Search for a singly produced third-generation scalar leptoquark decaying to a $\tau$ lepton and a bottom quark in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search is presented for a singly produced third-generation scalar leptoquark decaying to a $\tau$ lepton and a bottom quark. Associated production of a leptoquark and a $\tau$ lepton is considered, leading to a final state with a bottom quark and two $\tau$ leptons. The search uses proton-proton collision data at a center-of-mass energy of 13 TeV recorded with the CMS detector, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Upper limits are set at 95% confidence level on the production cross section of the third-generation scalar leptoquarks as a function of their mass. From a comparison of the results with the theoretical predictions, a third-generation scalar leptoquark decaying to a $\tau$ lepton and a bottom quark, assuming unit Yukawa coupling ($\lambda$), is excluded for masses below 740 GeV. Limits are also set on $\lambda$ of the hypothesized leptoquark as a function of its mass. Above $\lambda =$ 1.4, this result provides the best upper limit on the mass of a third-generation scalar leptoquark decaying to a $\tau$ lepton and a bottom quark.

Events of interest are selected using a two-tiered trigger system [40]. 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 time interval of less than 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 about 1 kHz before data storage.
The generators are interfaced with PYTHIA 8.212 [57] to model the parton showering and fragmentation, as well as the decay of the τ leptons. The PYTHIA parameters affecting the description of the underlying event are set to the CUETP8M1 tune [58]. The NNPDF3.0 parton distribution functions [59,60] with the QCD order matching that of the matrix element calculations are used with all generators.
Simulated events are processed with a model of the CMS detector based on GEANT4 [61] and are reconstructed with the same algorithms used for data. The effect of pileup, additional pp collisions within the same or adjacent bunch crossings, is taken into account by adding minimum bias events, generated with PYTHIA, to the hard scattering event. The additional events are weighted such that the frequency distribution matches that in data, with an average of approximately 23 interactions per bunch crossing [62].

