Search for the production of an excited bottom quark decaying to tW in proton-proton collisions at sqrt(s) = 8 TeV

A search is presented for a singly produced excited bottom quark (b*) decaying to a top quark and a W boson in the all-hadronic, lepton + jets, and dilepton final states in proton-proton collisions at sqrt(s) = 8 TeV recorded by the CMS experiment at the CERN LHC. Data corresponding to an integrated luminosity of 19.7 inverse femtobarns are used. No significant excess of events is observed with respect to standard model expectations. We set limits at 95% confidence on the product of the b* quark production cross section and its branching fraction to tW. The cross section limits are interpreted for scenarios including left-handed, right-handed, and vector-like couplings of the b* quark and are presented in the two-dimensional coupling plane based on the production and decay coupling constants. The masses of the left-handed, right-handed, and vector-like b* quark states are excluded at 95% confidence below 1390, 1430, and 1530 GeV, respectively, for benchmark couplings. This analysis gives the most stringent limits on the mass of the b* quark to date.


Introduction
Following the discovery of a Higgs boson [1][2][3], the standard model (SM) may be complete.However, there are phenomena such as baryon asymmetry, neutrino mass, and dark matter, questions of naturalness, and hierarchy problems for which the SM offers no explanation.Various theories with new physics beyond the SM exist that address these problems, including a variety of models that predict the existence of excited quarks, such as Randall-Sundrum models [4,5] and models with a heavy gluon partner [6][7][8].Searches for excited quarks have been performed at the CERN LHC [9][10][11] and elsewhere [12].These searches focus on the strong and electroweak interactions of the excited quark with the SM up-or down-type quarks.This paper reports on a search by the CMS Collaboration, using the tW decay mode, for an excited third-generation bottom quark (b * ), which preferentially couples to the third-generation SM quarks.A previous search in the same channel by the ATLAS Collaboration resulted in a lower limit on the b * quark mass of about 1 TeV [11].A search for a b * quark has also been performed in the gb decay mode by CMS [10] resulting in an exclusion region between 1.2 and 1.6 TeV, assuming a branching fraction of 100% for b * decaying to gb.At the LHC, a b * quark can be produced in a gluon and a bottom quark interaction as shown in Fig. 1.This interaction is described by the effective Lagrangian: where g s is the strong coupling, G µν is the gauge field tensor of the gluon, and Λ [13] is the scale of compositeness, which is chosen to be the mass of the b * quark.The quantities P L and P R are the chiral projection operators and κ b L and κ b R are the corresponding relative coupling strengths.The branching fractions of b * quark decays are reported in Ref. [14].Possible b * quark decay modes include gb, bZ, bH, and tW.The branching fraction of the b * → tW process increases as a function of b * quark mass and becomes the largest for m b * > 400 GeV, reaching a plateau at almost 40% of the total b * quark decay width.
The decay of interest in this analysis proceeds through the weak interaction as is described by the Lagrangian: This analysis searches for a singly produced b * decaying to a top quark and a W boson. Since there are both left-and right-handed operators in the production and decay interaction Lagrangians, the b * quark could have generic couplings.We consider the benchmark cases of a purely left-handed b * (b * L ) quark with g L = 1, κ b L = 1, g R = 0, κ b R = 0, a purely right-handed b * (b * R ) quark with g L = 0, κ b L = 0, g R = 1, κ b R = 1, and a vector-like b * quark with g L = 1, The analysis is performed in three different channels distinguished by the number of leptons (electrons and muons) appearing in the b * → tW → bWW decay.The all-hadronic channel has two jets: one from a boosted top quark and the other from the boosted W boson.As the Lorentz boosts of the top quark and W boson increase, the angular distance between their direct decay products decreases, leading to only two resolvable jets.The lepton+jets channel has one lepton, one b jet, two light-flavor (u-, d-, s-quark) or gluon jets, and significant transverse momentum (p T ) imbalance.The dilepton channel has two leptons, at least one jet, and significant p T imbalance.

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter, 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.A 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. [15].

