Search for heavy neutrinos and third-generation leptoquarks in hadronic states of two τ leptons and two jets in proton-proton collisions at $$ \sqrt{s}=13 $$ TeV

A search for new particles has been conducted using events with two high transverse momentum $\tau$ leptons that decay hadronically and at least two energetic jets. The analysis is performed using data from proton-proton collisions at $\sqrt{s} =$ 13 TeV, collected by the CMS experiment at the LHC in 2016 and corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The observed data are consistent with standard model expectations. The results are interpreted in the context of two physics models. The first model involves right-handed charged bosons, W$_\mathrm{R}$, that decay to heavy right-handed Majorana neutrinos, N$_\ell$ $(\ell = $e, $\mu, \tau)$, arising in a left-right symmetric extension of the standard model. The model considers that N$_\mathrm{e}$ and N$_\mu$ are too heavy to be detected at the LHC. Assuming that the N$_\tau$ mass is half of the W$_\mathrm{R}$ mass, masses of the W$_\mathrm{R}$ boson below 3.50 TeV are excluded at 95% confidence level. Exclusion limits are also presented considering different scenarios for the mass ratio between N$_\tau$ and W$_\mathrm{R}$, as a function of W$_\mathrm{R}$ mass. In the second model, pair production of third-generation scalar leptoquarks that decay into $\tau\tau$bb is considered, resulting in an observed exclusion region with leptoquark masses below 1.02 TeV, assuming a 100% branching fraction for the leptoquark decay to a $\tau$ lepton and a bottom quark. These results represent the most stringent limits to date on these models.


Introduction
Despite its undeniable success, the standard model (SM) fails to answer some of the most fundamental questions in particle physics. Among these are the source of matter-antimatter asymmetry, the particle nature of dark matter, the origin of dark energy, and the acquisition of neutrino mass. The aim of this paper is to present a search for physics beyond the standard model in final states containing two hadronically decaying τ leptons (τ h ) and two high transverse momentum (p T ) jets. The analysis is performed using data from proton-proton (pp) collisions at √ s = 13 TeV, collected by the CMS experiment at the CERN LHC and corresponding to an integrated luminosity of 35.9 fb −1 . To illustrate the sensitivity of this search for processes not included in the SM, two benchmark physics scenarios are considered for the interpretation of the results: the production of heavy, right-handed Majorana neutrinos and the production of third-generation leptoquarks (LQs). A description of the two models is given below.
The observation of neutrino oscillations implies nonzero neutrino masses, prompting a corresponding extension of the SM. Results from neutrino oscillation experiments together with cosmological constraints imply very small values for these masses [1][2][3][4]. The most popular explanation for very small neutrino masses is the "seesaw" mechanism [5][6][7] in which the observed left-handed chiral states are paired with very heavy right-handed partners. This mechanism can be realized in the left-right symmetric model (LRSM) [2][3][4], in which the SM group SU(2) L has a right-handed counterpart, originally introduced to explain the nonconservation of parity in weak interactions. The SU(2) R group, similarly to SU(2) L , predicts the existence of three new gauge bosons, W ± R and Z , and three heavy right-handed Majorana neutrino states N ( = e, µ, τ), partners of the light neutrinos ν . A reference process allowed by this model is the production of a right-handed W R boson that decays to a heavy neutrino and a lepton of the same generation (W R → + N → + ( qq )) and gives rise to two jets and two leptons of the same flavor in the final state. Of particular interest for this analysis is the scenario in which the W R decay chain results in a pair of high-p T τ leptons, W R → τ + N τ → τ + (τqq ). Figure 1 shows the leading order (LO) Feynman diagram for the production of a N τ . Figure 1: Leading order Feynman diagram for the production of a right-handed W R that decays to a heavy neutrino N τ , with a final state of two τ leptons and two jets.