Event reconstruction
The reconstruction of observed and simulated events uses a particle-flow (PF) algorithm [63], which combines the information from the CMS subdetectors to identify and reconstruct the particles emerging from pp collisions: charged and neutral hadrons, photons, muons, and electrons. Combinations of these PF objects are used to reconstruct higher-level objects such as jets, τ h candidates, or missing transverse momentum ( p miss T ), taken as the negative vector sum of the transverse momenta (p T ) of those jets.
The reconstructed vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp collision vertex. In this case, the physics objects are the objects constructed by a jet finding algorithm [64,65] applied to all charged tracks associated with the vertex, including tracks from lepton candidates, and the corresponding associated p miss T .
Electrons are identified with a multivariate (MVA) [66] discriminant combining several quantities describing the track quality, the shape of the energy deposits in the ECAL, and the compatibility of the measurements from the tracker and the ECAL [67]. The electrons must pass a cutbased discriminant to reject electrons coming from photon conversions. Muons are identified with requirements on the quality of the track reconstruction and on the number of measurements in the tracker and the muon systems [68]. Electron and muon candidates are required to have p T > 50 GeV. To reject leptons that do not come from the primary vertex and particles misidentified as leptons, a relative lepton isolation I ( = e, µ) is defined as follows: In this expression, ∑ ch p T is the scalar sum of the p T of the charged hadrons, electrons, and muons originating from the primary vertex and located in a cone of size ∆R = √ (∆η) 2 + (∆φ) 2 = 0.03 (0.04) centered on the electron (muon) direction, where η is pseudorapidity and φ is azimuthal angle in radians. The sum ∑ neut p T represents the same quantity for neutral hadrons and photons. The contribution of pileup photons and neutral hadrons is estimated from the scalar sum of the p T of charged hadrons originating from pileup vertices, ∑ ch, PU p T . This sum is multiplied by a factor of 1/2, which corresponds approximately to the ratio of neutral-to charged-hadron production in the hadronization process of inelastic pp collisions, as estimated from simulation. In this analysis, I e < 0.10 (I µ < 0.15) is used as an isolation requirement for the electron (muon). With these cut-off values, the combined efficiency of identification and isolation is around 80 (95)% for the electron (muon). Small differences, up to the 5% level, between data and simulation are corrected for by applying scale factors to simulated events.
Jets are reconstructed from PF candidates using an anti-k T clustering algorithm with a distance parameter of 0.4, implemented in the FASTJET library [65,69]. Charged PF candidates not associated with the primary vertex of the interaction are not considered when reconstructing jets. An offset correction is applied to jet energies to take into account the contribution from additional pp collisions within the same or nearby bunch crossings. Jet energy corrections are derived from simulation to bring the average measured response of jets to that of particle-level jets [70]. Further identification requirements are applied to distinguish genuine jets from those coming from pileup [71,72]. In this analysis, jets are required to have p T greater than 30 GeV and |η| less than 4.7, and must be separated from the selected leptons by a ∆R of at least 0.5. Jets originating from the hadronization of bottom quarks are identified (b tagged) using the combined secondary vertex algorithm [73], which exploits observables related to the long lifetime and large mass of B hadrons. The chosen b tagging working point corresponds to an identification efficiency of approximately 60% with a misidentification rate of approximately 1%, for jets originating from light (up, down, charm, strange) quarks and gluons.
The τ h candidates are reconstructed with the hadron-plus-strips algorithm [74,75], which is seeded with anti-k T jets. This algorithm reconstructs τ h candidates in the one-prong, one-prong + π 0 (s), and three-prong decay modes, based on the number of tracks and on the number of strips of ECAL crystals with energy deposits. An MVA-based discriminator, including isolation as well as lifetime information, is used to reduce the incidence of jets being misidentified as τ h candidates. The typical working point used in this analysis has an efficiency ≈60% for a genuine τ h , with a misidentification rate for quark and gluon jets of ≈0.1%.
Electrons and muons misidentified as τ h candidates are suppressed using criteria based on the consistency between the measurements in the tracker, the calorimeters, and the muon detectors. The criteria are optimized separately for each final state studied.
All particles reconstructed in the event are used in the determination of p miss T [76]. The calculation takes into account jet energy corrections. Corrections are applied to correct for the mismodeling of p miss T in the simulated samples of the Z+jets and W+jets processes. The corrections are performed on the variable defined as the vectorial difference between the measured p miss T and the total p T of neutrinos originating from the decay of the W or Z boson.

Event selection
The search for scalar LQs is performed in three channels, each containing a b-tagged jet. Channels containing in addition an electron or a muon, together with a τ h candidate are labeled eτ h and µτ h , and collectively referred to as τ h . The third channel, which has two τ h candidates in addition to the b-tagged jet, is labeled τ h τ h . The selection criteria have been optimized based on the expected sensitivity to a single-LQ signal.
Firstly, events are required to be compatible with ττ production. In the eτ h (µτ h ) channel, events are selected using a trigger that requires an isolated electron (muon) with p T > 25 (24) GeV. Offline, the selected electron (muon) is required to have p T > 50 GeV and |η| < 2.1 (2.4). The τ h candidate is required to have p T > 50 GeV and |η| < 2.3. In the τ h τ h channel, events are selected online by requiring two isolated τ h candidates with p T > 35 GeV. Offline, both τ h candidates are required to have p T > 50 GeV and |η| < 2.1. The selected and τ h candidate, or two τ h candidates, must meet isolation requirements as detailed in Section 4, have opposite-sign (OS) electric charges and be separated by ∆R > 0.5. They must also meet the requirement that the distance of closest approach to the primary vertex satisfies |d z | < 0.2 cm along the beam direction, and |d xy | < 0.045 cm in the transverse plane. Events with additional isolated muons or electrons (p T > 10 GeV and |η| < 2.4 or 2.5) that pass a looser identification requirement are discarded to reduce Z+jets and diboson backgrounds and to avoid correlations between channels.
Further event selection is applied to increase the signal purity. Since signal events contain at least one energetic bottom quark jet coming from the LQ decay, at least one b-tagged jet with p T > 50 GeV and |η| < 2.4 is required. To reduce the Z+jets background, the invariant mass, m vis , of the and τ h candidate (two τ h candidates), is required to be greater than 85 (95) GeV in the τ h (τ h τ h ) channels.
The product of acceptance (A), efficiency (ε), and the branching fraction (B) of the ττ to a specific final state ranges from 0.2 to 1.3% in the eτ h channel for m LQ between 200 and 1500 GeV. The ε increases with increasing m LQ due to the harder p T spectra of the final state particles. Beyond 1000 GeV, however, ε starts to decrease, mainly because of the lower b tagging efficiency. Similarly, AεB in the µτ h (τ h τ h ) channels range from 0.3 to 1.8% (0.5 to 2.5%). Figure 2 shows AεB for the signal, in each final state considered in this analysis, as a function of m LQ .
After applying the event selection, an excess of events over the SM backgrounds is searched for using the distribution of the scalar p T sum of all required final-state particles, S T , which is defined as p T ( ) + p T (τ h ) + p T (leading jet) for the τ h channels, and p T (leading τ h ) + p T (subleading τ h ) + p T (leading jet) for the τ h τ h channel, where leading and subleading refer to p T . Because of the p T threshold requirements, S T is always greater than 150 GeV.

