Measurement of the W-boson helicity in top-quark decays from ttbar production in lepton+jets events in pp collisions at sqrt(s) = 7 TeV

The W-boson helicity fractions in top-quark decays are measured with ttbar events in the lepton+jets final state, using proton-proton collisions at a centre-of-mass energy of 7 TeV, collected in 2011 with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 5.0 inverse femtobarns. The measured fractions of longitudinal, left-, and right-handed helicity are F0 = 0.682 +/- 0.030 (stat.) +/- 0.033 (syst.), FL = 0.310 +/- 0.022 (stat.) +/- 0.022 (syst.), and FR = 0.008 +/- 0.012 (stat.) +/- 0.014 (syst.), consistent with the standard model predictions. The measured fractions are used to probe the existence of anomalous Wtb couplings. Exclusion limits on the real components of the anomalous couplings gL, gR are also derived.


Introduction
Following the discovery of the top quark in proton-antiproton collisions at the Tevatron collider [1,2], measurements of W-boson helicity fractions in top-quark decays have been an important subject of investigation, because of their relationship to the V−A structure of the weak charged current and their sensitivity to physics beyond the standard model (SM).With the large samples of tt events produced in proton-proton collisions at the Large Hadron Collider (LHC), the W-boson helicity fraction measurements can be improved considerably, enhancing the search for anomalous Wtb couplings, i.e. those that do not arise from the SM.Previous measurements of W-boson helicity fractions in top-quark decays have been performed by the CDF, D0 [3], and ATLAS [4] Collaborations.
The helicity fractions of the W boson produced in a t → Wb decay are defined as the partial rate for a given helicity state divided by the total decay rate: F L,R,0 ≡ Γ L,R,0 /Γ, where F L , F R , and F 0 are the left-handed, right-handed, and longitudinal helicity fractions, respectively.For SM couplings and unpolarised top-quark production, the helicity fractions are approximately 70% longitudinal and 30% left-handed.At leading order (LO) and in the limit m b = 0 (where m b is the b-quark mass), the right-handed helicity fraction is zero due to helicity suppression.For finite m b , the helicity fractions are [5] : where x = M W /m t , y = m b /m t , λ = 1 + x 4 + y 4 − 2x 2 y 2 − 2x 2 − 2y 2 , and M W , m t are the masses of the W boson and top quark, respectively.These fractions are minimally modified by higher-order corrections.Recent next-to-next-to-leading-order (NNLO) calculations [6] predict F 0 = 0.687 ± 0.005, F L = 0.311 ± 0.005, and F R = 0.0017 ± 0.0001 for a top-quark mass of m t = 172.8± 1.3 GeV/c 2 .
Experimentally, the W-boson helicity components can be extracted through the study of angular distributions of top-quark decay products in tt final states.The helicity angle θ * is defined as the angle between the W-boson momentum in the top-quark rest frame and the momentum of the down-type decay fermion in the rest frame of the W boson.The distribution of the cosine of the helicity angle has a dependence on the helicity fractions given by: Deviations of the measured helicity fractions from the SM predictions can be interpreted in terms of anomalous Wtb couplings [7,8], using the most general dimension-six Lagrangian: where V L , V R , g L , g R are dimensionless complex constants, q = p t − p b , where p t (p b ) is the four-momentum of the top quark (b quark), P L (P R ) are the left (right) projector operators, and h.c.denotes the Hermitian conjugate.Hermiticity conditions on the possible dimension-six Lagrangians also impose Im(V L ) = 0 [8].In the SM and at tree level, V L = V tb , where V tb is the Cabibbo-Kobayashi-Maskawa matrix element V tb 1, and V R = g L = g R = 0.The relation between helicity fractions and anomalous couplings, including dependencies on the b-quark mass, are given in ref. [9].
We report on a study of the W-boson helicity fractions in top-quark decays using a sample of tt events where one of the top quarks decays semileptonically (e.g.t → W + b → + ν b, where is either an electron or a muon) and the other decays hadronically (e.g.t → W − b → qq b).A kinematic fit is used to determine the best association of b jets, other jets, and lepton candidates to the top quark and antiquark decay hypotheses, interpreting the measured momentum imbalance as due to the presence of a neutrino.In this kinematic fit, top-quark and W-boson mass constraints are employed to improve the resolution of the measured jet and lepton energies, resulting in an improved reconstruction of the W-boson rest frame and the helicity angles in the weak decays of top quarks.In this article, the cosine of the helicity angles in the semileptonic and hadronic top-quark decays will be referred to as cos θ * and cos had θ * , respectively.In the leptonic branch, the down-type fermion corresponds to the charged lepton.In the hadronic branch, since the down-type quark is not experimentally identified, only the absolute value of cos had θ * is used, providing information on the relative proportion between longitudinal (F 0 ) and total transverse (F L + F R = 1 − F 0 ) fractions.The resulting helicity angle distributions are fitted to measure the W-boson helicity fractions and to determine possible anomalous Wtb couplings.