Signal and background simulations
The simulation of b * quark production and decay is performed with MADGRAPH 5.1.5.12 [16] based on the Lagrangian in the b * quark model [14], and uses the CTEQ6L1 parton distribution functions (PDF) set [17].The renormalization and factorization scales are set to the b * quark mass.The b * quark is forced to decay to tW, with the top quark subsequently decaying into bW.The simulated samples are produced for b * quark masses ranging from 800 to 2000 GeV, in steps of 100 GeV.Left-handed and right-handed b * quark samples are generated.The vectorlike b * quark samples are the sum of the right-and left-handed samples.The values for the b * quark production cross section times b * tW branching fraction in proton-proton collisions at a center-of-mass energy of 8 TeV are listed in Table 1.
Several simulated background samples are used.The samples for t-channel, tW-channel, and schannel production of single top quarks, and the tt sample are generated using the POWHEG 1.0 event generator [18][19][20] with the CT10 PDF set [21].A next-to-next-to-leading-order (NNLO) cross section of 245.8 pb is used for the tt sample [22].The total prediction is normalized to the next-to-next-to-leading-log values of 87.1, 22.2, and 5.55 pb for the t-, tW-, and s-channels, respectively [23].
The Drell-Yan sample (denoted as Z+jets in the following) with the invariant mass of two leptons being greater than 50 GeV, and the W inclusive sample (W+jets) are generated using MADGRAPH with the CTEQ6L1 PDF set.The NNLO cross sections of 3500 pb and 36700 pb are used for the Z+jets and W+jets normalization, respectively [24].
Table 1: Estimates of the total cross section for gb → b * at a center of mass energy of 8 TeV times the branching fraction for b * → tW for b * quark masses from 800 to 2000 GeV.The values are identical for left-handed and right-handed quark hypotheses.The uncertainties are determined by varying the factorization (µ F ) and renormalization (µ R ) scales simultaneously by a factor of 0.5 or 2 of their nominal value.The estimated cross section of a b * quark with vector-like coupling is twice as large at each mass point as the value shown.The diboson (WW, WZ, and ZZ) background samples are generated inclusively using PYTHIA 6.426 [25] with the CTEQ6L1 PDF set and normalized to a NNLO cross section of 57.1, 32.3, and 8.26 pb, respectively, calculated from MCFM 6.6 [26].
All of the samples are then interfaced to PYTHIA for parton showering and hadronization, based on the Z2* tune [27].The generated samples are then passed to the CMS detector simulation based on GEANT4 [28], with alignment and calibration determined from data or dedicated calibration samples.The average number of pileup interactions (additional inelastic protonproton collisions within the same bunch crossing) is observed to be approximately 20 for the data recorded in 2012.Proton-proton collisions are added to simulated signal and background events so that the distribution of reconstructed primary vertices agrees with what is observed in data.