Background estimation
The dominant background in all channels is tt production because of the presence of genuine electrons, muons, τ leptons, and bottom quark jets produced in the tt decays. Additional backgrounds that satisfy the signal selection are W+jets, Z+jets, diboson, and single top quark processes, as well as QCD multijet events. In this section, background estimation methods and their validation are described separately for the τ h and τ h τ h channels.

The τ h channels
The normalization and shape of the tt background are obtained from data, making use of an eµ control region (CR), containing events with an electron, a muon, and at least one b-tagged jet. The same p T and |η| requirements as in the signal region (SR) are placed on all three objects. The invariant mass of the selected electron and muon is required to be greater than 85 GeV. The purity of tt events in this CR, estimated from simulation, is 92%, with negligible signal contamination. A good agreement between data and simulation is found for both the normalization and the shape, validating the method used to estimate the tt background in the SR.
In order to allow for possible remaining mismodeling related to tt backgrounds, this CR is included in the maximum likelihood fit, as described in Section 7, together with relevant nuisance parameters such as the b tagging efficiency and tt cross section uncertainties. In this way, the normalization and the shape of the tt backgrounds can be constrained from the data. This procedure also helps to constrain tt backgrounds in the τ h τ h channel, although its contribution is less significant than in the τ h channels.
For the W+jets background, the shape is taken from simulation, while the normalization is determined from data in a high (>80 GeV) transverse mass (m T ) sideband; here m T is defined as where p T is the lepton p T and ∆φ is the azimuthal angle between the lepton direction and p miss T . The normalization factor is calculated before the b tagging requirement is applied. A 30% uncertainty is assigned for the W+jets background estimate to account for the limited event counts in the high m T sideband, as well as the extrapolation uncertainty to the SR.
The QCD multijet background, in which one of the jets is misidentified as the τ h candidate and another as the , is small and is estimated using a CR where the and τ h candidate have samesign (SS) electric charges. In this CR, the QCD multijet yield is obtained by subtracting from the data the contribution of the Z+jets, tt, and W+jets processes. The expected contribution of the QCD multijet background in the OS SR is then derived by rescaling the yield obtained in the SS CR by a factor of 1.06, which is measured using a pure QCD multijet sample obtained by inverting the lepton isolation requirement. To determine the uncertainty associated with this procedure, the measurement is repeated with several different S T requirements. The maximum variation observed is 30%, and this is taken to be the uncertainty in the QCD background estimate.
Minor backgrounds such as diboson and single top quark processes are estimated from the simulation.

