Measurement of the W Boson Helicity in Top Quark Decays at D0

We present the first model-independent measurement of the helicity of $W$ bosons produced in top quark decays, based on a 1 fb$^{-1}$ sample of candidate $t\bar{t}$ events in the dilepton and lepton plus jets channels collected by the D0 detector at the Fermilab Tevatron $p\bar{p}$ Collider. We reconstruct the angle $\theta^*$ between the momenta of the down-type fermion and the top quark in the $W$ boson rest frame for each top quark decay. A fit of the resulting \costheta distribution finds that the fraction of longitudinal $W$ bosons $f_0 = 0.425 \pm 0.166 \hbox{(stat.)} \pm 0.102 \hbox{(syst.)}$ and the fraction of right-handed $W$ bosons $f_+ = 0.119 \pm 0.090 \hbox{(stat.)} \pm 0.053 \hbox{(syst.)}$, which is consistent at the 30% C.L. with the standard model.

The top quark is by far the heaviest of the known fermions and is the only one that has a Yukawa coupling to the Higgs boson of order unity in the standard model (SM). In the SM, the top quark decays via the V − A charged-current interac-tion, almost always to a W boson and a b quark. We search for evidence of new physics in the t → W b decay by measuring the helicity of the W boson. A different Lorentz structure of the t → W b interaction would alter the fractions of W bosons produced in each polarization state from the SM values of 0.697±0.012 [1] and 3.6×10 −4 [2] for the longitudinal fraction f 0 and right-handed fraction f + , respectively, at the world average top quark mass m t of 172. 5 ± 2.3 GeV [3].
In this Letter, we report a simultaneous measurement of f 0 and f + (the negative helicity fraction f − is then fixed by the requirement that f − + f 0 + f + = 1). This is the first modelindependent W boson helicity measurement. A measurement of the W boson helicity fractions that differs significantly from the SM values would be an unambiguous indication of new physics [4]- [6]. In addition, the model-independent W boson helicity measurement can be combined with measurements of single top production cross sections to fully specify the tbW vertex [7].
Measurements of the b → sγ decay rate assuming the absence of gluonic penguin contributions have indirectly limited the V + A contribution in top quark decays to less than a few percent [8]. Direct measurements of the longitudinal fraction (f + set to zero) found f 0 = 0.85 +0. 16 −0.23 [9] and f 0 = 0.56 ± 0.31 [10]. Direct measurements of f + ( f 0 set to 0.7) have found f + = −0.02 ± 0.08 [11] and f + = 0.06 ± 0.10 [12]. The analysis presented here improves upon that reported in Ref. [12] by using a larger data set, employing enhanced event selection techniques, making use of hadronic W boson decays, and introducing the model-independent analysis.
The angular distribution of the down-type decay products of the W boson (charged lepton or d, s quark) in the rest frame of the W boson can be described by introducing the decay angle θ * of the down-type fermion with respect to the top quark direction. The dependence of the distribution of cos θ * on the W boson helicity fractions, where c = cos θ * , forms the basis for our measurement. We proceed by selecting a data sample enriched in tt events, reconstructing the four vectors of the two top quarks and their decay products, and then calculating cos θ * . The down-type fermions in leptonic W boson decays are the charged leptons. For hadronic W boson decays, we choose a W boson daughter jet at random to calculate cos θ * . Since this introduces a sign ambiguity into the calculation, we consider only | cos θ * | for hadronic W boson decays. The | cos θ * | variable does not discriminate between left-and right-handed W bosons, but adds information for determining the fraction of longitudinal W bosons. These distributions in cos θ * are compared with templates for different W boson helicity models, accounting for background and reconstruction effects, using a binned maximum likelihood method. This measurement uses a data sample recorded with the D0 experiment [13] that corresponds to an integrated luminosity of about 1 fb −1 of pp collisions at √ s = 1.96 TeV. Events were selected by the trigger system based on the presence of energetic leptons or jets. The data sample consists of tt candidate events from the lepton plus jets (ℓ+jets) decay channel tt → W + W − bb → ℓνqq ′ bb and the dilepton channel tt → W + W − bb → ℓνℓ ′ ν ′ bb, where ℓ and ℓ ′ are electrons or muons. The ℓ+jets final state is characterized by one charged lepton, at least four jets, and large missing transverse energy ( E T ). The dilepton final state is characterized by two charged leptons, at least two jets, and large E T . In both final states, at least two of the jets are b jets.
