couplings to the lepton-quark pairs. They allow a relevant portion of the parameter space preferred by the B-physics anomalies in several models [42,43]            [31] LHCb Collaboration, "Measurement of the ratio of branching fractions [32] LHCb Collaboration, "Measurement of the ratio of the B 0 → D * − τ + ν τ and B 0 → D * − µ + ν µ branching fractions using three-prong τ-lepton decays", Phys. Rev. Lett. 120 (2018) 171802, doi:10.1103/PhysRevLett.120.171802, arXiv:1708.08856.