The τ h τ h channel
In the τ h τ h channel, the shape and normalization of all background processes with genuine hadronic τ decays are estimated using simulated samples. The backgrounds concerned are Z → τ h τ h , and contributions from the tt, diboson and single top quark processes.
Other backgrounds arising from jets misidentified as τ h candidates, most of which are from QCD multijet backgrounds, are estimated from CRs in data using the fake-factor method [77,78]. An application region (AR) is defined containing the same selection criteria as in the SR, except for an inverted τ h isolation requirement for one of the two τ h candidates. The AR is primarily populated by events with jets misidentified as τ h candidates, and has a contamination from genuine hadronic τ decays at the level of a few percent or below.
The ratio of the number of events with a misidentified τ h in the AR to the number in the SR (fake factor) is assumed to be the same as the ratio measured in samples with an SS τ h τ h pair. The fake factor is then applied to the number of events in the AR to estimate the number of events with a misidentified τ h in the SR. The fake factor is calculated as a function of the p T and decay mode of the τ h candidate, and it ranges from 0.1 to 0.25. In order to take combinatorial effects into account, a weight factor of 0.5 is applied. Since the presence of small backgrounds in the AR that contain a genuine τ h results in up to a 2% underestimation of the number of events with a misidentified τ h in the SR, a correction is applied based on the fractions of these processes in simulated events. Corresponding uncertainties are incorporated in the fit model, as described in Section 7.
The fake-factor method is tested in two validation regions (VRs); one is constructed by inverting the leading jet p T requirement (i.e. p T < 50 GeV) and the other by using events with two τ h candidates that do not fulfill the tight isolation criteria used to define the SR. For both VRs, all other selection criteria are kept identical to the SR, except that the b tagging requirement is removed to increase the number of events. The signal contamination is negligible in both VRs. Agreement between data and simulation is found, within statistical uncertainties, demonstrating the validity of the fake-factor method.
Finally, small contributions coming from the Z+jets background are validated using the same event selection as in the SR, except that we require m vis < 95 GeV. Data and simulated events show agreement within statistical uncertainty. A 30% uncertainty is attributed to the Z+jets background yield due to the limited event count in this CR.

Systematic uncertainties and signal extraction
A binned maximum likelihood method is used for the signal extraction [79]. As discussed in Section 5, the S T distribution for S T greater than 150 GeV is used as the final discriminant. The fit is performed simultaneously in the eτ h , µτ h , and τ h τ h signal regions, as well as in the eµ control region, as defined in Section 6. Systematic uncertainties may affect the normalization and the shape of the S T distribution of the signal and background processes. These uncertainties are represented by nuisance parameters in the fit, as described below. The relevant uncertainties are summarized in Table 1.

Normalization uncertainties
The uncertainty in the integrated luminosity amounts to 2.5% [62] and affects the normalization of the signal and background processes that are based on simulation. Uncertainties in the electron identification and trigger efficiency amount to 8 and 2%, respectively, while those in the muon identification and trigger efficiency amount to 2% each. The τ h identification and trigger efficiency have been measured using the "tag-and-probe" technique [74,75] and an uncertainty of 5% per τ h candidate is assigned. The acceptance uncertainty due to the b tagging efficiency (misidentification rate) is taken to be 3 (5)%. A 30% uncertainty is attributed to the W+jets, Z+jets, and QCD multijet backgrounds in the τ h channels, as discussed in Section 6. The cross section uncertainties in the tt, diboson, and single top quark processes are 5.5, 6.0, and 5.5%, respectively. For events where electrons or muons are misidentified as τ h candidates, predominantly Z → ee events in the eτ h channel and Z → µµ events in the µτ h channel, rate uncertainties of 12 and 25%, respectively, are allocated, based on the tag-and-probe method.

