Search for W' to tb in proton-proton collisions at sqrt(s) = 8 TeV

A search is performed for the production of a massive W' boson decaying to a top and a bottom quark. The data analysed correspond to an integrated luminosity of 19.7 inverse femtobarns collected with the CMS detector at the LHC in proton-proton collisions at sqrt(s) = 8 TeV. The hadronic decay products of the top quark with high Lorentz boost from the W' boson decay are detected as a single top flavoured jet. The use of jet substructure algorithms allows the top quark jet to be distinguished from standard model QCD background. Limits on the production cross section of a right-handed W' boson are obtained, together with constraints on the left-handed and right-handed couplings of the W' boson to quarks. The production of a right-handed W' boson with a mass below 2.02 TeV decaying to a hadronic final state is excluded at 95% confidence level. This mass limit increases to 2.15 TeV when both hadronic and leptonic decays are considered, and is the most stringent lower mass limit to date in the tb decay mode.


Introduction
Many extensions of the standard model (SM) predict new massive charged gauge bosons [1][2][3].The W boson, for example, is a heavy partner of the SM W gauge boson that could manifest itself in proton-proton collisions at the CERN LHC.Searches for a high-mass W boson resonance have been performed at the Tevatron [4,5] and the LHC [6][7][8][9][10][11][12][13][14][15] in the lepton, diboson, and diquark final states.We present a search based on the W + → tb (and charge conjugate) decay.This decay channel is of particular interest because the SM backgrounds can be greatly reduced compared to those for W decays to light quarks, and some models predict a stronger W coupling to third generation quarks [16].The hadronic decay channel (W → tb → qqbb) is presented in detail, along with the combination with the already published leptonic channel (W → tb → νbb) [6].The combination of these two channels leads to a significant increase in sensitivity.
The most general, lowest dimension effective Lagrangian that describes the interaction of the W boson with quarks [17] can be written as:

L =
V q i q j 2 √ 2 g w q i γ µ a R q i q j (1 + γ 5 ) + a L q i q j (1 − γ 5 ) W q j + h.c., (1) where the parameters a L q i q j and a R q i q j represent the left-handed and right-handed couplings of the W boson to quarks, g W is the SM weak coupling constant, and V q i q j is the Cabibbo-Kobayashi-Maskawa matrix.For a SM-like W boson, a L q i q j = 1, a R q i q j = 0.
Strict cross section upper limits have previously been placed in the case of low mass W signals [5,6].At higher masses, specifically M W 1.3 TeV, the top quark is highly energetic.Because of the Lorentz boost, the angular separation between the top quark decay products (W boson and b quark) is small.The final state particles resulting from the hadronization of the b quark and the decay of the W boson into light quarks usually overlap, resulting in a single jet with top flavour, the "top quark jet", or t jet.Dedicated methods, applied to resolve the substructure of this t jet, enable background processes to be strongly suppressed.We apply b jet identification algorithms (b tagging) to the b jet from the W decay in order to further reduce the SM background.
We reconstruct the W boson mass as the invariant mass of the top and bottom quarks (M tb ), and use the M tb distribution to derive limits on the production cross section of the W boson.We also obtain limits on the couplings of the W boson to quarks, and present the W production cross section limits obtained from a combination of hadronic and leptonic decay channels.The leptonic decay channel alone excludes a W boson with a mass less than 2.05 TeV [6], which prior to this paper was the most restrictive limit obtained to date in the tb final state.The combination of the leptonic and hadronic channels makes it possible to extend this limit.

The CMS detector
The central feature of the CMS apparatus [18] is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the field volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections.Forward calorimeters extend the pseudorapidity coverage provided by the barrel and endcap detectors.Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid.
The silicon tracker detects charged particles within the pseudorapidity range |η| < 2.5.It consists of 1440 silicon pixel and 15 148 silicon strip detector modules and is located in the field of the superconducting solenoid.For non-isolated particles with 1 < p T < 10 GeV and |η| < 1.4, the track resolutions are typically 1.5% in p T and 25-90 (45-150) µm in the transverse (longitudinal) impact parameter [19].Non-isolated particle tracks are of particular importance to this analysis, as they are typically the constituents of jets, and are found within the detector barrel acceptance with an efficiency larger than 90%.
In the region |η| < 1.74, the HCAL towers have widths of 0.087 in pseudorapidity and 0.087 radians in azimuth (φ).In the η-φ plane, and for |η| < 1.48, the HCAL towers map on to 5 × 5 ECAL crystal arrays to form calorimeter towers projecting radially outwards from close to the nominal interaction point.At larger values of |η|, the size of the ECAL and HCAL towers increases and the matching ECAL arrays contain fewer crystals.Within each tower, the energy deposits in ECAL and HCAL towers are summed to define the calorimeter tower energies, which are subsequently used to provide the energies and directions of hadronic jets.
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. [18].