A similar ττjj final state can be realized in other extensions of the SM, such as grand unified theories [8][9][10][11], technicolor models [12][13][14][15], compositeness scenarios [16,17], and R parity [18] violating supersymmetry [19][20][21][22][23][24][25][26][27]. These theories predict a new scalar or vector boson, referred to as a leptoquark in the literature, which carries nonzero lepton and baryon numbers, as well as color and fractional electric charge [9,17]. In order to comply with experimental constraints on flavor changing neutral currents and other rare processes [28,29], three types of LQs are generally considered, each coupled to the leptons and quarks of its generation. The LQs recently gained notable theoretical attention as one of the most suitable candidates to explain the B → D * τν and b → s anomalies reported by the BaBar [30,31], Belle [32][33][34][35], and LHCb [36][37][38][39][40] Collaborations. In particular, models containing enhanced couplings to the third-generation SM particles are favored to interpret these results [41][42][43][44]. In this search, we consider pair-produced scalar LQs, each decaying to a τ lepton and a bottom quark (b). [50] and exclude W R masses below 2.9 TeV, assuming that the mass of the right-handed neutrino is half of the mass of the W R boson, and scalar LQ masses below 850 GeV, assuming that the LQ decays to a τ lepton and a bottom quark with 100% branching fraction. Moreover, searches for third-generation LQs have been performed in other final states: pairs of scalar LQs each of which decays to a τ lepton and a top quark [53], pairs of scalar and vector LQs each of which decays to a quark (top, bottom, or light-flavor) and a neutrino [54], and singly produced scalar LQs in association with a τ lepton with the LQ decaying to a τ lepton and a bottom quark [55]. In this analysis we focus on the ττjj search channel in which both of the τ leptons decay hadronically. Hadronic τ lepton decays account for approximately 65% of all possible τ lepton final states, so that the pair branching fraction is 42%.
The paper is organized as follows. Section 2 gives a brief description of the CMS detector. The event reconstruction is described in Section 3, followed by the description of the simulation of the signal and background samples in Section 4. The selection criteria defining the signal region (SR), described in Section 5, reduce the background contributions to achieve maximum discovery potential. A main challenge of this analysis is to achieve high and well-understood signal selection and trigger efficiencies, with small systematic uncertainty, with SM signatures containing genuine τ h candidates. The strategy is described in Section 6 and relies on the selection of Z(→ )+jets events. A number of additional background-enriched regions are described in Section 6. These regions are defined to minimize the systematic uncertainty of the background contributions as well as to cross-check the accuracy of the efficiency measurements. Relevant

Event reconstruction and particle identification
Jets are reconstructed using the particle-flow (PF) algorithm [57]. In the PF approach, information from all detectors is combined to reconstruct and identify final-state particles (muons, electrons, photons, and charged and neutral hadrons) produced in the pp collision. PF particles are clustered into jets using the anti-k T clustering algorithm [58] with a distance parameter of 0.4. Jets are required to pass identification criteria designed to reject anomalous behavior from the calorimeters. The identification efficiency is >99% for jets with p T > 30 GeV and |η| < 2.4 that are within the tracking acceptance [59]. The jet energy scale and resolution in simulation are corrected to match their measured values in data using factors that depend on the p T and η of the jet [60, 61]. Jets originating from the hadronization of bottom quarks are identified using the combined secondary vertex algorithm [62] which exploits observables related to the long lifetime of b hadrons. For b quark jets with p T > 30 GeV and |η| < 2.4, the algorithm's identification efficiency at the loose working point used in this analysis is about 80%, while misidentification rate for light-quark and gluon jets is about 10% [62]. Although a b-tagged jet requirement is not used to define the LQ SR, b quark jets are used to obtain tt-enriched control samples for estimation of the background rate in the SR.
Although muons and electrons are not used to define the SR, they are utilized to obtain control samples for the background estimations. Electron candidates are reconstructed by first matching clusters of energy deposited in the ECAL to reconstructed tracks. Selection criteria based on the distribution of the shower shape, track-cluster geometric matching, and consistency between the cluster energy and track momentum are then used in the identification of electron candidates [63]. Muons are reconstructed using the tracker and muon chambers. Quality requirements based on the minimum number of measurements in the silicon tracker, pixel detector, and muon chambers are applied to suppress backgrounds from decays in flight and hadron shower remnants that reach the muon system [64]. The muon and electron identification efficiencies for the quality requirements and kinematic range used in this analysis are larger than 98%.
The electron and muon candidates are required to satisfy isolation criteria in order to reject nonprompt leptons that originate from the hadronization process. Isolation is defined as the scalar sum of the p T values of reconstructed charged and neutral particles within a cone of radius ∆R = √ (∆η) 2 + (∆φ) 2 = 0.4 around the lepton-candidate track, excluding the lepton candidate, divided by the p T of the lepton candidate. A correction is applied to the isolation variable to account for the effects of additional pp interactions (pileup) [65]. For charged particles, only tracks associated with the primary vertex are included in the isolation sums. The reconstructed vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex. The corresponding physics-objects are the leptons, jets, and the missing transverse momentum (p miss T ) reconstructed from those objects. The jets are clustered using the anti-k T jet finding algorithm [58,66] with the tracks assigned to the vertex as inputs.
Hadronic decays of the τ lepton are reconstructed and identified using the hadrons-plus-strips algorithm [67], designed to optimize the performance of τ h reconstruction by considering specific τ h decay modes. This algorithm starts from anti-k T jets and reconstructs τ h candidates from tracks (also referred to as "prongs") and energy deposits in strips of the ECAL, in the 1-prong, 1-prong + π 0 , 2-prong, and 3-prong decay modes. The 2-prong decay mode allows τ h candidates to be reconstructed even if one track has not been reconstructed. However, given the large rate for jets to be misidentified in this decay mode, the 2-prong decay mode is not used to reconstruct τ h candidates in the signal region of this analysis. To suppress backgrounds from light-quark or gluon jets, identification and isolation conditions are enforced by requiring the τ h candidates to pass a threshold value of a multivariate (MVA) discriminator [67] that takes isolation variables and variables related to the τ lepton lifetime as input. The isolation variables are calculated using a cone of radius ∆R = 0.5 in the vicinity of the identified τ h candidate and considering the energy deposits of particles not included in the reconstruction of the τ h decay mode. The "tight" MVA isolation working point [67] is used to define the SR, which results in a τ h identification efficiency of typically 55% for the kinematic range used in this analysis. Additionally, τ h candidates are required to be distinguishable from electrons and muons. The algorithm to discriminate a τ h from an electron utilizes observables that quantify the compactness and shape of energy deposits in the ECAL, to distinguish electromagnetic from hadronic showers, in combination with observables that are sensitive to the amount of bremsstrahlung emitted along the leading track and to the overall particle multiplicity. The discriminator against muons is based on the presence of measurements in the muon system associated with the track of the τ h candidate.
The presence of neutrinos from the ττ decays must be inferred from the imbalance of total momentum in the detector. The magnitude of the negative vector sum of the transverse momenta of visible PF objects is the missing transverse momentum. Information from the forward calorimeter is included in the calculation of p miss T , and the jet corrections described above are propagated as corrections to p miss T [68]. Missing transverse momentum is one of the most important observables for differentiating the signal events from background events that do not contain neutrinos, such as quantum chromodynamics (QCD) multijet events.

Signal and background samples
The production of top quark pairs (tt), the production of a Z boson decaying to a τ h pair plus associated jets from initial-state radiation (Z+jets), and QCD multijet processes are the prevailing backgrounds for this search. Background from tt events is characterized by two b quark jets in addition to genuine isolated τ h leptons. The contribution of Z+jets events constitutes an irreducible background since it has the same final state containing genuine, well-isolated τ h candidates, associated energetic jets, and true p miss T from neutrinos present in the τ lepton decays. The QCD multijet events are characterized by jets with a high-multiplicity of particles, which can be misidentified as τ h .
To estimate the main backgrounds, a combination of Monte Carlo (MC) simulated samples and techniques based on data are employed. The dominant backgrounds are estimated from data, using control regions (CR) enriched in the contributions of targeted background processes and with negligible contamination from signal events. Samples of events produced by MC simulation are used to extrapolate background yields from a CR to the SR and to model the shape of the of the distributions of observables defined in Sec. 5 aiming to estimate the mass of the W R (m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T )) and that of the LQ (S MET T ). Subdominant background contributions are estimated using MC simulations. The MADGRAPH5 aMC@NLO 2.6.0 program [69] is used for Z+jets, W+jets, tt+jets, and single-top quark production. The MADGRAPH5 aMC@NLO generator is interfaced with PYTHIA 8.212 [70], using the CUETP8M1 tune [71], for parton shower and fragmentation. The LO PYTHIA generator is used to model the diboson (VV) processes. The MC background and signal yields are normalized to the integrated luminosity using next-tonext-to-leading order or next-to-leading order (NLO) cross sections [72].
The N τ signal samples are generated at the leading order using PYTHIA 8.212 with W R masses ranging from 1 to 4 TeV, in steps of 0.25 TeV. It is assumed that the gauge couplings associated with the left-and right-handed SU(2) groups are equal and the N τ decays are prompt. It is also assumed that the N e and N µ are too heavy to play a role in the decay of W R , and thus W R → τN τ and W R → qq are the dominant decay modes. The branching fraction for the W R → τN τ decay is approximately 10-15%, depending on the W R and N τ masses. For the W R mass range of interest for this analysis, the N τ → τqq branching fraction is close to 100%. The signal cross sections are calculated at the NLO accuracy. The ratios of the NLO and the LO results provide factors of 1.3, known as K factors, for the W R mass range relevant to this analysis [73].
Simulated samples for the scalar LQ signal processes are generated for a range of masses between 250 and 1500 GeV in steps of 50 GeV. The signal MC generation uses PYTHIA 8.212 and CTEQ6L1 parton distribution functions (PDF) [74]. Signal cross sections are calculated at NLO accuracy using the CTEQ6.6M PDF set [72]. The NLO-to-LO K factors range from 1.3 to 2.0 in the mass range 200-1500 GeV [72]. The branching fraction of the LQ to a τ lepton and a b quark is assumed to be 100%.
The mean number of interactions in a single bunch crossing in the analysed dataset is 23. In MC events, multiple interactions are superimposed on the primary collision, and each MC event is re-weighted such that the distribution of the number of true interactions matches that in data.

Event selection
Events are selected with a trigger requiring at least two τ h candidates with p T > 32 GeV and |η| < 2.1 [67]. Additional kinematic criteria on p T and η are applied to achieve a trigger efficiency greater than 90% per τ h candidate. Preselected events are required to have at least two τ h candidates, each with p T > 70 GeV and |η| < 2.1. The |η| < 2.1 requirement ensures that the τ h candidates are fully reconstructed within the tracking acceptance. In addition, the two τ h candidates must be separated by ∆R > 0.4, to avoid overlaps. Selected τ h candidates must also pass the reconstruction and identification criteria described in Section 3. In the LRSM, ττ pairs can be of the opposite or same-sign charge.
The associated jet selection criteria include at least two jets with p T > 50 GeV and |η| < 2.4. To avoid overlaps, only jet candidates separated from the selected τ h candidates by ∆R > 0.4 are considered. The background contribution from QCD multijet events is larger in this analysis than in channels with one or both τ leptons decaying leptonically. To suppress the contribution from QCD multijet events, p miss T is required to be larger than 50 GeV. Finally, the visible invariant mass of the τ h τ h pair, m(τ h,1 , τ h,2 ), is chosen to be greater than 100 GeV, to reduce the Z+jets contribution.
The visible τ lepton decay products, the two highest p T jets, and the missing transverse momentum vector p miss T are used to define an observable for each benchmark scenario considered in the analysis. The heavy neutrino search strategy consists in looking for a broad enhancement of events above the expected background in the distribution of the partial mass indicative of new physics, defined as: On average the partial mass is large in the heavy-neutrino case, m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) ≈ m(W R ). For the pair production of LQs, the scalar sum of the transverse momenta of the decay products and the p miss The set of events satisfying the preselection together with the associated jet selection define the SR. The total expected background yield in the SR, estimated from simulation, is 126 events, with tt, QCD multijet, Z+jets, W+jets, single-top quark, and diboson production composing 38.0, 27.0, 18.4, 11.0, 4.0 and, 1.6% of the rate, respectively. The analysis strategy is similar to that of previous heavy neutrino and leptoquark searches [50, 51]. However, unlike heavy neutrino searches in the eejj or µµjj final states [45, 52], the W R resonance mass in the τ h τ h jj channel cannot be fully reconstructed because of the presence of neutrinos from the τ lepton decays.
The signal selection efficiency for the W R process, assuming that the N τ mass is half of the W R mass, is 2.0% for m(W R ) = 1.0 TeV and 6.6% for m(W R ) = 4.0 TeV. The corresponding efficiency for LQ → τb events is 5.1% for m(LQ) = 0.6 TeV and 8.2% for m(LQ) = 1.0 TeV. These efficiencies include the 42% branching fraction of ττ to τ h τ h .

Background estimation
The tt, QCD multijet, and Z+jets processes are expected to account for 84% of the total background. Dedicated CRs are used to check the modeling of tt and Z+jets events in simulation and to determine if any corrections need be applied. The estimation of the QCD multijet background is performed using a method fully based on data. The remaining contributions arising from W+jets, single-top quark, and diboson events are obtained from simulation.
A tt-enriched control sample is obtained with similar selections to the SR, except selecting two well-identified muons instead of two τ h candidates, requiring at least one b-tagged jet, and vetoing dimuon candidates around the Z boson mass peak (80 < m µµ < 110 GeV). Since the dijet and p miss T selection criteria are the same as in the SR, the data-to-simulation scale factor SF tt µµ = 0.93 ± 0.01 measured in this CR represents a correction for the modeling of the dijet and p miss T selection efficiencies by simulation. Figure 3 (right) shows the S MET T distribution in this CR, after correcting the tt normalization from simulation using the measured scale factor SF tt µµ . The agreement gives confidence that the S MET T shape for the tt background can be taken from simulation. An alternate estimate of the scale factor is obtained from a CR defined with the same dijet and p miss T requirements as for the SR but selecting events with one muon and one electron (instead of a τ h τ h pair). The resulting estimate, SF tt eµ = 0.90 ± 0.01, is combined with the measurement from the dimuon CR; the average of the two scale factors (SF tt ) is used to estimate the tt prediction in the SR, and the absolute difference between the two scale factors, 3%, is considered a systematic uncertainty in the estimated tt yield. Therefore, the tt contribution in the SR, N tt SR , is given by N tt SR = N tt SR (MC)SF tt . The measurement of the Z+jets background component is based on both simulation and data. Ideally the Z+jets contribution to the SR would be obtained using a CR obtained with similar τ h τ h jj criteria to the SR, but with minimal modifications to the selection to achieve negligible signal contamination. However, such a CR has too few events, resulting in large systematic uncertainty. Instead, since the efficiency of the requirement of two high quality τ h candidates is known to be well modeled by simulation [67], we use a Z+jets-enriched control sample obtained by requiring two well-identified muons with an invariant mass compatible with the Z-mass peak, instead of two τ h candidates, and all of the other event selection criteria used in the SR. Since muons are produced in Z-decays as often as τ leptons, a µµjj control sample can be used to measure a correction factor SF Z→µµ dijet for the modeling of two additional jets, independently from the τ h τ h requirement, and with reduced systematic uncertainty. Candidate events for the Z(→ µµ)+jets control sample were collected using a trigger that requires at least one isolated muon with p T (µ) > 24 GeV per event. The measured correction factor is SF Z→µµ dijet = 1.02 ± 0.02. Therefore, the Z(→ ττ) contribution in the SR can be calculated The modeling of the shapes of the m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) and S MET T distributions is checked in Z(→ ττ)+jets events that pass relaxed conditions on the τ h p T threshold (p T > 60 GeV) and an inverted requirement on the mass of the τ h τ h pair (m(τ h,1 , τ h,2 ) < 100 GeV). Figure 3 (left) shows the m(τ h,1 , τ h,2 , j, p miss T ) distribution in this CR. The simulated and observed distributions of m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) and S MET T are found to be in agreement.
Events from QCD multijet processes become a background when two jets are misidentified as τ h candidates. To avoid reliance on simulation, which may not be trustworthy at the high values of p T , m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ), and S MET T of the search region, the QCD multijet background is estimated from data using the matrix ("ABCD") method. Since p miss T and τ h isolation are the main discriminating variables against QCD multijet events, the estimation methodology for this background utilizes CRs obtained by inverting the requirements on these observables. It has been checked that the p miss T and the τ h isolation variables are uncorrelated. In the remainder of this section, events obtained by inverting the isolation requirement on both τ h candidates will be referred to as nonisolated τ h τ h samples. The regions used to perform the QCD multijet estimation, referred to as ABCD, are defined as follows: Here N B QCD /N A QCD is referred to as the isolation "tight-to-loose" (TL) ratio. The shapes of QCD multijet events in data containing two nonisolated τ h candidates are normalized using the TL ratio. This procedure yields a QCD multijet estimate of N SR QCD = 33.8 ± 6.0. The uncertainty is based on the event counts in the data and MC samples. To check that the shapes of the m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) and S MET T distributions obtained from the nonisolated CR are the same as the ones in the isolated region, we use events from QCDenriched CRs A and B. Figure 4 shows the m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) and S MET T distributions in CR B. The shape of QCD multijet events is obtained from data in CR A, after subtracting non-QCD contributions using the simulation. The expected QCD multijet yield is calculated as N B QCD = N B Data − N B =QCD , such that the total background yield matches the observed number of events in data. Therefore, the focus of this test is the overall agreement of the QCD multijet shapes extracted from the nonisolated τ h region, as applied to the isolated region. The agreement between the data and the predicted background distributions in Fig. 4 gives confidence that the m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) and S MET T shapes for the QCD multijet background can be extracted from the nonisolated side-band and helps reduce the uncertainty in the final QCD multijet background estimate. (right). The shape of the QCD background is found from data in the loose τ h region, CR A and then applied to CR B, defined by p miss T < 50 GeV and tight τ h isolation. For both samples, the non-QCD contributions are estimated from simulation. Note that the normalizations match by construction. The bottom frame shows the ratio between the observed data in CR B and the total background estimation.

Systematic uncertainties
The imperfect MC modeling of the background processes considered in this analysis can affect the normalizations and shapes of the m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) and S MET T distributions used for the final result. Therefore, these effects are included as systematic uncertainties. The following systematic uncertainties are considered. A p T -dependent uncertainty per τ h candidate in the measured trigger efficiency results in a 6% uncertainty in the signal and background predictions that rely on simulation. The trigger efficiency is measured per τ h candidate by calculating the fraction of Z(→ ττ → µτ h ) events (selected with a single-µ trigger), that also pass a µτ h trigger that has the same τ h trigger requirements as the τ h τ h trigger used to define the SR. Systematic effects related to the correct τ h identification are measured to be 5% per τ h candidate [75]. This effect is estimated from a fit to the Z(→ ττ) visible mass distribution, using the production cross section measured in the Z(→ ee) and Z(→ µµ) final states. An additional asymmetric systematic uncertainty of +5% and −35% at p T = 1 TeV] [67] that increases linearly with p T is included to account for the extrapolation in the τ h identification efficiency estimate, which is mostly determined by low-p T hadronic τ lepton decays close to the Z boson peak, to the higher-p T regimes relevant to this analysis. A 3% uncertainty in the reconstructed τ h energy scale (TES) is used to assign a systematic uncertainty in both the predicted yields and the mass and S MET T shapes for signal and background with total or partial MC estimation [67]. This effect ranges from 3 to 9% depending on the sample. Systematic effects on normalization and shapes due to the uncertainty in the jet energy scale (JES) (2-5% depending on p T and η) are also included, resulting in 5 to 9% uncertainty in the normalization, depending on the sample. Systematic uncertainties in the shapes, based on the level of agreement between the data and MC distributions in the control samples, are also assigned. The data-to-simulation ratios of the mass and S MET T distributions are fit with a first-order polynomial. The deviation of the fit from , is assigned as a systematic uncertainty in the shape. This results in up to 20% systematic uncertainty in a given bin. We have checked that the choice of a first-order polynomial for the fit function adequately describes potential differences between data and MC simulation. A 2.5% uncertainty comes from the measurement of the total integrated luminosity [76], and affects signal and all backgrounds that are determined (in part or entirely) by simulation.
Other contributions to the total systematic uncertainty in the predicted background yields arise from the validation tests and from the statistical uncertainties associated with the data control regions used to determine the SF tt , SF Z→µµ dijet , and TL factors. The relative systematic uncertainties in SF tt and SF Z→µµ dijet related to the statistical precision in the CRs range between 1 and 2%, depending on the background component. For the QCD multijet background, the systematic uncertainty is dominated by the statistical uncertainty in the TL factor (18%). The systematic uncertainties in the SF tt , SF Z→µµ dijet , and TL factors, evaluated from the validation tests with data and from the subtraction of nontargeted backgrounds, range from 3% for SF tt to 10% for TL.
The uncertainty in the signal acceptance (6%) associated with the choice of the PDF set included in the simulated samples is evaluated in accordance to the PDF4LHC recommendation [77][78][79]. The absence of higher-order contributions to the cross sections affect the signal acceptance calculation. This effect is estimated by varying the renormalization and factorization scales a factor of two with respect to their nominal values, and by considering the full change in the yields. They are estimated from simulation and found to be small for both signal (2.5%) and background (1% for diboson and 3.5% for tt). Table 1 summarizes the systematic uncertainties considered in the analysis. The total systematic uncertainties in the background normalizations range from 18 to 37%, depending on the background, while the total systematic uncertainty in the signal normalization is approximately 15%.