The CMS detector
The central feature of the Compact Muon Solenoid (CMS) detector is a superconducting solenoid, 13 m in length and 6 m in diameter, which provides a uniform axial magnetic field of 3.8 T. The CMS experiment uses a right-handed coordinate system, with the origin at the nominal interaction point, the x axis pointing to the centre of the LHC, the y axis pointing up (perpendicular to the LHC plane), and the z axis along the anticlockwise-beam direction.The polar angle θ is measured from the positive z axis and the azimuthal angle φ is measured in the x-y plane.The bore of the solenoid is instrumented with various particle detection systems.Charged-particle trajectories are measured with a silicon pixel tracker with three barrel layers at radii between 4.4 and 10.2 cm, and a silicon strip tracker with 10 barrel detection layers that extend outward reaching a radius of 1.1 m.Each system is completed by two endcaps, and provides angular coverage of 0 < φ < 2π in azimuth and |η| < 2.5, where the pseudorapidity η is defined as η = − ln[tan(θ/2)], with θ the polar angle of the trajectory of the particle with respect to the z axis.A lead-tungstate crystal electromagnetic calorimeter (ECAL) and a brass/scintillator hadron calorimeter (HCAL) surround the tracking volume and cover the region |η| < 3. The forward calorimeter further extends the HCAL coverage in the region 3 < |η| < 5, improving the determination of the momentum imbalance.
Muons are measured and identified in gas-ionisation detectors embedded in the steel flux return yoke outside the solenoid in the range |η| < 2.4.The barrel region is covered by drift-tube chambers and the endcap region by cathode strip chambers, each complemented by resistive plate chambers.The detector is nearly hermetic, allowing for energy balance measurements in the plane transverse to the beam.A two-level trigger system selects the most interesting pp collision events for use in physics analysis.The first level of the CMS trigger system, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select the most interesting events in a fixed time interval of less than about 3.2 µs.The second level, known as the high-level trigger (HLT), is a processor farm that further decreases the event rate from around 100 kHz to around 300 Hz, before data storage.A more detailed description of the CMS detector can be found elsewhere [10].

Data and simulated samples
The measurements presented in this paper are performed using events from proton-proton collisions at a centre-of-mass energy of 7 TeV, collected by the CMS detector in 2011.The data correspond to an integrated luminosity of 5.0 ± 0.1 fb −1 [11].In order to account for effects of detector resolution and acceptance, as well as to estimate the contribution from background processes that can satisfy the tt event selection criteria, simulated event samples based on Monte Carlo (MC) event generator programs are used.
A tt signal sample was generated using the MADGRAPH generator version 5.1.1 [12] with matrix elements having up to three extra partons in the final state and an assumed top-quark mass of 172.5 GeV/c 2 .MADGRAPH is interfaced with PYTHIA generator version 6.424 [13] to simulate hadronization and parton fragmentation and with TAUOLA program version 27.121.5 [14] to simulate τ-lepton decays.The helicity fractions used as a SM reference are the LO predictions for m t = 172.5 GeV/c 2 : F 0 = 0.6902, F L = 0.3089, F R = 0.0009, consistent with next-to-leadingorder (NLO) and NNLO expectations [5,6].
Single-top quark events in t and tW (or W-boson associated) channels were generated using POWHEG program version 1.0 [15] and PYTHIA interfaced with TAUOLA.Other relevant background processes, such as W boson and Drell-Yan production accompanied by multiple jets, were simulated using MADGRAPH.In all LO simulations, the parton distribution function (PDF) set CTEQ6L1 [16] is used.The POWHEG simulations use the NLO set CT10 [17].
The effect of multiple proton-proton collisions occurring within the same bunch crossing (pileup events) is taken into account in the simulation and matches the pileup distribution observed in data.