Trigger, event quality, and object selection
At least one reconstructed primary vertex that is associated with at least four reconstructed tracks [29] is required to be present in the event.
Events that are due to beam halo, poor calibration, and malfunctioning detector electronics are rejected.The particle-flow (PF) algorithm [30] is used for both data and simulated events to reconstruct physics objects such as electrons, muons, and charged and neutral hadrons.
Electron candidates are reconstructed within the range of pseudorapidity |η| < 2.5 using the energy clusters in the ECAL [31].The clusters are associated with charged-particle tracks reconstructed in the tracking detector.The absolute value of the electron candidate transverse impact parameter should be smaller than 0.02 cm.Identified electrons from photon conversions are vetoed.The relative isolation requires I rel < 0.1, where I rel is the ratio of the sum of the p T of other particles around the electron candidate to the p T of the electron candidate.The p T summation is over the charged hadrons, photons, and neutral hadrons, in a cone size of ∆R = (∆η) 2 + (∆φ) 2 < 0.3, where φ is the azimuthal angle in radians.The estimated contribution from pileup is removed from the sum on an event-by-event basis [32].Electron candidates with clusters in the transition region between barrel and endcap (1.4442 < |η| < 1.5660) are removed since the electron reconstruction is not optimal in this region.The p T of the elec-tron candidate is required to be larger than 30 GeV in the dilepton channel and 130 GeV for the lepton+jets channel.
Muon candidates are reconstructed within |η| < 2.4 by combining the information from the muon detectors and the inner tracking detectors [33].For the muon selection used in the lep-ton+jets channel, a requirement of |η| < 2.1 is imposed, to match the coverage of the single muon trigger.The candidate's trajectory fit has to satisfy χ 2 /n < 10 (where n is the number of degrees of freedom in the fit), have at least one hit in the muon detectors, and have more than five hits in the silicon tracker, of which at least one should be in the pixel detector.The absolute value of the muon candidate transverse impact parameter should be smaller than 0.02 cm.In order to suppress the small background due to cosmic ray muons, the absolute value of the muon candidate longitudinal impact parameter must be less than 0.5 cm.Isolated muons are selected by the requirement I rel < 0.12 in a cone size of ∆R < 0.4 around the muon candidate.The p T of the muon candidate has the same threshold as the electron candidate.
The events are divided into all-hadronic, lepton+jets, and dilepton channels based on the number of leptons (0, 1, or 2 leptons).To suppress possible overlap between lepton+jets and dilepton channels, events with additional electrons (muons) with p T > 20 GeV and I rel < 0.15 (0.2) are rejected.
For the lepton+jets and dilepton analyses, jets are reconstructed by clustering the PF candidates using the anti-k T algorithm [34] implemented by FastJet 3.0.4[35] with a distance parameter of 0.5.Charged PF particles that are inconsistent with the primary vertex with the highest value of ∑ p 2 T are removed from the clustering.This requirement significantly suppresses contamination from charged particles associated with pileup vertices.The neutral component from pileup is removed by applying an estimated residual energy correction based on the jet area [36].
Jets from b quark decays (b jets) are identified with the combined secondary vertex (CSV) b tagging algorithm [37].This is based on the presence of a displaced secondary vertex in a jet, reconstructed from charged tracks, combined with other quantities comprising track impact parameters, charged hadron kinematic variables, track multiplicity, etc.The tight CSV selection criteria (CSVT) with a misidentification probability of 0.1% for light-flavor jets with an efficiency around 55% for b jets is used.
The negative vector sum of the p T of all the PF candidates ( E miss T ) is calculated for each event.The magnitude of E miss T (E miss T ) [30] is used in the lepton+jets and dilepton analysis.The all-hadronic channel uses a trigger that requires the scalar sum of the transverse momenta of all jet candidates in the event (H T ) to be at least 750 GeV.The lepton+jets channel uses a single-electron trigger with a p T threshold of 27 GeV and single-muon trigger with a p T threshold of 24 GeV.The dilepton channel uses the dilepton (ee, eµ, and µµ) triggers, with leading and sub-leading lepton p T thresholds of 17 and 8 GeV, respectively.
In the all-hadronic channel, the selected W bosons and top quarks are sufficiently energetic for their decay products to have a large Lorentz boost and are reconstructed as single jets.Such jets are identified within |η| < 2.4 using the jet decomposition into subjets, followed by application of criteria based on the kinematic properties of subjets.The Cambridge-Aachen (CA) algorithm [38] with distance parameter of 0.8 is used to cluster jets that are considered for the W boson and top quark selections, instead of the anti-k T algorithm that is used in the lepton+jets and dilepton analyses.
The identification of a boosted W boson (W tagging) attempts to identify the two daughter quarks of the W boson by using the N-subjettiness [39] variable: where ∆R ji is the angular separation between the axis of the subjet candidate j and the axis of the constituent particle i, and d 0 is a normalization factor.The variable τ N is a p T -weighted angular distance from a jet constituent to the nearest subjet axis, and is close to zero if a given jet is consistent with having N or fewer subjets.The τ 2 /τ 1 ratio is used to discriminate between the signal W-tagged jets with two subjets and jets from light quarks and gluons with a single hard subjet (τ 2 /τ 1 < 0.5).In addition, jet pruning [40] is used to remove soft and wide-angle radiation, which significantly reduces the measured mass of QCD multijet events, while leaving the measured mass of W-tagged jets close to the nominal W boson mass.The mass of the pruned jet is required to be consistent with the W boson mass (70 < m jet < 100 GeV).The difference in W tagging efficiency between data and simulation is corrected by a simulation-to-data scale factor derived from the W+jets and dijet control samples [41].
Boosted top quark identification (t tagging) discriminates signal from background events by using the three-prong substructure of a merged t jet.We use the CMS t tagging algorithm [42], which reclusters the jet until it finds one to four subjets that are consistent with daughters of the top quark decay [43].We require at least three subjets and determine the lowest mass m min of the pairwise combinations of the three highest-p T subjets.This m min is required to be compatible with the mass of the W boson (m min > 50 GeV).Finally, the mass of the CA jet from the t tagging algorithm is required to be consistent with the top quark mass (140 < m jet < 250 GeV).
The t tagging selection in this analysis also uses N-subjettiness discrimination.In this case the variable of interest is τ 3 /τ 2 , since t jets are expected to have three subjets (τ 3 /τ 2 < 0.55).
Exactly one of the three subjets originating from the top quark decay should be a b jet, which we identify by requiring the largest subjet CSV discriminator value to satisfy the medium selection criteria.This requirement has a misidentification probability of 0.1% for light-flavor jets and an efficiency of around 65% for b jets [44].
This t tagging algorithm was studied in lepton+jets data and simulated samples enriched in top quarks with high Lorentz boost.We use a simulation-to-data scale factor for t tagging derived from these studies to correct the Monte Carlo (MC) samples in the all-hadronic channel [45].