The ℓ+jets event selection [14] requires an isolated lepton with transverse momentum p T > 20 GeV, no other lepton with p T > 15 GeV in the event, E T > 20 GeV, and at least four jets. In the dilepton channel, events are required to have two leptons with opposite charge and p T > 15 GeV and two or more jets. Electrons are required to have pseudorapidity [15] |η| < 1.1 in the ℓ+jets channel and |η| < 1.1 or 1.5 < |η| < 2.5 in the dilepton channel, and are identified by their energy deposition, isolation, and shower shape in the calorimeter, and information from the tracking system [14]. Muons are identified using information from the muon and tracking systems and must be isolated from jets, significant calorimeter energy, and energetic tracks. They are required to have |η| < 2.0. Jets are reconstructed using a cone algorithm with cone radius 0.5 [16] and are required to have rapidity |y| < 2.5 and p T > 20 GeV. The E T is calculated from the vector sum of calorimeter cell energies, corrected to account for the response of the calorimeter to jets and electrons and also for the momenta of identified muons.
We simulate tt signal events with m t = 172.5 GeV for different values of f + with the ALPGEN Monte Carlo (MC) program [17] for the parton-level process (leading order) and PYTHIA [18] for gluon radiation and subsequent hadronization. We generate samples corresponding to each of the three W boson helicity configurations by reweighting the generated cos θ * distributions.
Backgrounds in the ℓ+jets channel arise mainly from W +jets production and multijet production. In the dilepton channel, backgrounds arise from processes such as W W +jets or Z+jets. The MC samples used to model background events with real leptons are also generated using ALPGEN and PYTHIA. Both the signal and background MC samples are passed through a GEANT3 [19] simulation of the detector response and reconstructed with the same algorithms used for data. In the ℓ+jets channel we estimate the number N mj of multijet background events from data, using the technique described in Ref. [14]. We calculate N mj for each bin in the cos θ * distribution from the data sample to obtain the multijet cos θ * templates.
To increase the signal purity, a multivariate likelihood discriminant D [14] with values in the range 0 to 1 is calculated using input variables which exploit differences in kinematics and jet flavor. The kinematic variables considered are: H T (scalar sum of the jet p T values), centrality C (the ratio of H T to the sum of the jet energies), k ′ T min (the distance in η − φ space between the closest pair of jets multiplied by the E T of the lowest-E T jet in the pair and divided by the E T of the W boson), the sum of all jet and charged lepton energies h, the minimum dijet mass of the jet pairs m jjmin , aplanarity A, sphericity S [20], E T , and the dilepton invariant mass m ℓℓ . In the dimuon channel, the χ 2 of a kinematic fit to the Z → µµ hypothesis χ 2 Z [21] is used instead of E T . Since jets in background events arise mostly from light quarks or gluons while two of the jets in tt events arise from b quarks, we form a neural network discriminant between b and light jets [22] with output value NN b that tends towards one for b jets and towards zero for light jets.. In the ℓ+jets channels we use the average of the two largest NN b values to form a continuous variable NN b whose value tends to be large for tt events and small for backgrounds, while in the dilepton channels the NN b values for the two leading jets (NN b1 , NN b2 ) are taken as separate variables.
The discriminant is built separately for each of the five final states considered, using the method described in Refs. [14,23]. We consider all possible combinations of the above variables for use in the discriminant, and all possible requirements on the D value, and choose the variables and D criterion that give the best expected precision for the W boson helicity. The variables chosen and the requirement placed on D for each channel are given in Table I. An example of the distributions of signal, background and data events in D is shown in Fig. 1.