Event reconstruction and selection
A set of requirements is applied to all samples, selecting candidate events compatible with the topology of tt production.Almost all top quarks decay into a W boson and a b quark.In the decay modes considered for this study, one of the W bosons decays hadronically into two jets and the other W boson decays leptonically into an electron or muon and a neutrino.Hence, final states containing a muon or electron and at least four jets are selected for further consideration.
Top-quark decay products are reconstructed using the particle-flow (PF) algorithm described in detail in refs.[18] and [19].The particle-flow event reconstruction identifies and measures the properties of each particle, using an optimised combination of the information from all subdetectors.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 momentum of the track originated at the main interaction vertex, the corresponding ECAL cluster energy, and the energy sum of all bremsstrahlung photons attached to the track.The energy of muons is obtained from the corresponding track momentum.The energy of charged hadrons is determined from a combination of the track momentum and the corresponding ECAL and HCAL energy, corrected for zero-suppression effects, and calibrated for the nonlinear response of the calorimeters.Finally, the energy of neutral hadrons is obtained from the corresponding calibrated ECAL and HCAL energy.The missing transverse energy E miss T is defined as the mag-nitude of the transverse momentum imbalance, p miss T , which is the negative of the vectorial sum of the transverse momenta p T of all the particles reconstructed with the particle-flow algorithm.Tracks belonging to the primary or secondary vertices of the most energetic pp interaction are retained, while particles identified as coming from pileup interactions are removed from the event.
Events in the muon+jets channel were selected by a trigger that required at least one isolated, high-momentum muon with a HLT p T threshold varying between 17 and 24 GeV/c for the running period used in this analysis.Events containing a muon, well measured in the silicon tracker and identified in the muon chambers with p T > 25 GeV/c and pseudorapidity |η| < 2.1, are then selected offline.The track associated with the muon candidate is required to have a minimum number of hits in the silicon tracker, to be consistent with originating from the beam spot, and to have a high-quality global fit including a minimum number of hits in the muon detector.More details on the muon quality requirements are given in [20].
The trigger used to collect events in the electron+jets channel required at least one isolated electron with p T > 25 GeV/c, accompanied by at least three jets with p T > 30 GeV/c.Electron candidates are reconstructed from clusters of energy deposits in the electromagnetic calorimeter, which are then matched to hits in the silicon tracker [21].Electrons are identified by using shower shape and track-cluster matching variables.Offline, events with exactly one electron candidate with p T > 30 GeV/c and |η| < 2.5 are selected.Events having electron candidates in the transition region between the barrel and endcap calorimeters, 1.44 < |η| < 1.56, are excluded because reconstruction in this region is degraded due to additional material there.The electron track must lie within 0.02 cm of the primary vertex in the plane transverse to the beam axis.Additionally, the background due to electrons from photon conversions is reduced by rejecting tracks with missing hits in the inner tracker layers or that are near a track with an opposite charge and a similar polar angle.
Events with an additional muon with p T > 10 GeV/c or and additional electron with p T > 15 GeV/c are vetoed in order to reject backgrounds from dileptonic tt and Drell-Yan events.
To reduce backgrounds further, muons and electrons are required to be prompt and are therefore typically well isolated from the rest of the event.This is achieved via an offline particleflow-based relative isolation (PFIso) algorithm, which is defined as the sum of the transverse momenta over all charged hadrons, neutral hadrons, and photons reconstructed inside a cone of radius ∆R = (∆η) 2 + (∆φ) 2 = 0.3, centered around the lepton (muon or electron) and divided by the lepton transverse momentum.In top-quark decays, where the b jet coincidentally overlaps with the prompt lepton, cos θ * takes values close to −1.The offline lepton isolation requirement therefore has the effect of reducing the signal selection efficiency near cos θ * ≈ −1.
In addition, both the muon and electron online triggers impose loose isolation criteria.Hence, selected muons (electrons) are required to have PFIso < 0.125 (0.100).These values are chosen to be tight enough to provide a high trigger efficiency, yet loose enough to maintain reasonable signal efficiency near cos θ * ≈ −1.In order to mitigate effects of pileup, a correction based on the average energy density in the event is applied to the electron isolation.
Jets are reconstructed using the anti-k T clustering algorithm [22,23], with a distance parameter of 0.5, applied to the entire list of reconstructed particles that are not identified as isolated muons or electrons in the event.The resulting uncalibrated jet momenta are found to be within 5% to 10% of the true momenta over the whole p T spectrum and detector acceptance.Charged particles not associated with the primary vertex are explicitly removed from the jet, as stated above.A residual correction is applied to account for the energy of any extra neutral particles arising from pileup interactions.Further residual jet energy calibrations are derived from simulation and corrected for any discrepancies with data using in situ measurements of object balancing in both dijet events (to render the jet response in pseudorapidity uniform) as well as photon+jet events (to provide the absolute jet energy scale) [24].Additional selection criteria are applied to remove spurious events with identified noise patterns in the HCAL.Calibrated jets with p T > 10 GeV/c are used to correct the scale of E miss T [25].Jet candidates from the topquark decay are required to have calibrated p T > 30 GeV/c and |η| < 2.4.Events with less than four jets passing the above mentioned top-quark decay product criteria are not used in the analysis.
To reduce the QCD multijet background, the transverse mass, M T , of the leptonically decaying W boson, is required to be greater than 30 GeV/c 2 , where M T =

√
2p T E miss T (1 − cos(∆φ)) × 1/c 3 and ∆φ is the angle in the x-y plane between the direction of the lepton and p miss T .In events where the top-quark pair decays dileptonically and one lepton escapes detection, the M T variable can assume very high values.Background events from this process are rejected by requiring M T < 200 GeV/c 2 .
Due to its relatively high rate and similar final state topology, the main remaining background source for this analysis is the production of several jets in association with a W boson that decays leptonically.This background source can be reduced, and the QCD multijet background even further suppressed, by requiring that at least two of the selected jets be identified as b jets.A high-efficiency tagging algorithm, known as the combined secondary-vertex (CSV) algorithm [26], is used to separate jets originating from light quarks (or gluons) and heavy quarks, i.e. charm or bottom quarks.Jets are first divided into categories according to the probability of reconstructing a secondary vertex and its quality.Then, within each category, several variables including the three-dimensional signed impact parameter significance, secondary vertex mass, fractional charge, and charged particle multiplicity are used to form a likelihood that discriminates light-flavour jets from heavy-flavour jets.A selection working point is chosen so that the efficiency to identify a b jet is high (nearly 70%), while the probability that a light-flavour jet is mistaken as a b jet is small (about 1%).Requiring that there be two b-tagged jets in the event reduces the remaining QCD multijet background to negligible levels (less than 0.4%).
Trigger, lepton identification, and lepton isolation efficiencies are estimated with a tag-andprobe method [27] using leptons from a sample of events containing Z → + − decays.The efficiencies are computed for the Z-boson events both in data and simulation, as a function of the lepton p T and η.The overall efficiencies in the typical p T and η ranges of the selected leptons are 80% for muons and 70% for electrons.The ratio of the efficiencies in data and simulation, DATA / MC , is used as a scale factor to correct the simulated samples.Likewise, simulated samples are scaled to account for any differences in b-tagging efficiencies between data and simulation according to the ratio of efficiencies DATA b-tag / MC b-tag , which is determined as a function of the p T of the b jet [26].
The number of data events reconstructed with these selection criteria is 9268 in the muon channel and 6526 in the electron channel.Comparisons between data observations and the SM expectations are presented in section 8.