Event reconstruction
The particle-flow (PF) event algorithm [20,21] reconstructs and identifies each individual particle with an optimized combination of information from the various elements of the CMS detector.The energy of photons is directly obtained from the ECAL measurement, corrected for zero-suppression effects.The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track.The momentum of muons is obtained from the curvature of the corresponding track as determined by the tracker and muon system.The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for zero-suppression effects and for the response function of the calorimeters to hadronic showers.Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energies.
Jets are reconstructed using the Cambridge-Aachen (CA) [22,23] algorithm with a distance parameter of 0.8 (CA8 jets) as implemented by FastJet 3.0.4[24,25] to cluster PF candidates into jets.This algorithm clusters constituents (the reconstructed PF candidates in each event) to form jets based only on the angular distance between them.The CA algorithm has been shown to have higher efficiency for distinguishing jet substructure [26] than competing jet clustering algorithms.
Jet momentum is determined as the vector sum of all particle momenta in the jet, and is found in the simulation to be equal to the true momentum at hadron level within 5% to 10% over the full p T spectrum and detector acceptance.
The jet energy resolution amounts typically to 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV, to be compared to about 40%, 12%, and 5% obtained jet clustering is based on calorimeter information only rather than on PF candidates.
The jet energy in simulation is corrected using measurements derived from data.The jet energy corrections for the CA jets are derived from the anti-k T (AK) jet clustering algorithm [27] with a distance parameter value of 0.7.The AK jet energy corrections have been shown to be applicable to CA jets [28].The uncertainty associated with this procedure is noted in Section 6.1.
We use the charged hadron subtraction method [29] to remove charged hadrons that originate from a non-leading vertex prior to the application of the jet clustering algorithm, where the leading vertex is defined as the vertex with the largest sum of p 2 T .After this procedure, the neutral component of pileup (inelastic proton-proton pair interactions in the same bunch crossing) is subtracted using an area based method [30].

Signal modeling
The signal samples are generated at leading order with the CompHEP [31] package and then scaled to next-to-leading order using a factor of 1.2 [17].We generate signal samples using three coupling hypotheses (see Eq. ( 1)): • W R -purely right-handed W boson where a L q i q j =0 and a R q i q j =1; • W L -purely left-handed W boson where a L q i q j =1 and a R q i q j =0; • W LR -mixed-coupling W boson where a L q i q j =1 and a R q i q j =1.
The W R width varies from 44 to 91 GeV for the mass range considered in this analysis.The generation of the left-handed and mixed-coupling samples takes into account the interference with the SM s-channel single top quark production.

Combined CMS t-tagging algorithm
When the W boson decays to hadrons, the top quark can be detected as three jets.The high boost of the top quark from a W boson decay causes the three jets to merge into one large jet with a distinct substructure.The CMS t-tagging algorithm [32] discriminates signal from background by using this characteristic substructure.The algorithm reclusters the CA jet until it finds anywhere from 1 to 4 subjets In this process, particles with low p T or at a large angular distance from the jet centre are omitted.The t-tagging algorithm is based on the following selection: • Jet mass 140 < M jet < 250 GeV -The mass of the CA jet is required to be consistent with the top quark mass.
• Number of subjets N subjets > 2 -The number of subjets found by the algorithm must be at least 3.
• Minimum pairwise mass M min > 50 GeV -The three highest p T subjets are taken pairwise, and the pair with the lowest invariant mass is calculated (M min ).The value of M min is required to be greater than 50 GeV for consistency with the W boson mass.
In addition to these requirements, the N-subjettiness algorithm is used for t-jet identification [33].This algorithm defines the τ N variables, which describe the consistency between the jet energy and the number of assumed subjets, N: where ∆R J,i is the angular distance (∆R = √ (∆η) 2 + (∆φ) 2 ) measured between the subjet candidate (J) axis and a specific constituent particle (i), and d is the normalization factor: where R is the characteristic distance parameter used by the jet clustering algorithm.A jet with energy consistent with N subjets will typically have a low τ N variable.A t jet should be more consistent with three subjets than two (when compared to jets originating from a gluon or a light quark), therefore the ratio of τ 3 and τ 2 allows top jets to be distinguished from multijet events from QCD processes (labeled in the following as QCD background).We select events with τ 3 /τ 2 < 0.55.
We apply the combined secondary vertex (CSV) b-tagging algorithm to all of the subjets found by the t-tagging algorithm.We require the maximum CSV discriminator value to pass CSV b tagging at the medium operating point (SJ CSVMAX ≥ 0.679) [34].The CMS t tagger with the addition of N-subjettiness and subjet b tagging is referred to as the combined CMS t tagger.
Substructure variables in the signal region exhibit known differences between data and simulation that affect the t-tagging efficiency.We derive a scale factor that is the ratio of the t-tagging efficiency measured in data to simulation [32], using hadronic top quark decays from a control region that consists of an almost pure sample of semileptonic tt events.This ratio, which is measured to be 1.04 ± 0.13, is applied as a correction factor to the signal samples that are used in this analysis.