We perform a binned Poisson maximum likelihood fit to compare the observed distribution of events in D to the sum of the distributions expected from tt and background events. In the ℓ+jets channels, N mj is constrained to the expected value within the known uncertainty, while in the dilepton channels the ratio of the various background sources is fixed to the expectation from the cross sections times efficiency of the kinematic selection. The likelihood is then maximized with respect to the numbers of tt and background events, which are multiplied by the efficiency for the D selection to determine the composition of the sample used for measuring the W boson helicity fractions. Table I lists the composition of each sample as well as the number of observed events in the data.
The top quark and W boson four-momenta in the selected ℓ+jets events are reconstructed using a kinematic fit which is subject to the following constraints: two jets must form the invariant mass of the W boson [24], the lepton and the E T together with the neutrino p z component must form the invariant mass of the W boson, and the masses of the two reconstructed top quarks must be 172.5 GeV. The four highest-p T jets in each event are used in the fit, and among the twelve possible jet combinations, the solution with the maximal probability, considering both the χ 2 from the kinematic fit and the NN b values of the four jets, is chosen. The cos θ * distributions for leptonic and hadronic W boson decays obtained in the ℓ+jets data after the full selection are shown in Fig. 2(a) and (b).
Since the two neutrinos in the dilepton final state are not detected, the system is kinematically underconstrained. However, if m t is assumed, the kinematics can be solved algebraically with a four-fold ambiguity in addition to the twofold ambiguity in pairing jets with leptons. For each of the two leading jets, we calculate the value of cos θ * resulting from each solution with each of the two leptons associated with the jet. To explore the phase space consistent with the measured jet and lepton energies, we fluctuate them according to their resolution many times, and repeat the above procedure for each fluctuation. The average of these values is taken as cos θ * for that jet. The cos θ * distribution obtained in dilepton data is shown in Fig. 2(c).
To extract f 0 and f + , we compute the binned Poisson likelihood L(f 0 , f + ) for the data to be consistent with the sum of signal and background templates at any given value for these fractions. The background normalization is constrained to be consistent within uncertainties with the expected value by a Gaussian term in the likelihood. The fit also accounts for the differences in selection efficiency for tt events with different W helicity configurations [25].
Systematic uncertainties are evaluated in ensemble tests by varying the parameters that can affect the measurement. Ensembles are formed by drawing events from a model with the parameter under study varied. These are compared to the standard cos θ * templates in a maximum likelihood fit. The average shifts in the resulting f 0 and f + values are taken as the systematic uncertainty and are shown in Table II. The total systematic uncertainty is then taken into account in the likelihood by convoluting the likelihood with a Gaussian with a width that corresponds to the total systematic uncertainty. The mass of the top quark is varied by ±2.3 GeV, and the jet reconstruction efficiency, energy calibration, and b fragmentation parameters by ±1σ around their nominal values. The tt model uncertainty is studied by comparing tt events generated by PYTHIA to the standard ALPGEN samples, considering samples with a different model for the underlying event and ones in which only a single primary vertex is reconstructed. Effects of mis-modeling the background distribution in cos θ * are assessed by comparing data to the background model for events with low D values. The uncertainty due to template statistics is evaluated by fluctuating the templates according to their statistical uncertainties and repeating the fit to the data for each fluctuation. Uncertainties due to jet resolution, jet flavor composition in the background, the modeling of the NN b variable, and parton distribution functions are all found to be less than 0.01 for both f 0 and f + .   The measured values of f 0 and f + are: (2) f + = 0.119 ± 0.090 (stat.) ± 0.053 (syst.), with a correlation coefficient of −0.83. The inclusion of the | cos θ * | measurement from hadronic W boson decays improves the uncertainties on f 0 and f + by about 20% relative to those obtained using only the leptonic decays. The 68%, and 95% C.L. contours from the fit, including systematic uncertainties, are shown in Fig. 3. The data indicate fewer longitudinal and more right-handed W bosons than the SM predicts,  but the difference is not significant as there is a 30% chance of observing a larger discrepancy given the statistical and systematic uncertainties in the measurement.