Top-quark reconstruction
Once events are selected according to the criteria described in section 4, the reconstruction of each top-quark candidate proceeds by testing all selected jets, p miss T , and the lepton for their compatibility with decay products of the hadronic branch (t → bW → bqq ) and the leptonic branch (t → bW → b ν).The initial value for the neutrino momentum is set to where p ν z is determined by requiring that the invariant mass of the neutrino and lepton be equal to the W-boson mass, which is assumed to be 80.4 GeV/c 2 [28].For each possible neutrino solution and jet assignment to either the leptonic branch or hadronic branch, a χ 2 is built, containing the following terms: where m t , m t , M lep W and M had W are the reconstructed invariant masses for a given combinatorial assignment of four jets to the final-state particles in the tt decay.The reference value for the top-quark mass m ref t is taken to be 173.3GeV/c 2 [29] for data and 172.5 GeV/c 2 for the simulated samples.The term p i (disc| f ) is the probability for the i-th jet to have flavour f (either a b jet from the direct top-quark decay or a jet from the hadronically decaying W boson), given its measured value from the CSV tagger discriminant (see section 4).Since the top-quark and Wboson reconstructed masses are dominated by experimental resolution effects, the parameters σ m t,t and σ M lep, had W in eq. ( 6) are approximated as Gaussian widths, which are determined from simulation.
In the process, a constrained kinematic fit is performed, which leads to an improved determination of the unmeasured neutrino momentum component p ν z , or in some cases a valid physical solution to be found when the analytical solution is imaginary due to detector mismeasurements, and to a more accurate reconstruction of the tt system.The momenta of the measured jets and lepton are allowed to vary within their resolutions and are required to comply with the same kinematic constraints used in eq. ( 6).The t and t candidates that are chosen for further analysis correspond to the particular configuration of lepton, neutrino, and jets that minimise χ 2 comb .Any additional jets passing the event selection criteria that are not chosen as one of the four jets belonging to the tt system are discarded and no longer used in the analysis.Events for which the kinematic fit fails to find a real solution complying with the constraints are discarded.
Following the full event selection in simulation studies, including the requirement of at least two identified b jets, this top-quark reconstruction algorithm associates the correct jet to the leptonic top-quark decay branch in 71% of all cases.If instead one loosens the requirement to at least one b jet in the event, the fraction of correctly assigned jets to the leptonic branch decreases to 63%.

Background estimation
The main source of backgrounds in the analysis comes from top-quark pairs that decay into either fully leptonic or fully hadronic modes, or into semileptonic tt decays involving taus, and that pass the +jets selections.Other backgrounds are, in order of decreasing importance: single top-quark events, events from processes involving W-boson production with jets (W+jets) and Drell-Yan production with jets (DY+jets).The normalisation of the tt processes is determined by the fitting procedure described in section 7, and the predictions for single top-quark processes are determined from simulation (see section 3).
The cross section for inclusive W+jets and DY+jets production could be poorly predicted in the specific phase space region where those events become background for top-quark production, corresponding to high jet multiplicities and events containing heavy-flavour jets.For this reason, the normalisation of the background coming from W+jets and DY+jets is determined using an approach partially based on the data.Muons and electrons are treated separately, since important requirements on background rejection, such as lepton isolation, are different.

Normalisation and shape of DY production with jets
The normalisation and shape of distributions from DY+jets production, are studied using a data control sample defined by applying the same selection criteria described in section 4, except that events are required to contain an additional lepton of the same flavour and opposite charge.In this case, the M T variable is computed with the event E miss T and the highest-p T lepton.Using a reference cross section of 3048 pb [30] for the DY production decaying into pairs of muons, electrons, and taus with invariant mass above 50 GeV/c 2 , the normalisation of simulated samples for DY+jets is found to agree with the data within the statistical uncertainty of about 10%.The following systematic uncertainties are then considered in the estimation of the normalisation scale factor N data /N simulation , between the amount of data and simulated events: • the PDFs [31,32] used to generate the samples: ±3.6%; • the uncertainties in the jet energy scale: ±12.7%; • the uncertainties in the jet energy resolution: ±2.6%; • the uncertainty in the integrated luminosity [11]: ±2.2%; • the difference observed on N data /N simulation for events inside and outside a window of 30±20 GeV/c 2 around the Z-boson mass, where the DY+jets background is probed: ±20.0%.
Including all systematic sources, this leads to a total estimated uncertainty of 30.0% for the DY+jets normalisation.
The shape of the cos θ * distribution from DY+jets background events is verified using this same control sample.The top-quark reconstruction algorithm described in section 5 is applied, except that the highest-p T lepton is used in the kinematic fit.The shapes observed in data and simulation are found to be in agreement.

Normalisation and shape of W-boson production with jets
Due to the charge of the valence quarks in the colliding protons, more positively ( + ) than negatively ( − ) charged leptons are produced in pp collisions for single top-quark production and W+jets events.On the other hand, the amount of + and − produced in DY+jets and tt processes is, to a very good approximation, the same in pp collisions.Hence, by keeping the predicted cross section of single-top-quark production fixed, the background contribution from W+jets production can be determined from the charge asymmetry N + − N − , where N + (N − ) is the number of + ( − ).The total number of W+jets events in the data sample is thus predicted to be where W+jets MC is estimated using simulated events and (N + − N − ) data is the measured asymmetry in data.The fixed contribution of single-top quark from simulation is subtracted from the total charge asymmetry in eq.(7) The predicted normalisation is found to be consistent with the expectations from the simulation within relatively large statistical uncertainties.A total systematic uncertainty of 100% is assigned to the normalisation of the predicted W+jets background.To test the effect of possible biases due to the assumed background shape from simulation, the analysis is repeated by dividing the data sample in bins of cos θ * .To increase the statistical power of the test, the jet selection criteria are partially relaxed.Within the precision of the test, the shape of the cos θ * distribution predicted from the simulation is found to be in agreement with the data, and any possible bias is negligible compared with the normalisation uncertainty considered.