Event selection and background estimation
We search for the presence of a b * quark decaying to tW by looking for deviations from the expected background in the distributions of kinematic variables for the all-hadronic, lepton+jets, and dilepton channels.The event selections and background estimations of these three channels are presented below.

All-hadronic channel
The all-hadronic channel is characterized by a top quark and a W boson, both of which decay hadronically.After the trigger selection, exactly two CA jets with p T of at least 425 GeV are required to be present in the event.One high-p T jet is required to be W-tagged, while the other is required to be t-tagged.The main backgrounds for this channel are tt and multijet events, which are estimated using control regions in data.The small background contribution from single top quark production is estimated from simulation.
The multijet contribution is estimated by applying the top quark mistagging (t mistagging) rate on events before t tagging is applied.We measure the t mistagging rate using a control region where the contribution of signal events is suppressed.For this control region we select a W-tagged jet in the region of 30 < m jet < 70 GeV or m jet > 100 GeV.After applying this selection we take the ratio of the number of jets that are t-tagged to the number of all top quark candidate jets to define the t mistagging rate.Here we use the t tagging algorithm described in Section 4 but exclude the top quark candidate mass requirement that is applied to the pretagged top quark candidate jets.The tt contamination is determined from simulation and is accounted for when extracting the t mistagging rate.The tt fraction in this region is about 25% of the post-tag sample (numerator) and 1% of the pre-tag sample (denominator).To extract a multijet background estimate, we weight the events that pass the pre-t-tagged selection by the t mistagging rate.The parameterization of the t mistagging rate is done as a function of the candidate jet p T and |η|, in order to account for kinematic correlations inherent in t tagging.The mass distribution of the top quark candidate in the multijet background estimate is corrected on a bin-by-bin basis by a weight extracted from simulation, to correct for differences in the top quark candidate mass spectrum before and after t tagging.This correction is such that it only changes the shape of the distribution and has no effect on the overall normalization.The correction factor depends on the mass of the top quark candidate and ranges from 0.45 at low mass to 2.25 at high mass.The corresponding change in shape of the m tW spectrum is taken into account in the systematic uncertainties, and makes a contribution that is much smaller than the total systematic uncertainty, shown in Fig. 2 as the hatched band.
The contribution from tt production is estimated by using a control region defined by requiring one of the jets to pass inverted W tagging requirements: m jet > 130 GeV and τ 2 /τ 1 > 0.5.This selection has an enhanced tt fraction.We compare the multijet and simulation-based tt background estimates to the selection in data, then perform a fit to the invariant mass of the top quark candidate jet.The template-based fit constrains the multijet background template to move within its uncertainties, whereas the normalization on tt is unconstrained.This study suggests that, in addition to the scale factors that are applied, the tt contribution needs to be further scaled by 0.79 ± 0.17.The uncertainty in this normalization is obtained from the fitting procedure.
The invariant mass of the top quark and W boson candidate jets, m tW , for the selected events in the signal region is shown in Fig. 2 and is used for limit setting.The expected number of events is 359 ± 57, and the observed number of events is 318 (Table 2).

Lepton+jets channel
The lepton+jets channel is characterized by the presence of exactly one isolated electron or muon and a b jet, as well as at least two light-flavor jets.The signal region is defined to have exactly three jets with p T > The multijet background is estimated by performing a fit to the E miss T distribution for the electron channel, and a fit to the transverse mass distribution of the leptonically decaying W boson in the muon channel.The choice of the variables used to estimate the background depends on the accuracy with which they are modeled, the choice is different for the electron and muon .The p z component is estimated by constraining the reconstructed mass of the W boson to be 80.4 GeV [12], resulting in two solutions.If both solutions are real, the one with the lowest |p z | is selected.If there is no real solution, p x and p y are varied until there is a single solution that minimizes the distance between the neutrino momentum and the missing momentum in the transverse plane.For the fit to the m b ν distribution, the multijet background template is fixed to the result of the multijet background estimated from data, with the shape taken from the multijet-enriched control region.The SM tt, single top quark, Z+jets, and diboson templates are taken from the simulation with a common normalization scale factor of 1.09 ± 0.10 obtained from the fit.The W+jets template is taken from the simulation, and normalized to the fitted yield.The possibility of a small contamination from a signal is taken into account in the scale factors applied to backgrounds with a top quark signature.
The expected b * quark signal and background events and observed data events are listed in Table 3 for the electron and muon channels separately.
We search for the b * signal as an excess above the predicted backgrounds in the distribution of  the invariant mass m tW of the lepton, three jets, and E miss T .In this calculation, the neutrino p x and p y components are obtained from E miss T , and p z is set to zero since it cannot be measured by the detector and could have multiple solutions from the analytical second order W mass constraint.The distribution of m tW is shown in Fig. 3.The widths of the bins are chosen to be comparable to the resolution in the reconstructed m tW .