Identification of b jets
To identify the b quark daughter of the W boson, we start with the b-candidate jet, which is the highest p T jet that is hemispherically separated from the top-tagged jet.We apply the CSV algorithm used to identify b jets to this b-candidate jet.The medium operating point is used, which has a light-flavour jet misidentification probability of 1% for an efficiency around 70%.A scale factor is applied to correct for differences in b-tagging efficiency between data and simulation [34].The uncertainties in this scale factor are described in Section 6.1.Backgrounds from SM tt production are reduced by requiring the invariant mass of the b-candidate CA jet to be below 70 GeV.

Reconstruction of W mass
We select candidate W → tb events by using the following criteria, which are applied to the two leading jets: • One jet with p T > 450 GeV identified with the combined CMS t-tagging algorithm; • One jet with p T > 370 GeV with a CSV b tag at the medium operating point and mass <70 GeV; • The two jets are in opposite hemispheres (|∆φ| > π/2); • The difference in rapidity between the two jets (|∆y|) is less than 1.6.
The number of events after each successive selection remaining in data, SM tt production, schannel single top, and right-handed W boson signal simulations is shown in Table 1.

Event samples
The data used for this analysis correspond to an integrated luminosity of 19.7 fb −1 of pp collisions provided by the LHC at a centre-of-mass energy of 8 TeV.We select events online using a trigger algorithm that requires the scalar p T sum of reconstructed jets in the detector to be >750 GeV.The trigger is nearly 100% efficient for events selected in the offline analysis.The small trigger inefficiency is measured from data and applied to the simulated events.Table 1: Numbers of observed and expected events at successive stages of the event selection.The expected numbers are scaled to an integrated luminosity of 19.7 fb −1 .Statistical uncertainties in the event yields are quoted.The QCD background contribution is only reported for the final selection.The first row implies a 150 GeV p T selection on the jets, the trigger selection, and the requirement that the two leading jets be in opposite hemispheres.The row labeled "p T " represents the transverse momentum requirements placed on the two leading jets.The signal events, shown for several values of the W boson mass, are normalized to the theoretical cross section.The s-channel single top contribution (ST s ) is given as well as it is used when deriving the shape of the signal distribution when calculating the generalized coupling limits.

Background modeling
The primary sources of background are SM QCD multijet and tt production.These backgrounds dominate because of QCD background events after selecting an all-jet final state is selected and the large contribution from tt production that remains after t-jet discrimination criteria are applied.
The principal background in this analysis is QCD multijet production, and is estimated using a data-driven technique to extract both the shape and the normalization.The average b-tagging rate, measured from events with an enhanced QCD multijet component and a negligible signal contamination component, is used to estimate the QCD multijet contribution in the signal region.We account for the background contribution from SM tt production when measuring the b-tagging rate.In addition to the region used to extract the average b-tagging rate, we define two test regions to check the QCD background prediction, both of which have small tt background and possible signal contamination.
The shape of the M tb distribution for tt production is estimated from Monte Carlo (MC) simulation, and the yield is measured from data using a control sample enriched in tt events.