Determination of helicity fractions
A fitting procedure based on a MC simulation reweighting technique is used to simultaneously account for experimental resolution effects and for the dependencies on the W-boson helicity fractions.Any new helicity configuration can be obtained from the original configuration used in the simulation via an algorithm that (re)weights each event according to the generated, matrix-element level cos θ * values for each W → ν and W → qq decay in the tt simulated sample.
Because of the QCD production mechanism for tt events, top quarks can be considered as unpolarised on average, to a high degree of precision.Spin correlations between the two top quarks in the event do not modify this picture.This is because the average spin properties of the top quark associated with the leptonic W-boson decay branch do not change after averaging over the phase space variables of the other top quark (from the hadronic W-boson decay branch) in the event.This scenario, which has been assumed in past and recent W-boson helicity studies [4,33,34], implies that the phase space density for the reconstructed cos θ * variable of each decay branch, ρ(cos θ * rec ), can be decoupled from the rest of the event.Therefore, at matrix-element (generator) level, we assume the following dependence: where (F L , F 0 , F R ) ≡ F are the helicity fractions to be measured, and θ * gen is the matrix-element level quantity for the helicity angle.For normalisation reasons, the helicity fractions are constrained to satisfy F L + F 0 + F R = 1.A new cos θ * rec distribution for a particular configuration of helicity fractions F L , F 0 , F R is then obtained by reweighting each fully simulated event by the weight where W lep, had is defined for the leptonic and hadronic branches respectively as: In the expression above, F SM L , F SM 0 , F SM R are the helicity fractions that correspond to the expected SM values and which are used to generate the reference simulated sample.The new reweighted distribution automatically takes into account, by construction, all detector resolution and acceptance effects, as described by the simulation.
The helicity fractions are measured by maximising a binned Poisson likelihood function, which is constructed using the numbers of observed N data (i) and expected N MC (i; F) events in each cos θ * rec bin i.The numbers of expected events are given by: The normalisation parameter for the tt component F tt is not sensitive to the helicity fractions, but it does absorb a large fraction of the experimental and theoretical systematic uncertainties in the predicted rates.Uncertainties on the normalisation of backgrounds are considered as a separate source of systematics.
Two types of fits are performed.In the fits denoted by 3D, the fractions F 0 , F L , and the normalisation factor F tt (see eq. ( 13)) are treated as free parameters, and F R is determined by the In the fits denoted by 2D, F 0 and F tt are taken as free parame- ters, setting F R = 0, and solving for F L from the constraint F L = 1 − F 0 .Within the expected experimental uncertainties, the F R = 0 condition is satisfied both in the SM and in anomalous coupling scenarios where only g R is different from zero.
We perform the measurements by fitting either the cos θ * distribution from the leptonic branch or the |cos had θ * | distribution from the hadronic branch.The two variables are fitted separately and not simultaneously, so as to avoid any possible biases due to top-quark spin correlations.
At matrix-element level, |cos had θ * | is only sensitive to the F 0 fraction (or, alternatively, to the combination F L + F R ), and is therefore only used in the context of the 2D fits.

Comparison between data and SM predictions
The agreement between data and expectation from the SM is extensively investigated.First, the normalisations of simulated samples involving W+jets and DY+jets are determined and applied using control data samples discussed in section 6. Next, reference cross sections 64.6 pb [35] for single-top-quark (t-channel), and 15.74 pb [36] for W-boson-associated single-top-quark processes, which correspond to approximated NNLO predictions, and NLO tt cross sections are used to scale the respective simulated samples to an integrated luminosity of 5.0 fb −1 .Finally, the simulated samples involving top quarks are corrected for both the presence of pileup and the efficiency correction factors DATA / MC and DATA b-tag / MC b-tag .Table 1 presents the number of data events observed in the muon+jets and electron+jets channels which is compared to the predictions for the signal (tt) and background processes.In the table, columns two and four display the number of remaining events after applying the selection criteria described in section 4. Columns three and five display the subsample of these events where a tt pair candidate is found, reconstructed as described in the previous section.The yields observed in data are in agreement with the predicted yields expected from the SM.
A comparison of shapes between data and simulation, after having applied the kinematic fit, for the variables relevant to this analysis is presented in figures 1 to 3. Figure 1 shows the Table 1: Number of events expected from signal and background processes, together with the observed number of events in data for both the muon+jets and electron+jets channels.The columns labelled as "Selected" represent the number of events passing the analysis selection criteria; the columns labelled as "KF" represent the fraction of those events containing a reconstructed top-quark pair via a kinematic fit that has converged.kinematic distributions for the leptons in the event: transverse momentum and pseudorapidity of muons and electrons, and the neutrino transverse momentum.Figure 2 displays the p T distributions for jets related to the top-quark reconstruction, including the b jets (from leptonic and hadronic tops) and the jets from the hadronic W-boson decay.The shapes of all important kinematic distributions in the data, which describe the tt system, are well reproduced by the simulation, including those that do not depend strongly on the W-boson helicity (i.e.global properties of top-quark and W-boson systems).
The most relevant distributions for this analysis, the cosine distributions of the helicity angles computed according to the definitions discussed in section 1, are shown in figure 3 for both the muon+jets and electron+jets channels.The agreement between data and simulation for cos θ * and |cos had θ * | is observed to be satisfactory.This suggests that, even before any attempt to measure the W-boson helicity fractions is made, the data prefer values close to the SM predictions.