Dilepton channel
The dilepton channel is characterized by two isolated, oppositely charged electrons or muons and at least one jet.The signal region is defined to have at least one jet with p T > 30 GeV and |η| < 2.5, together with at least two leptons having p T > 30 GeV and |η| < 2.5 (2. 4) for electrons (muons).A minimum distance requirement of 0.3 between the two leptons in ∆R removes photons radiated from muons in W+jets events, which can mimic extra electrons.Most of the diboson background is removed by requiring that the invariant mass of the two leptons is greater than 120 GeV.In addition to the basic selections, events are required to have E miss T > 40 GeV.This requirement reduces top quark background by 30%, W+jets background by 50%, diboson events by 60%, and removes over 95% of Z+jets events, while keeping 90% of the signal events.The dominant backgrounds for this channel are tt, single top quark, W+jets, Z+jets, and diboson, and are predicted by simulation.
A study is conducted to check the W+jets and multijet backgrounds using same-sign events; the multijet background is found to be negligible, and the W+jets estimate agrees with the MC simulation prediction within the statistical uncertainties.Control regions, defined by reversing the E miss T cut or by adding a b tagging requirement, are compared with data to confirm that the dominant background sources are simulated correctly.
We search for the b * quark signal events using the distribution of the scalar sum S T of the p T of the two leading leptons, the jet with the highest p T , and E miss T .The distribution of this variable is shown in Fig. 4. The results of the full selection are listed in Table 4.

Systematic uncertainties
Systematic uncertainties are divided into four groups: theoretical, background normalization, instrumental, and other measurement-related uncertainties.These uncertainties are summarized in Table 5.

Theoretical uncertainties
Several uncertainties in event simulation are considered.The PDF uncertainties are estimated with the CT10 PDF eigenvector set [21].
In order to estimate uncertainties originating from the top quark mass, additional simulated samples are produced by varying the top quark mass up and down by 5 GeV.A linear extrapolation is applied to scale down the top quark mass uncertainty to 1 GeV.This is applied to tt and single top quark t-channel samples.In order to estimate uncertainties originating from the choice of the renormalization and factorization scales (µ R and µ F ), for the tt, and single top quark t-channel simulation, the nominal samples use [16], where ∑ p 2 T sums over outgoing partons.To evaluate the effect of this scale choice, additional MC samples are produced by varying µ R and µ F simultaneously by a factor of 0.5 or 2.0.

Background normalization uncertainty
For the lepton+jets and dilepton analysis, the tt cross section uncertainty of ±5.3% [46] is used.
The all-hadronic channel extracts the tt normalization from data, resulting in an uncertainty of 22% obtained from the fit.
The normalization uncertainties in single top quark t-, tW-, and s-channel cross sections are 15%, 30% and 20%, respectively [23].The normalization uncertainties in diboson production cross sections are 30%, which is the sum of the experimentally measured cross section uncertainty [47] and uncertainties due to extra jet production.The normalization uncertainty in the Z+jets background is 20%, which is the sum of the experimentally measured cross section un-  certainty [48] and uncertainties due to extra jet production.The normalization uncertainty in the W+jets background is 45% for the electron+jets channel and 30% for the muon+jets channel, estimated from data and described in Section 5.2.Detector effects and modeling uncertainties that affect the templates are included in the uncertainty.
The normalization uncertainties in the multijet backgrounds are ±33% and +170 −100 % for the elec-tron+jets and the muon+jets channels, respectively, estimated from data and described in Section 5.2.The uncertainties originating from detector effects, theoretical modeling, and the multijet background control region choice are summed in quadrature to give the uncertainties in the multijet and W+jets background estimations.