QCD background estimate
A control sample is obtained by inverting the N subjets selection criteria used to identify t jets: 140 < M jet < 250 GeV; (4) N subjets ≤ 2; (5) We apply the b tagging criteria to the b-candidate jet in the event to measure the average btagging rate for QCD jets.We assume that this rate is the same for QCD jets in the signal region.We include the subjet CSV discriminant in this control sample in order to ensure similar parton flavour distributions in the signal and control regions.Because of the similar parton flavour distributions, and the fact that this region has a low tt and signal contamination component, this control sample is an ideal selection to extract the average b-tagging rate.The average btagging rate is parameterized as a function of the p T of the b-candidate jets (which pass all requirements except the b tag) in three |η| regions: Events in the signal region that do not have b tagging applied are then weighted by this average b-tagging rate to estimate the QCD background contribution in the final selection.Events in the signal region before b tagging is applied are largely from QCD background, but the small tt background component (less than 1%) is subtracted when deriving the QCD background contribution to avoid double counting.
We use a bifurcated polynomial to fit the average b-tagging rate in each of these |η| ranges.This fitting function, which provides a satisfactory description of the data, is defined as follows: Here, the parameters p 0 to p 3 are the polynomial coefficients, and x is the p T of the b-candidate jet.The parameter a is the bifurcation point, and is optimized for each region in |η|.It is chosen to be 500, 500, and 550 GeV for the low, transition, and high |η| regions, respectively.The parameterization of the average b-tagging rate helps to constrain the known p T and |η| kinematic correlation inherent in b tagging, which is due to detector geometry and tracking resolution.
The uncertainty in the average b-tagging rate is extracted using the full covariance matrix obtained from the output of the fitting algorithm.Additionally, we assign a systematic uncertainty to cover the choice of the fit function (see Section 6.1) based on several alternative functional forms (such as second degree polynomial or exponential functions).Fig. 1 shows the measured average b-tagging rate and associated uncertainty bands.

The tt background estimate
We obtain the normalization of the background contribution from SM tt production using a control sample in data.A sideband region is defined (CR3) by inverting the b-candidate mass requirement (see Section 3.3) in the signal region.This region has an enhanced fraction of tt events and is statistically independent from all other sidebands in the analysis.
We compare the sum of the QCD background estimate from data and the SM tt contribution obtained from MC simulation to the observed yield in data.The tt and single top quark production samples used in this analysis are generated using the POWHEG [35][36][37] 1.0 event generator and are normalized to the SM expectation using next-to-next-to leading-order cross sections [38,39].
For the QCD background determination in this sideband region, we use the procedure outlined in Section 5.1.However, we invert the b-candidate mass requirement when extracting the average b-tagging rate in order to account for potential correlations between the b-candidate mass and the b-tagging rate.
We perform a binned maximum likelihood fit to the invariant mass distribution of the bcandidate jets, using the shape of the tt background MC prediction as one template, and the QCD background prediction from data as the other.The normalization of the QCD background template is allowed to vary within its systematic uncertainty envelope, whereas the normalization of the tt template is left unconstrained.The result of the fit is shown in Fig. 2. The contamination from tt events must be taken into account when obtaining the QCD background template in this sideband from data.The fit described above independently varies the QCD and tt templates, however the component of the QCD background from tt events introduces a small anticorrelation between the two templates.We account for this by first fitting the QCD background before the tt component is subtracted and correcting the resulting tt normalization by the factor 1+C/S, where C/S is the ratio of the nominal number of tt events in the control region (C) to that in the signal region (S).After applying this correction, the tt normalization obtained from the fit is independent of the fraction subtracted from the QCD background template.Following this procedure we find that the SM tt production rate in the signal region must be scaled by a factor of 1.23 ± 0.24.
In order to correct for known differences in the top quark p T spectrum between data and MC simulation of SM tt production [40], we reweight the MC events using the generator level p T of the top quark and top anti-quark.Although this procedure was not designed for the kinematic range in our analysis, we still use it as the change to the normalization of the tt background template is consistent with our measurement of this extra normalization factor.

Control region closure test
To investigate the applicability of the QCD background estimation in data, we apply the average b-tagging rate to control regions of the t-tagging selection defined in Section 3.2.First, we define a control region with inverted minimum pairwise mass and N-subjettiness selections (CR1).This region is orthogonal to both the signal region and the control region that is used for the determination of the average b-tagging rate.The selection also has a very low yield of tt production, which allows for a precise measurement of the QCD background contribution.The average b-tagging rate used for this closure test is extracted from the same control region as the signal region, and is applied to events that are not b tagged.This test shows good agreement as shown in Fig. 3 (top).Additionally, we define a control region with an inverted subjet b-tagging selection (CR2).This test also shows good agreement as seen in Fig. 3

(bottom).
These control regions have low signal contamination.For the 1.90 TeV W R sample, the signal contamination is less than 1%.These control regions are summarized in Table 2.

Results
After constraining the SM tt normalization using a particular control region (see Section 5.2), and investigating the agreement of the data and the QCD background estimate in two additional control regions (see Section 5.3), the background estimate is used to predict the data distribution in the signal region, in the absence of a W boson contribution.The results are shown in Fig. 4. Good agreement between data and expectation from SM processes are observed, with no signs of a new physics signal.

Systematic uncertainties
We consider several sources of systematic uncertainty, corresponding to uncertainties in both the shape and normalization of the M tb distribution, which are summarized in Table 2.
A 19% normalization uncertainty is assigned to the estimate of the SM tt normalization (see Section 5.2).The scale factor used to account for differences in the t-tagging efficiency between MC and data has an uncertainty of 13% [32].The uncertainty in the integrated luminosity is 2.6% [41].Finally, the MC to data scale factor for the b-tagging efficiency is evaluated using AK jets but is applied to CA jets, which requires a systematic uncertainty of 2% in addition to the b-tagging scale factor uncertainty of around 8%.
Several uncertainty sources contribute to the estimation of the average b-tagging rate, which is used to evaluate the QCD background prediction.We include a contribution due to the uncertainties obtained from the polynomial fit used to parameterize the b-tagging rate, and investigate the effect of choosing alternative functional forms in the fit.We also obtain an estimate of the uncertainty caused by the specific parameterization of the average b-tagging rate by studying an alternative parameterization using p T , η, and M tb .
We derive an uncertainty in the effect of p T reweighting on the shape of the tt background by taking the unweighted M tb distribution as the +1σ shape.
The uncertainty arising from the variation of the renormalization and factorization scales in tt production is evaluated from MC samples generated with two times (+1σ) and one half (−1σ) the nominal renormalization and factorization scales.
The b-tagging scale factor ±1σ values are applied to tt production and signal MC [34].The nominal jet energy corrections created for use with AK jets are applied in the analysis.The ±1σ uncertainties in jet energy scale and resolution arising from the application of AK jet energy scale corrections are also considered.Additionally, a 3% uncertainty is applied to the jet energy scale to account for differences in CA and AK jets.Finally, the uncertainty in the trigger turn-on efficiency that is applied to the MC samples is taken as one half of the trigger inefficiency.
Uncertainties arising from parton distribution functions are studied by varying the eigenvalues of the parton distribution functions that are used in the simulation.Pileup modeling in simulation is corrected by comparing the number of pileup interactions to the mean number of interactions in data.The uncertainty on this correction is studied by varying the minimum bias cross section.These sources, along with the jet angular resolution variation, are negligible.
The two largest systematic effects arise from the uncertainties in the average b-tagging rate for the QCD background (approximately a 6% normalization effect) and in the top tagging scale factor for the signal (13%).
The distribution of M tb shown for data, tt, QCD, single top, and several example signal W boson mass hypotheses.The normalization for the W signal samples assumes the cross section from theory.The distributions are shown after the application of all selection criteria.The background contribution from single top quark production is not considered when setting limits.The hatched region shows the background uncertainty, obtained by adding the statistical and systematic uncertainties in quadrature.The bottom plot shows the pull ((databackground)/σ) between the data and the background estimate distributions.