Shape uncertainties
The energy scales of the τ h candidate and the leading jet affect the shape of the S T distribution, as well as the normalization of the signal and background processes. The uncertainty is estimated by varying the τ h and jet energies within their respective uncertainties and recomputing S T after the final selection. The uncertainty in the τ h energy scale amounts to 3% [74], whereas the variations due to the jet energy scale are in the 1-2% range, depending on the jet p T and η [70].
The uncertainty in the extrapolation of the τ h identification efficiency to higher p T s is treated as a shape uncertainty. It is proportional to p T (τ h ) and has a value of +5%/−35% at p T (τ h ) = 1 TeV. The effects of the uncertainties due to the electron and muon energy scales are found to be negligible. The probability of a jet being misidentified as a τ h candidate has been checked using a tt control region in data. The difference between data and simulated events is fit using a linear function, and its functional form, 1.2 − 0.004[max(120, p T ) GeV], is considered as a onesided shape uncertainty for the τ h channels.
In the τ h τ h channel, additional shape uncertainties related to the fake-factor method are considered. There are eight variations coming from factors such as the finite number of events in the samples, possible neglected effects in the fake factor determination, additional uncertainties in the correction of the SS to OS extrapolation, and the uncertainties in the background composition in the AR, which is estimated with simulated events. When added in quadrature, these additional uncertainties are of order 10%.
Finally, uncertainties related to the finite number of simulated events, and to the limited number of events in data CRs, are taken into account. They are considered for all bins of the distributions that are used to extract the results. The binning of the histograms are adjusted such that the uncertainty, for a given bin, does not exceed 15%. They are uncorrelated across the different samples, and across the bins of a single distribution. Figure 3 shows the S T distributions after the combined fit to the eτ h , µτ h , and τ h τ h signal regions, as well as to the eµ control region. The background uncertainty bands on the histograms of simulated events represent the sum in quadrature of statistical and systematic uncertainties, taking the full covariance matrix of all nuisance parameters into account. The dominant uncertainty in the background estimate comes from the limited event counts in simulated samples. However, this uncertainty is unimportant for m LQ > 500 GeV, where the mass limit is set, and the sensitivity is ultimately constrained by the size of the data sample. Table 2 shows the event yields for a signal-enriched region with S T > 500 GeV, together with event yields expected for a representative LQ signal with m LQ = 700 GeV.

Results
The data are consistent with the background-only (SM) hypothesis. In the τ h τ h channel, one bin at around 250 GeV shows a slight excess in data, corresponding to two standard deviations. This, however, has little impact on the results, as the sensitivity is dominated by the S T tail,    (lower left) signal regions, as well as in the eµ (lower right) control region, compared to the expected SM background contributions. The distribution labeled "electroweak" contains the contributions from W+jets, Z+jets, and diboson processes. The signal distributions for single-LQ production with mass 700 GeV are overlaid to illustrate the sensitivity. For the signal normalization, λ = 1 and β = 1 are assumed. The background uncertainty bands represent the sum in quadrature of statistical and systematic uncertainties obtained from the fit. The lower panels show the ratio between the observed and expected events in each bin. In all plots, the horizontal and vertical error bars on the data points represent the bin widths and the Poisson uncertainties, respectively. rather than the main part of the distribution.
We set an upper limit on the cross section times branching fraction β as a function of m LQ , by using the asymptotic CL s modified frequentist criterion [79][80][81][82]. Figure 4 shows the observed and expected upper limits at 95% confidence level. The blue solid line corresponds to the theoretical cross sections [45], calculated with λ = 1 and β = 1. The intersection of the blue and the black lines determines the lower limit on m LQ . Assuming λ = 1 and β = 1, thirdgeneration scalar LQs with masses below 740 GeV are excluded at 95% confidence level, to be compared with an expected lower limit of 750 GeV.
The sensitivity of the analysis is dominated by the τ h τ h channel, followed by the µτ h channel,

CMS
Observed 95% CL Figure 4: Observed (black solid) and expected (black dotted) limits at 95% confidence level on the product of cross section σ and branching fraction β, obtained from the combination of the eτ h , µτ h , and τ h τ h signal regions, as well as from the eµ control region, as a function of the LQ mass. The green and yellow bands represent the one and two standard deviation uncertainties in the expected limits. The theory prediction is indicated by the blue solid line, together with systematic uncertainties due to the choice of PDF and renormalization and factorization scales [45], indicated by the blue band. and then the eτ h channel. The better sensitivity in the τ h τ h channel comes from the larger branching fraction of B(ττ → τ h τ h ) = 42%, compared to B(ττ → µτ h ) = B(ττ → eτ h ) = 21%. Furthermore, the τ h channels are contaminated by tt → WWbb → τ h ννbb process, in addition to the tt → WWbb → τ τ h ννbb background, which is not the case for the τ h τ h channel. Here, τ denotes a leptonically-decaying τ lepton.
Since the single-LQ signal cross section scales with λ 2 , it is straightforward to recast the results presented in Fig. 4 in terms of expected and observed upper limits on λ as a function of m LQ , as shown in Fig. 5. Values of λ up to 2.5 are considered, such that the width of the LQ signal stays narrow and to satisfy constraints from electroweak precision measurements [43]. Here we have made the assumption that the shape of the S T distribution does not depend on λ over the range of λ used in the analysis. This assumption has been verified using simulated events. The blue band shows the preferred parameter space (95% CL) for the scalar LQ preferred by the B physics anomalies: λ = (0.95 ± 0.50)m LQ (TeV) [36]. The plot also shows the limit from the pair-produced LQ search overlaid as an orange vertical line, which does not depend on λ, as discussed in Section 1. For values of λ > 1.4, the mass limit obtained by this analysis exceeds that of the search considering pair production [37] and provides the best upper limit on m LQ of the third-generation scalar LQ decaying to a τ lepton and a bottom quark. For λ = 2.5 and β = 1, the observed and expected lower limits on mass are both 1050 GeV. This result, together with the pair-produced search, begins to constrain the region of parameter space implied by the B physics anomalies. Obs. 95% CL Figure 5: Expected and observed exclusion limits at 95% confidence level on the Yukawa coupling λ at the LQ-lepton-quark vertex, as a function of the LQ mass. A unit branching fraction β of the LQ to a τ lepton and a bottom quark is assumed. The orange vertical line indicates the limit obtained from a search for pair-produced LQs decaying to τ h bb [37]. The left-hand side of the dotted (solid) line shows the expected (observed) exclusion region for the present analysis. The gray band shows ±1 standard deviations of the expected exclusion limit. The region with diagonal blue shading shows the parameter space preferred by one of the models proposed to explain anomalies observed in B physics [36].

Summary
A search for singly produced third-generation scalar leptoquarks, each decaying to a τ lepton and a bottom quark has been presented. The final state of an electron or a muon plus one hadronically decaying τ lepton and the final state with two hadronically decaying τ leptons are explored. In all final states at least one energetic jet identified as originating from a bottom quark is required. The search is based on a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the CMS detector, corresponding to an integrated luminosity of 35.9 fb −1 . The data are found to be in agreement with the standard model predictions. Upper limits as a function of the leptoquark mass are set on the third-generation scalar leptoquark production cross section. Results are compared with theoretical predictions to obtain lower limits on the leptoquark mass. Assuming the leptoquark always decays to a τ lepton and a bottom quark with unit Yukawa coupling λ = 1, third-generation scalar leptoquarks with mass below 740 GeV are excluded at 95% confidence level. Mass limits are also placed as a function of λ. For values of λ > 1.4, the mass limit obtained by this analysis exceeds that of the search considering pair production and provides the best upper limit. For λ = 2.5, leptoquarks are excluded in the mass range up to 1050 GeV. This is the first time that limits have been presented in the λ versus mass plane, allowing the results to be considered in the preferred parameter space of models that invoke third-generation leptoquarks to explain anomalies observed in B hadron decays. These results thus demonstrate the important potential of single leptoquark production studies to complement pair production constraints on such models, as additional data become available.

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. [19] Belle Collaboration, "Measurement of the branching ratio ofB → D ( * ) τ −ν τ relative tō B → D ( * ) −ν decays with hadronic tagging at Belle", Phys. Rev. D 92 (2015) 072014, doi:10.1103/PhysRevD.92.072014, arXiv:1507.03233.