Other measurement uncertainties
In the all-hadronic channel, we correct the simulation by using the trigger efficiency extracted from data that is obtained from a control sample triggered with a lower H T threshold than in the standard event selection.The scale factors are parameterized as a function of the summed leading and sub-leading jet p T .To obtain a systematic uncertainty for this correction, we vary the trigger efficiency by ±(1 − )/2, which results in less than a 1% change of the yields for all samples.
The differences between data and simulation due to the electron trigger, identification, and isolation efficiencies are corrected with p T -and η-dependent scale factors by comparing simulation with a Z → ee data sample.The uncertainties due to the statistically limited Z → ee samples and the uncertainties in the theoretical inputs to the simulation are taken into account.
The scale factor measurements define the uncertainties for electron trigger, identification, and isolation requirements, and these uncertainties are less than 1%.Scale factors related to the muon trigger, identification, and isolation efficiency are measured in a similar way to those for electrons, but use Z → µµ, where the uncertainties are less than 2% [49], instead of Z → ee events.
The jet energy resolution [50] systematic uncertainty is an η-dependent smearing of the jet energy resolution for simulated events, which results in a less than 0.4% acceptance change.The jet energy scale [50] systematic uncertainty is parameterized in p T and η and applied to simulated samples to cover the difference between data and simulation, which is typically 5% or less.The all-hadronic channel has an additional 3% uncertainty because the jet energy scale is measured from anti-k T jets, but applied to CA jets.The jet energy scale uncertainty is propagated in the E miss The typical acceptance change due to b tagging efficiency is less than 3%.The mistagging rate brings about an uncertainty of 0.3% for samples that have at least one b jet and of 9.0% for samples that have no b jets.The all-hadronic channel includes a 13% uncertainty in the t tagging scale factor, which is used to correct for differences in subjet identification efficiencies between data and simulation [45].
The result of a polynomial fit to the t mistagging rate extracted from a control region as a function of jet p T is applied to events before applying the t tagging algorithm to estimate the multijet background contribution in the all-hadronic channel.The fit introduces a 9% statistical uncertainty and a 12% uncertainty to allow for the possibility of choosing alternative functional forms.There is a difference between the shape of the jet mass distribution of the top quark candidate in the control and signal regions.This is corrected by a top quark jet mass dependent weight derived from the multijet simulation.This correction contributes an extra 0.3% uncertainty in the total multijet yield.The uncertainty due to the choice of parameterization in the t mistagging rate is taken to be the difference between a parameterization in p T , η and a parameterization in p T , η, m tW .This difference is about 2% of the total multijet yield, with an additional 20% statistical uncertainty from the higher dimensional parameterization.
To estimate the uncertainty due to pileup modeling in simulation, we vary the measured minimum bias cross section of 69.4 mb by ±5%.These variations are then propagated to analysis results by modifying the pileup multiplicity accordingly [51].The uncertainty in the integrated luminosity is measured in dedicated samples and applied to the signal and backgrounds based on simulation.The size of this uncertainty is 2.6% [52].
Table 5: Sources of systematic uncertainty for the three analysis channels.For the shape-based uncertainties, the parameterization used for the uncertainty deviation is given in parentheses.Sources marked with "sideband" are measured from data, and contain various uncertainty sources.Uncorrelated uncertainties that apply to a given channel are marked by .Uncertainties correlated between channels are marked by ⊕.

Results and interpretation
A binned maximum likelihood fit to the m tW distribution is performed in both the all-hadronic and lepton+jets channels, and to the S T distribution in the dilepton channel to extract the signal cross section.The observed distributions are consistent with those from the background only prediction.A Bayesian method [12,Ch. 38] with a flat signal prior is used within the THETA framework [53] to set limits on σ gb→b * →tW .The systematic uncertainties are accounted for as nuisance parameters, and are integrated out using Bayesian marginalization.Rate uncertainties are modeled using log-normal priors.Uncertainties varying as functions of the fitted variables are modeled using Gaussian priors, and template morphing is employed to model the shape of these systematic uncertainties.The limits on the cross section times branching fraction (σ gb→b * →tW ) at 95% confidence level (CL) are shown in Figs. 5, 6, and 7 for the all-hadronic, lepton+jets, and dilepton channels, respectively.
To enhance the sensitivity of the measurement of the upper limit on the gb → b * → tW production cross section, the all-hadronic, lepton+jets, and dilepton channels are combined.In forming the combination of separate channels, systematic uncertainties affecting both the shape and the event yield are taken into account.The procedure adopted is as follows: For each channel the shape of each distribution is determined and the normalization is set to 1.Then, for each bin "i", an estimate is made of the systematic uncertainty σ i (not necessarily symmetric), which takes into account the contributions from all the sources affecting the shape."Upper" and "lower" distributions are then obtained, each normalized to unity, and used to estimate event yields in two limiting cases.The systematic uncertainties are treated as being completely correlated between bins of the distribution, while the statistical uncertainties are treated as uncorrelated.In the combination, the uncertainty sources due to jet energy scale, jet energy resolution, b tagging scale factor, single top quark cross section, and integrated luminosity are treated as correlated, and the remaining uncertainties are assumed to be uncorrelated, as shown in Table 5.The limits are shown in Fig. 8.The expected (observed) mass exclusion region at 95% CL for the left-handed, right-handed, and vector-like b * quark hypotheses is below 1480, 1560, and 1690 GeV (1390, 1430, and 1530 GeV), respectively as summarized in Table 6.
The upper limits on the cross section times branching fraction may be generalized as a function of the couplings κ and g, defined in equations 1 and 2. The results are shown in Fig. 9.

Summary
A search for a singly produced b * quark decaying to tW in the all-hadronic, lepton+jets, and dilepton final states 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 .No deviations that are inconsistent with standard model expectations are found in the various spectra of variables used to search for the signal in the three channels.Upper limits are set at 95% confidence level on the product of cross section and branching fraction for the production of a b * quark that subsequently decays to tW.Excited bottom quarks are excluded with masses below 1390, 1430, and 1530 GeV for left-handed, right-handed, and vector-like b * quark couplings, respectively.The mass limits are also extrapolated to the two dimensional κ-g coupling plane.These are the most stringent limits on the b * quark masses to date.[44] CMS Collaboration, "Performance of b tagging at √ s = 8 TeV in multijet, tt and boosted topology events", CMS Physics Analysis Summary CMS-PAS-BTV-13-001, 2013.

Figure 2 :
Figure2: The invariant mass of the tW system in the all-hadronic channel after the full selection of data, the estimated background, and the simulated signal with a b * mass of 1300 GeV.The combined statistical and systematic uncertainties are indicated by the hatched band.The bottom plot shows the pull ((data-background)/σ Data ⊕ σ Exp. ) between the data and the background estimate distributions.The quantities σ Data and σ Exp.refer to the statistical uncertainty in data, and the systematic uncertainty in the background respectively.

Figure 3 :
Figure 3: The invariant mass, m tW , in data compared to the SM background estimation for the electron (left) and muon (right) channels.The combined statistical and systematic uncertainties are indicated by the hatched band.The bottom plots show the pull ((databackground)/σ Data ⊕ σ Exp. ) between the data and the background estimate distributions.The quantities σ Data and σ Exp.refer to the statistical uncertainty in data, and the systematic uncertainty in the background, respectively.

Figure 4 :
Figure 4: The S T distribution for data and simulated samples after the event selection is applied, for ee (top left), eµ (top right), µµ (bottom left), and inclusive dilepton (bottom right) channels.The combined statistical and systematic uncertainties are indicated by the hatched band.The bottom plots show the pull ((data-background)/σ Data ⊕ σ Exp. ) between the data and the background estimate distributions.The symbols σ Data and σ Exp.refer to the statistical uncertainty in data, and the systematic uncertainty in the background, respectively.
T calculation.The estimation of E miss T includes an additional uncertainty due to the effect of unclustered energy arising from the jets or leptons.The b tagging efficiency and mistagging rate uncertainty are estimated by comparing a b jet enriched µ+jets data sample with simulation [44].The differences are corrected by jet flavor (b jet, c jet, and light jets from u/d/s/gluon), p T -and η-dependent b tagging and mistagging scale factors.The uncertainties in these scale factors are propagated to the b tagging event weight calculation independently, giving the uncertainties in b tagging efficiency and mistagging rate.

Figure 5 :
Figure 5: The expected (dashed) and observed (solid) production cross section limits at 95% CL for the all-hadronic channel as a function of b * quark mass for gb → b * → tW.The theoretical cross section (solid line with hatched area) is also shown for comparison.The 1σ and 2σ uncertainties in the expected limit bands are shown.Limits for the left-handed, righthanded, and vector-like b * quark coupling hypotheses are shown in the top left, top right, and bottom plots, respectively.