Cross section limits
To set limits on the production cross section of the W R boson model described in Eq. ( 1), we compare, for each bin in the M tb distribution, the numbers of observed and expected events.The small background contribution from single top quark production is not considered when setting limits.The following expression is used to compute the expected contribution from W R boson production: where σ W R is the W R cross section, B W R →tb;W→hadrons is the branching fraction W R → tb with the W boson decay constrained to the hadronic branching fraction, ε is the signal efficiency, and L dt is the integrated luminosity of the data set.We perform a binned maximum likelihood fit to compare the M tb distribution from data with the W R boson signal hypothesis, summed together with the SM distribution obtained from the background estimation procedure described in Section 5.
A Poisson model is used for each bin of the M tb distribution.The mean of the Poisson distribution for each bin is taken to be: where k includes both the signal and background models, β k is the Poisson mean for process k, and T k,i represents the fraction of events expected for each process k in bin i.
The likelihood function is then: where N data i is the number of events in data for bin i.
Using a Bayesian approach with a flat prior for the signal cross section, we obtain 95% confidence level (CL) upper limits on the production cross section of W R .Pseudo-experiments are used to derive the ±1σ deviations in the expected limit.The systematic uncertainties described above are accounted for by nuisance parameters and the posterior probability is refitted for each pseudo-experiment.The cross section upper limits are shown in Fig. 5.We exclude a W R boson with a mass less than 2.02 TeV at 95% CL .
We combine the results from the hadronic and leptonic W decay modes to enhance the sensitivity of the analysis to W production and the measurement of the coupling strengths of the W boson to quarks.The analysis of the leptonic channel excludes a W mass below 2.05 TeV, and is described in Ref. [6].The all hadronic and leptonic channels have similar sensitivity in the high W mass regime, which leads to a large increase in sensitivity in the combined result.
The hadronic channel probes W signal generated from a mass of 1.3 to 3.1 TeV because of the sensitivity of the boosted top jet tagging techniques, whereas the leptonic channel probes W masses from 0.8 to 3.0 TeV because of the higher sensitivity at low W mass. Therefore, the region of combined sensitivity ranges from a W mass of 1.3 to 3.0 TeV.Below this region, only the leptonic channel limits are quoted.
There are points within the region of combined sensitivity where the signal sample exists for the leptonic channel but not for the hadronic channel.These intermediate mass points are reproduced using ROOFIT [42] template morphing to interpolate the shape of the M tb spectrum.The generator level selection on the p T of the b quark for the left-handed and mixed-coupling W samples is taken into account by interpolating the selection efficiency for the intermediate mass points.
We assume that the uncertainties in jet energy scale, jet energy resolution, b-tagging scale factors, and the total integrated luminosity are correlated between the two samples.All other systematic uncertainties are assumed to be uncorrelated.These include the renormalization and factorization scale and p T reweighting uncertainties, since different generators are used for the simulation of tt events and the hadronic channel extracts the tt normalization from data.The method for setting combined cross section upper limits is identical to the limit setting procedure of the all hadronic channel, except a joint likelihood is used that considers both channels.
The W R combined cross section upper limits are shown in Fig. 6.A W R boson with a mass below 2.15 TeV is excluded at 95% CL. Figure 5: The W R boson 95% CL production cross section times B W R →tb limits for the hadronic channel.The observed (solid) and expected (dashed) limits, as well as the W R boson theoretical cross section (dot-dashed) are shown.As indicated in the legend, the shaded regions about the expected limits represent 1 and 2σ bands.

Generalized coupling limits
To set limits on generic couplings, we use the procedure outlined in Ref. [6].Because the left-handed and mixed-coupling samples cannot be separated from SM single top quark production, we set limits on the couplings a L and a R .The SM single top quark production is negligible when setting cross section limits.As it is used for signal modeling in the generalized coupling analysis, it needs to be included in that calculation.For limit setting, we reweight the Figure 6: The W R boson 95% CL production cross section times B W R →tb limits for the combined hadronic and leptonic channels.The observed (solid) and expected (dashed) limits, as well as the W R boson theoretical cross section (dash-dotted) are shown.As indicated in the legend, the shaded regions about the expected limits represent 1 and 2σ bands.The region to the left of the vertical dashed line shows the limits derived only from the leptonic channel.The right of the vertical dashed line shows limits based on the combined hadronic and leptonic channels.
signal templates (single top quark, W R , W L , W LR ) to form a combined signal template with the following cross section: where σ W R , σ W L , σ W LR are the cross section for right-handed, left-handed, or mixed samples, respectively and σ t is the SM s-channel single top quark production cross section.We assume that the left-handed and right-handed coupling constants are equal for first and third generation quarks (a L ud = a L tb and a R ud = a R tb ).The templates are then summed and cross section upper limits are set using the resultant yield as the signal process for the given values of a L and a R .Limits are calculated using pairwise combinations of the couplings from 0 to 1 in increments of 0.1.
Using these cross section upper limits, we obtain the values where the M W cross section limits are equal to the theoretical cross section prediction for a given combination of a L and a R .These points are the maximum excluded W boson mass for given values of a L and a R .Exclusion limits when considering generalized couplings can therefore be represented with contours on a two dimensional plot in a L and a R and the contour is the maximum excluded W boson mass.These contours in the (a L , a R ) plane are shown in Fig. 7 for both observed and expected limits in the hadronic channel.The mass upper limits for left-handed and mixed-coupling W bosons are 1.92 and 2.15 TeV, respectively.
For this procedure, no systematic uncertainty is considered from single top quark production since the templates are dominated by statistical uncertainties.
Additionally, we present combined limits on the W coupling strengths, a L and a R .The limits for the leptonic channel that are used for the combination are shown in Fig. 8.These are updated from Ref. [6] to include the effect of the W width on the cross section of an a L and a R combination.The limits for the combined hadronic and leptonic channels are shown in Fig. 9.