Systematic uncertainties
Several sources of systematic effects, which could possibly bias the measurement of the Wboson helicity fractions, have been investigated and their corresponding uncertainties in the measurement determined.
The scale of the jet energy (JES) calibration is determined from data, which is then applied as a p T -and η-dependent correction to the simulation; the JES calibration has an uncertainty that typically varies between 2% and 4% [24].To estimate the effect that the JES uncertainty has on the W-boson helicity measurement, the p T of all jets are systematically shifted together, either up or down, by their corresponding p T -and η-dependent uncertainty.Because the missing transverse energy is corrected due to the presence of JES calibrated jets, the systematic shifts of the jet p T 's in the event are propagated and lead to systematic shifts in the momentum imbalance.The full analysis, including the reconstruction of top quarks and the resulting measurements of the W-boson helicity fractions, is then repeated.The jet energy resolution (JER) is observed to be different in data compared with the simulation.Jet energy resolutions are typically 5-13% larger in data than in simulation, with uncertainties smaller than 5% [24].The systematic uncertainties related to JER are estimated by over-smearing the reconstructed jets  in simulated events, so that their transverse momentum resolution is the same as measured in the data.The effect is propagated to the missing transverse energy, and the full analysis is repeated, similar to the procedure used to estimate the JES uncertainty.
Uncertainties in the lepton identification efficiency are investigated by varying the efficiency correction factor DATA / MC .In the case of muons, the efficiency correction factor depends on the η position of the muon in the detector.Since the measurement of the W-boson helicity is mainly affected by shape-dependent effects, uncertainties due to the muon efficiency correction factor are estimated by repeating the full analysis replacing the η-dependent factors by an uniform correction.In the case of electrons, only a very mild dependency on η is observed and the corresponding uncertainty, derived by assuming a flat η-dependence, has very little impact on the W-boson helicity measurement.Therefore, the efficiency correction factor for electron identification is shifted together with a shift in the scale factor for the jet component of the trigger according to the p T and η position of the electrons and jets.The combination of electron and jet scale factors that lead to the maximum possible η-dependent effect is then applied and the full analysis is repeated.
The efficiencies for b tagging are measured using a control sample of multijet events [26], in data and simulation.The correction factors DATA b-tag / MC b-tag , which are applied to the simulated samples, are functions of the p T and η of the jets, the number of the required b tags, as well as the number of heavy-flavour and light-flavour jets in the event.The scale factors are relatively uniform in the typical p T range of the selected jets, resulting in only a very small dependence of the W-boson helicity results on the b-tagging efficiency.The scale factors are varied by their uncertainties and the resulting differences are taken as a systematic uncertainty in the measured fractions.
The effect of pileup is estimated by varying the number of minimum bias collisions superimposed on each simulated signal event, according to an uncertainty of 5% which includes the uncertainties in the inelastic pp cross section, luminosity and other modelling uncertainties.
To account for a bias on the W-boson helicity measurement due to uncertainties in the normalisation from simulated background samples involving single top quarks, relative to the signal, the assumed reference cross sections are varied.While CMS has measured the singletop-quark production cross section in the t-channel with a 9% precision (67.2 ± 6.1 pb [37]), a systematic variation of ±15% is applied to cover the case of single-top-quark events produced with additional jets from radiation, which comprise the main contribution to this background component.Likewise, while CMS measures a cross section of 16 +5 −4 pb [38] for the associated tW production case, the reference cross section used for the normalisation, 15.74 pb, is shifted by ±40%.Finally, since the tt sample normalisation is a free parameter in the helicity fits, the uncertainty associated with its initially assumed reference cross section does not affect the measurement.
The normalisation of the W+jets and DY+jets samples is estimated using the method described in section 6 with an uncertainty of 100% and 30%, respectively.In both the W+jets and DY+jets events cases, the shapes of all relevant distributions in the simulation agree with the data and any systematic effects from variations in normalisations are much larger than any variations arising from shape; hence, systematic uncertainties due to possible differences in shape are negligible.
While the sample size for the reference simulated tt dataset is chosen to be five times that of the processed data, it is possible for the reweighting method to introduce a systematic bias by degrading the statistical power of the simulated sample due to weights which can be larger than unity.Hence, special care must be taken to ensure that the statistical uncertainty of the MC prediction for each cos θ * rec bin is substantially smaller than the corresponding statistical uncertainty of the data.The uncertainties are estimated by repeating the analysis using a subsample of events that correspond to a fraction 1/N of the entire sample.The procedure is repeated many times, and the uncertainties on the W-boson helicity fractions taken as σ/ √ N where σ is the spread observed on the fraction.Several values of N, between 2 and 10, are tested, and result in very similar uncertainties.
Since the W-boson helicity fractions depend directly on the top-quark mass, uncertainties in the latter could bias the measurement.This systematic effect is studied and taken into account, via tt samples simulated using MADGRAPH for different m t hypotheses.A variation of ±1.4 GeV/c 2 [29] about the assumed central value of 172.5 GeV/c 2 is assumed.
Uncertainties on the helicity measurement from the choice of renormalisation and factorisation scales for the simulated signal samples are estimated using dedicated tt simulated samples that vary the renormalisation and factorisation scales and the scale of the first emission in the parton shower, in a consistent manner, by factors of 0.5 and 2 with respect to a central value of The kinematic scale used to match jets to partons in the signal simulation is estimated using dedicated tt samples where that matching parameter is varied by factors of 0.75 and 1.5 with respect to its central value of 40 GeV.
The systematic effects due to the PDFs used to simulate the signal and background samples are estimated using two different methods [32], according to a reweighting technique.Firstly, events are reweighted using 100 members [39] of the NNPDF21 set [40], and the W-boson helicity fractions are remeasured for each of them.For a given helicity fraction, the RMS of the distribution of measurements from the different PDF members provides an uncertainty estimate that corresponds to 68% confidence level (CL).Secondly, the difference between the central values for CTEQ6L1 [16] (used in the analysis simulations) and MSTW2008lo68cl [31] is estimated.The systematic uncertainties in the measurements for the W-boson helicity fractions, due to intrinsic PDF uncertainties, are then taken as the largest difference between two different estimates.
The impact of all of the above systematic effects on the W-boson helicity fractions is detailed in table 2, for the measurements for the leptonic side of the events (cos θ * ).The table shows results for the 3D and 2D fits, obtained by fitting two of the fractions or setting F R = 0, respectively.Measurements using final states containing either a muon or an electron are presented in columns two through seven.The last three columns display systematic uncertainties for the combined measurements of the muon+jets and electron+jets channels, using the measurements from columns two through seven as inputs.The measurements are combined taking into account both statistical and systematic uncertainties.Common sources of uncertainties between the different measurements are assumed to be fully correlated.The dominant sources of systematic uncertainties in the leptonic side are the W+jets background normalisation, the signal modelling (tt renormalisation and factorization scales, and top-quark mass), and the statistics of the simulated samples.Systematic uncertainties in the measurements for the hadronic branch, using the |cos had θ * |, are presented in table 3. Since |cos had θ * | has no sensitivity to a measurement of F L − F R , only the 2D fits are performed.Uncertainties on the individual measurements in the electron and muon channels are presented in the first two columns; in the last column, the combination of muons+jets and electrons+jets channels is shown.The hadronic branch is seen to have larger systematic uncertainties, compared with the leptonic branch, due, in part, to the dominant W+jets background and the importance of uncertainties from the JES and JER, as well as PDFs.