Figure 6 :
Figure 6: The expected (dashed) and observed (solid) production cross section limits at 95% CL for the lepton+jets channel as a function of b * quark mass for gb → b * → tW.The theoretical cross section (solid line with hatched area) is also shown for comparison.The 1σ and 2σ uncertainties in the expected limit bands are shown.Limits for the left-handed, right-handed, and vector-like b * quark coupling hypotheses are shown in the top left, top right, and bottom plots, respectively.

Figure 7 :
Figure 7: The expected (dashed) and observed (solid) production cross section limits at 95% CL for the dilepton channel as a function of b * quark mass for gb → b * → tW.The theoretical cross section (solid line with hatched area) is also shown for comparison.The 1σ and 2σ uncertainties in the expected limit bands are shown.Limits for the left-handed, right-handed, and vector-like b * quark coupling hypotheses are shown in the top left, top right, and bottom plots, respectively.

Figure 8 :Figure 9 :
Figure 8: The expected (dashed) and observed (solid) production cross section limits at 95% CL for the combined all-hadronic, lepton+jets, and dilepton channels as a function of b * quark mass for gb → b * → tW.The theoretical cross section (solid line with hatched area) is also shown for comparison.The 1σ and 2σ uncertainties in the expected limit bands are shown.Limits for the left-handed, right-handed, and vector-like b * quark coupling hypotheses are shown in the top left, top right, and bottom plots, respectively.
b * quark mass σ gb→b * →tW b * quark mass σ gb→b * →tW 40GeV and |η| < 2.4, together with exactly one electron with p T > 130 GeV and |η| < 2.4, or exactly one muon with p T > 130 GeV and |η| < 2.1.Of these three jets, there must be exactly one jet that satisfies the CSVT b tagging selection.The contributions of the b * quark signal, tt, single top quark, Z+jets, and diboson processes are taken from simulation.The multijet and W+jets background contributions are estimated from data.

Table 2 :
Event yields in the all-hadronic channel after the final selection, normalized to an integrated luminosity of 19.7 fb −1 .Both statistical and systematic uncertainties are shown.The systematic uncertainties are described in Section 6. Sample Yield ± stat.± syst.b *

Table 3 :
Event yields in the lepton+jets channel after the final selection, normalized to an integrated luminosity of 19.7 fb −1 .Both statistical and systematic uncertainties are included.The systematic uncertainties are described in Section 6. Sample Yield ± stat.± syst.Yield ± stat.± syst.

Table 4 :
Event yields for the dilepton channel after the final selection, normalized to an integrated luminosity of 19.7 fb −1 .Both statistical and systematic uncertainties are included.The systematic uncertainties are described in Section 6. Sample Yield ± stat.± syst.Yield ± stat.± syst.Yield ± stat.± syst.
The uncertainties varying as functions of variables in question are indicated if no uncertainty value is listed.

Table 6 :
The limit at 95% CL, for the case of unit couplings, on b * quark mass for the lefthanded, right-handed, and vector-like coupling hypotheses in the all-hadronic, lepton+jets dilepton, and combined channels.For each domain, two numbers linked with a dash indicate the excluded b * quark mass range, a single number indicates the excluded lower b * quark mass limit.Pakistan Atomic Energy Commission; the Ministry of Science and Higher Education and the National Science Centre, Poland; the Fundac ¸ão para a Ciência e a Tecnologia, Portugal; JINR, Dubna; the Ministry of Education and Science of the Russian Federation, the Federal Agency of Atomic Energy of the Russian Federation, Russian Academy of Sciences, and the Russian Foundation for Basic Research; the Ministry of Education, Science and Technological Development of Serbia; the Secretaría de Estado de Investigaci ón, Desarrollo e Innovaci ón and Programa Consolider-Ingenio 2010, Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the Ministry of Science and Technology, Taipei; the Thailand Center of Excellence in Physics, the Institute for the Promotion of Teaching Science and Technology of Thailand, Special Task Force for Activating Research and the National Science and Technology Development Agency of Thailand; the Scientific and Technical Research Council of Turkey, and Turkish Atomic Energy Authority; the National Academy of Sciences of Ukraine, and State Fund for Fundamental Researches, Ukraine; the Science and Technology Facilities Council, UK; the US Department of Energy, and the US National Science Foundation.Individuals have received support from the Marie-Curie programme and the European Research Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Science and Industrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund; the OPUS programme of the National Science Center (Poland); the Compagnia di San Paolo (Torino); the Consorzio per la Fisica (Trieste); MIUR project 20108T4XTM (Italy); the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF; the National Priorities Research Program by Qatar National Research Fund; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University (Thailand); and the Welch Foundation, contract C-1845.