Results
The observed yield is 117 events, while the total predicted background yield is 127.0 ± 11.8 events (see Table 2). Table 2 illustrates the relative importance of the different backgrounds. Note, however, that the relative yields of different background processes do not directly reflect the effect on the sensitivity of the analysis, as a binned maximum likelihood fit, in which shape information enters besides the yields, is used to set limits on the signal rate. Figure 5 shows the background predictions, the observed data, and the expected signal in the m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T )   Fig. 5 (right). The observed data event rate and shapes are consistent with the SM background expectation. Therefore, exclusion limits for the two signal benchmark scenarios are set, using the distribution in m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) for the N τ case and in S MET T for the LQ interpretation. The results are presented as 95% confidence level (CL) upper limits on the signal production cross sections, estimated with the modified frequentist construction CL s method [80][81][82]. Maximum likelihood fits are performed using the final m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) and S MET T discrimination variables to derive the expected and observed limits. Systematic uncertainties are represented by nuisance parameters, assuming a gamma function prior for the uncertainties in the data-driven background estimations, log-normal prior for MC-driven normalization parameters, and Gaussian priors for the shape uncertainties. Statistical uncertainties in the shape templates are accounted for by the technique described in Ref. [83]. Figure 6 shows the expected and observed limits on the cross section, as well as the theoretical prediction [72,73], as functions of m(W R ) and m(LQ). For heavy neutrino models with strict left-right symmetry, with the assumptions that only the N τ flavor contributes significantly to the W R decay width and that the N τ mass is 0.5 × m(W R ), W R masses below 3.50 TeV are excluded at 95% CL (expected exclusion 3.35 TeV). For the LQ interpretation using S MET T as the final fit variable, the observed (expected) 95% CL exclusion is 1.02 (1.00) TeV. These results are the most stringent limits to date. Figure 7 shows 95% CL upper limits on the product of the production cross section and branching fraction, as a function of m(W R ) and x = m(N τ )/m(W R ). The signal acceptance and mass shape are evaluated for each {m(W R ), x} combination and used in the limit calculation procedure described above. The W R limits depend on the N τ mass. For example, a scenario with x = 0.1 (0.25) yields significantly lower average jet and subleading τ h p T than the x = 0.5 mass assumption, and the acceptance is lower by a factor of about 16 (3) for m(W R ) = 1.0 TeV and about 5.8 (1.8) for m(W R ) = 3.0 TeV. On the other hand, the x = 0.75 scenario produces similar or larger average p T for the jet and the τ h than the x = 0.5 mass assumption, yielding an event acceptance that is about 10% larger. Masses below m(W R ) = 3.52 (2.75) TeV are excluded at 95% CL, assuming that the N τ mass is 0.8 (0.2) times the mass of the W R boson.

Summary
A search is performed for physics beyond the standard model in events with two energetic τ leptons and two energetic jets, using data corresponding to an integrated luminosity of 35.9 fb −1 collected in 2016 with the CMS detector in proton-proton collisions at √ s = 13 TeV. The search focuses on two benchmark scenarios: (1) the production of heavy right-handed Majorana neutrinos, N , and right-handed W R bosons, which arise in the left-right symmetric extensions of the standard model and where the W R and N decay chains result in a pair of high transverse momentum τ leptons; and (2) the pair production of third-generation scalar leptoquarks that decay to ττbb. The observed m(τ h,1 , τ h,2 , j 1 , j 2 , p miss T ) and S MET T distributions do not reveal any evidence for physics beyond the standard model. Assuming that only the N τ flavor contributes significantly to the W R decay width, W R masses below 3.52 (2.75) TeV are excluded at 95% confidence level, assuming the N τ mass is 0.8 (0.2) times the mass of the W R boson. In the second beyond the standard model scenario, leptoquarks with a mass less than 1.02 TeV are excluded at 95% confidence level, to be compared with an expected mass limit of 1.00 TeV. Both of these results represent the most stringent limits to date for ττjj final states.    [38] LHCb Collaboration, "Measurement of the ratio of branching fractions [39] LHCb Collaboration, "Angular analysis of the B 0 → K * 0 µ + µ − decay using 3 fb  [50] CMS Collaboration, "Search for third-generation scalar leptoquarks and heavy right-handed neutrinos in final states with two tau leptons and two jets in proton-proton collisions at √ s = 13 TeV", JHEP 07 (2017) 121, doi:10.1007/JHEP07(2017)121, arXiv:1703.03995.