Results
The W-boson helicity fractions are measured according to the fits described in section 7. The unitary condition F 0 + F L + F R = 1 is used to determine either (a) the right-handed fraction F R from measurements of the free parameters, F 0 and F L , in the 3D fits or (b) the left-handed fraction F L from the measurement of the free parameter F 0 in the 2D fits assuming F R = 0. Table 4 presents the fit measurement of each helicity parameter, one decay channel at a time, together with the statistical and systematic uncertainties.The statistical correlation factor ρ stat 0L between F 0 and F L is presented in the last column; the measurements are seen to be highly correlated.All measurements, from either the muon or electron channels, using either the leptonic or hadronic branches, are observed to be compatible within uncertainties.The measurements using the leptonic branch cos θ * are more precise, as expected.
Table 5 presents various combinations of the results presented in table 4. Firstly, the muon+jets and electron+jets channels are combined using the leptonic branch measurements from the 3D fits.The χ 2 per degree of freedom for that combination is 0.109/2, corresponding to a χ 2probability of 94.7%.Secondly, the 2D fit measurements of the F 0 helicity fraction from the leptonic (cos θ * ) and hadronic (cos had θ * ) branches are combined, separately for each decay channel.While the leptonic branch dominates with a weight of about 90%, the total uncertainty of the combination nevertheless decreases.Finally, the most precise measurement of Table 2: Summary of the systematic uncertainties for the analysis using only the leptonic branch of the event, for the 3D fit, fitting F 0 , F L , and F tt (columns 2-3 for muon+jets analysis, 5-6 for electron+jets analysis, and 8-9 for the combination of both decay modes); and the 2D fit, fitting F 0 and F tt only (column 4 for muon+jets analysis, 7 for electron+jets analysis, and 10 for the combination of both decay modes).The numbers given correspond to the absolute uncertainty with respect to the central analysis: ∆F = (F central − F check ).F 0 is obtained by subsequently combining the 2D fit measurements across the muon+jets and electron+jets channels, following the combination of the 2D fit measurements from the leptonic and hadronic branches.
Summaries of all measurements and their various combinations are presented in figures 4 and 5 for the 3D and 2D types of fits, respectively.All measurements are compatible with each other, and also compatible with the expectations from the SM [6].