Summary
A search for a new massive gauge boson W decaying to a top and a bottom quark with a hadronic signature has been performed using proton-proton collisions recorded by the CMS detector at √ s = 8 TeV, corresponding to an integrated luminosity of 19.7 fb −1 .The search is focused on W masses above 1.30TeV, where the main feature of this topology is a top quark whose decay products merge into a single jet.
The analysis uses jet substructure algorithms to distinguish the top quark jet from standard model hadronic jet backgrounds.The principal background, from QCD multijet production, is estimated from data using the average b-tagging rate measured in a QCD enhanced control region.The other important source of background, from standard model tt production, is estimated from simulation, and is corrected by a scale factor derived from control samples in data.
Limits are placed on the production cross section of a right-handed W boson, together with constraints on the left-handed and right-handed couplings of the W boson to quarks.The production of a right-handed W boson with a mass below 2.02 TeV decaying to a hadronic final state is excluded at 95% confidence level.The lower limit on the mass of the right-handed W boson increases to 2.15 TeV at 95% confidence level when both hadronic and leptonic decays are considered, and is the most stringent lower mass limit to date in the tb decay mode.the theoretical cross section is equal to the observed or expected 95% CL limit.These are updated from Ref. [6] to include the effect of the W width on the cross section of an a L and a R combination.

Figure 1 :
Figure 1: The average b-tagging rate for QCD jets parameterized as a function of the p T of the b-jet candidate from the low (top), transition (middle), and high (bottom) |η| regions.The measured average b-tagging rate is represented by the data points, the polynomial fit is shown as a solid line, and the propagated uncertainties from the fit are shown as the dashed lines.The horizontal lines on the data points indicate the bin widths.

Figure 2 :
Figure 2: Distribution of the mass of the b-jet candidate after the template fit to constrain the QCD multijet and tt backgrounds has been applied.A control region with inverted selection criteria on the mass of the b-jet candidate is used for the fit, and is shown as the area to the right of the vertical dashed line.The hatched region represents the background uncertainty, obtained by adding the QCD multijet uncertainty and the uncertainty on the tt normalization from the output of the fit in quadrature.The bottom plot shows the pull ((data-background)/σ) between the data and the background estimate distributions.

Figure 3 :
Figure 3: Distributions of M tb shown for data, tt, and QCD in the control regions CR1 (top) and CR2 (bottom) as defined in the text.The hatched region shows the background uncertainty, obtained by adding the statistical and systematic uncertainties in quadrature.The bottom plots show the pull ((data-background)/σ) between the data and the background estimate distributions.

Figure 7 :
Figure 7: Contour plots of M W in the (a L , a R ) plane in the hadronic channel.The top (bottom) plot shows observed (expected) limits.The contour shading indicates the values of M W where the theoretical cross section is equal to the observed or expected 95% CL limit.

Figure 8 :
Figure8: Contour plots of M W in the (a L , a R ) plane in the leptonic channel.The top (bottom) plot shows observed (expected) limits.The contour shading indicates the values of M W where the theoretical cross section is equal to the observed or expected 95% CL limit.These are updated from Ref.[6] to include the effect of the W width on the cross section of an a L and a R combination.

Figure 9 :
Figure9: Contour plots of M W in the (a L , a R ) plane using the combined hadronic and leptonic channels.The top (bottom) plot shows observed (expected) limits.The contour shading indicates the values of M W where the theoretical cross section intersects the observed or expected limit band.The solid contours represent combined limits, and the dashed contours indicate limits that are obtained purely from the leptonic channel.

Table 2 :
Numbers of observed and expected events for each of the sidebands used for closure tests of the QCD and tt background estimates.A summary of the inverted selection for each control region is provided.

Table 3 :
Sources of uncertainty that affect the M tb distribution and the ±1σ variations that are used in the fit.