Limits on anomalous couplings
The measured helicity fractions can be used to set limits on anomalous Wtb couplings.We assume the minimal parametrisation of the Wtb vertex suggested in refs.[7,8,41] and as described in the introduction.We consider two specific scenarios.First, we assume V L = 1, V R = g L = 0 and leave Re(g R ) as a free parameter.This CP-conserving scenario is particularly interesting because indirect constraints to g R from radiative B-meson decay measurements are currently poor, Re(gR) ∈ [−0.15, +0.57] [42].A specific feature of this scenario is that it does not provide any contribution to the right-handed helicity of the W boson, F R .The grand combination of the longitudinal helicity fraction F 0 measurements, across both the leptonic and hadronic branches including both the muon and electron channels, and assuming F R = 0, is reinterpreted in terms of Re(g R ), yielding Re(g R ) = −0.008± 0.024 (stat.)+0.029 −0.030 (syst.), which is consistent with the SM expectations within the quoted uncertainties.In quoting this result we have omitted another minimum of the fit closer to the Re(g R ) ≈ 0.8 region, which  [6] with their theoretical uncertainties are represented as hatched bands.Table 3: Systematic uncertainties for the 2D fits using the hadronic branch of the tt system, and for the muon channel, electron channel, as well as the combination of both decay channels.The numbers given correspond to the absolute uncertainty with respect to the central analysis: ∆F = (F central − F check ).4: Measurements of the W-boson helicity fractions from the cos θ * (leptonic branch) and |cos had θ * | (hadronic branch) distributions.The columns show the fit type, the decay channel, and the measurement of each helicity parameter, together with the statistical and systematic uncertainties.For the 3D fits, the last column presents the statistical correlation between F 0 and F L , while for the 2D fit, total anticorrelation (F L = 1 − F 0 ) is assumed.would lead to an increase of almost a factor of three in the single-top-quark cross section [43], which would not be consistent with the recent CMS measurement [37].In terms of the effective dimension-six Lagrangian O 33 uW defined in refs.[7,8] we obtain the equivalent result, Re(C 33 uW )/Λ 2 = −0.088± 0.280 (stat.)+0.339 −0.352 (syst.)TeV −2 , where Λ is the scale of new physics and Re(C 33 uW ) the effective operator coefficient.In the second scenario, again assuming CP is conserved, we choose Re(g L ) and Re(g R ) as free parameters of the fit.Limits on those parameters are determined using the combined measurements of the muon+jets and electron+jets channels from the 3D fit of the leptonic branch, cos θ * .The results of the likelihood fit for the parameters F 0 and F L can be reinterpreted in terms of Table 5: The combined helicity fractions and their uncertainties, including the type of fit performed, the channels ( = e, µ combination) and branches of the tt system ("l" for leptonic, cos θ * , and "h" for hadronic, |cos had θ * |, used in the combination, as well as the total correlation between F 0 and F L .Fit Channel(s) Branch Fraction ± (stat.) ± (syst.)[ the parameters Re(g L ) and Re(g R ). Figure 6 shows the regions of the Re(g L ), Re(g R ) plane allowed at 68% and 95% CL.As in the first scenario, a region near Re(g L ) = 0 and Re(g R ) 0, allowed by the fit but excluded by the CMS single-top quark measurement, is not shown.
The result obtained from the first scenario represents an improvement of about 50% on the precision of Re(g R ) with respect to previous measurements [4], while the limits from the second scenario are similar to those from ref. [4].: Limits on the real components of the anomalous couplings g L , g R at 68% and 95% CL, for V L = 1 and V R = 0.The SM prediction (g R = 0 and g L = 0) is also shown.

Summary
The W-boson helicity has been measured in top-quark-pair events decaying semileptonically, both in the muon+jets and in the electron+jets channels, using proton-proton collisions data at √ s = 7 TeV, corresponding to an integrated luminosity of 5.0 fb −1 .Both the leptonic and the hadronic branches of the decay have been studied.The most precise measurement, not constraining F R to the SM, corresponding to the combination of muon and electron channels, using only the leptonic branch, yields: F 0 = 0.682 ± 0.030 (stat.)± 0.033 (syst.),F L = 0.310 ± 0.022 (stat.)± 0.022 (syst.),F R = 0.008 ± 0.012 (stat.)± 0.014 (syst.), with a correlation coefficient of −0.95 between F 0 and F L .
The measured W-boson helicity fractions are in agreement with the predictions from the standard model.Assuming a minimal parametrisation of the Wtb vertex, stringent limits on the real components of the anomalous couplings g L and g R are also derived.

Figure 1 :Figure 2 :
Figure1: Distributions of data compared to SM predictions for signal and expected backgrounds: charged lepton p T (top), η (centre) and neutrino p T (bottom) for the muon+jets (left) and electron+jets (right) channels.Data are displayed as solid points, simulated tt signal distributions as red histograms, and the contribution from other background processes as coloured histograms.Overflows are displayed in the last bin of each histogram.At the bottom, the ratio between prediction and data is displayed.Only statistical uncertainties are shown.

Figure 3 :
Figure 3: Cosine of the helicity angles cos θ * (top) and |cos had θ * | (bottom) for the muon+jets (left) and electron+jets (right) channels.Data are displayed as solid points, simulated tt signal distributions as red histograms, and the contribution from other background processes as coloured histograms.At the bottom, the ratio between prediction and data is displayed.Systematic uncertainties are shown as hatched histograms.

Figure 4 :Figure 5 :
Figure4: Summary of the W-boson helicity measurements in semileptonic decays of top-quark pairs with 2011 data for 3D fits.The inner error bars represent the statistical uncertainties and the outer error bars the statistical and systematic uncertainties, added in quadrature.NNLO predictions from ref.[6] with their theoretical uncertainties are represented as hatched bands.
Figure6: Limits on the real components of the anomalous couplings g L , g R at 68% and 95% CL, for V L = 1 and V R = 0.The SM prediction (g R = 0 and g L = 0) is also shown.

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 National Science Council, 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 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 Czech Republic; the Council of Science and Industrial Research, India; the Compagnia di San Paolo (Torino); the HOMING PLUS programme of Foundation for Polish Science, cofinanced by EU, Regional Development Fund; and the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF.