Helicity of the W Boson in Lepton+Jets ttbar Events

We examine properties of ttbar candidates events in lepton+jets final states to establish the helicities of the W bosons in t->W+b decays. Our analysis is based on a direct calculation of a probability that each event corresponds to a ttbar final state, as a function of the helicity of the W boson. We use the 125 events/pb sample of data collected by the DO experiment during Run I of the Fermilab Tevatron collider at sqrt{s}=1.8 TeV, and obtain a longitudinal helicity fraction of F_0=0.56+/-0.31, which is consistent with the prediction of F_0=0.70 from the standard model.


Abstract
We examine properties of tt candidates events in lepton+jets final states to establish the helicities of the W bosons in t → W + b decays. Our analysis is based on a direct calculation of a probability that each event corresponds to a tt final state, as a function of the helicity of the W boson. We use the 125 events/pb sample of data collected by the DØ experiment during Run I of the Fermilab Tevatron collider at √ s=1.8 TeV, and obtain a longitudinal helicity fraction of F 0 =0.56±0.31, which is consistent with the prediction of F 0 =0.70 from the standard model. The observation of the top quark at the Fermilab Tevatron collider [1,2] has provided a new opportunity for examining detailed implications of the standard model (SM). In fact, the large mass of the top quark has led to speculation that its interactions might be especially sensitive to the mechanism of electroweak symmetry breaking and new physics that is expected to appear at the TeV energy scale. Several pioneering studies of the decays of the top quark have already appeared in the literature [3,4]. Although these have been limited by small size of the data sample of the 1992-1996 Run I of the Tevatron collider, they have indicated nevertheless that it is feasible to measure subtle properties of the top quark predicted by the SM.
In this letter we report a measurement of the longitudinal component of the helicity of W bosons from t → W b decays in tt candidate events. The helicity of the W boson is reflected in the angular distribution of the products of its decay. The analysis is based on a method of extracting parameters that was particularly effective for the measurement of the mass of the top quark [5,6].
An important consequence of a heavy top quark is that, to good approximation, it decays as a free quark. Its expected lifetime is approximately 0.5×10 −24 s, and it therefore decays about an order of magnitude faster than the time needed to form bound states with other quarks [7]. Consequently, the spin information carried by top quarks is expected to be passed directly on to their decay products, so that production and decay of top quarks provides a probe of the underlying dynamics, with minimal impact from gluon radiation and binding effects of QCD [7,8].
The standard top quark decays through a V-A charged-current weak interaction.  To examine the nature of the tbW vertex, we use tt candidates observed at the DØ experiment [11] in pp collisions at a center-of-mass energy √ s=1.8 TeV. The data correspond to an integrated luminosity of 125 events/pb, and this analysis is based on the same lepton+jets sample that was used to extract the mass of the top quark in a previous DØ publication [12]. That is, the signal is based on one of the W bosons decaying into l+ν l , with l=e or µ, and the other W decaying to two quarks (qq ′ ); this leads to a final state characterized by one lepton and at least four jets (two from the fragmentation of the b quarks). Making use of information contained in these events and comparing each individual event with the differential cross section for tt production and decay, we extract the fraction F 0 of longitudinal W -boson production in the data, assuming no contribution from right-handed W bosons. In particular, we rely on a direct comparison of data to the matrix element for the production and decay of tt states [5,6]. This method offers the possibility of increased statistical precision by using the decay of both W bosons in these events, and is similar to that suggested for tt dilepton decay channels, and used in previous mass analyses of dilepton events [13]. A similar approach was also suggested for the measurement of the mass of the W boson at the LEP collider at CERN [14].
An initial set of selection criteria was used to improve the acceptance for lepton+jets from tt events relative to background [12]. These requirements were: E lepton T > 20 GeV, and |η lepton+ E T | < 2. (Where η and E T denote pseudorapidities and transverse energy of the lepton or jets, and E T the imbalance in transverse energy in the event.) A total of 91 events remained after imposing these requirements [12]. The present analysis uses events that contain only four reconstructed jets (see below).
The probability density for tt production and decay in the e+jets final state, for given value of F 0 , is defined as: where M tt is the leading-order (LO) matrix element, f (q 1 ) and f (q 2 ) are the CTEQ4M parton distribution functions for the incident quarks [15], Φ 6 is the phase-space factor for using herwig [16], and processed through the DØ detector-simulation package) were used to determine W jets (E p , E j ). For µ+jets final state, W jets is expanded to include the known muon momentum resolution and an integration over muon momentum is added to Eq. 2.
All processes that contribute to the observed final state must be included in the probability density. The final probability density is therefore written as: where c 1 and c 2 are the signal and background fractions, and x is the set of variables needed to specify the measured event. P tt and P bgd refer to the signal and background production and decay probabilities, respectively. W +jets production contributes about 80% to the background. The remainder of the background arises from multijet production where one jet mimics an electron. The vecbos [17] W +jets matrix element is used to calculate the background probability density, which is integrated over the energy of the four partons that lead to jets, and over the W -boson mass, and summed over the 24 jet permutations and neutrino solutions. With the selections that we have used, the character of the multijet background is quite similar to that of W +jets, and we have therefore used vecbos to also represent this component of the background, and have estimated a systematic uncertainty resulting from this assumption [6].(Similarly, we have ignored the ≈ 10% contribution to tt production from gg fusion, and used only the qq → tt in M tt .) Effects such as geometric acceptance, trigger efficiencies, event selection, etc., are taken into account through a multiplicative function A(x) that is independent of F 0 . This function relates the tt and W +jets probability densities to their respective measured probability densities P m (x; F 0 ), as follows: Because the method involves a comparison of data with a leading-order matrix element for the production and decay process, we have restricted the analysis to events with exactly four jets, reducing the data sample from 91 to 71 events. To increase the purity of signal, a selection is applied on the probability of an event corresponding to background (P bgd ). This selection was used in Ref. [5,6] to minimize a bias introduced by the presence of background, and it yields a sample of only 22 events. The selected cutoff value of probability density is based on MC studies carried out before applying the method to data, and, for a top quark mass of 175 GeV/c 2 , it retains 71% of the signal and 30% of the background [5,6].
The probabilities are inserted into a likelihood function for N observed events. The tt probability density contains contributions from both W 0 (F 0 ) and W − (F − ) helicities, and the ratio of F 0 /F − is allowed to vary. The best estimate of F 0 is obtained by maximizing the following likelihood function with respect to F 0 , subject to the constraint that F 0 must be physical, i.e., 0≤ F 0 ≤1, and F − + F 0 =1 [6]: where P m is the probability density for observing that event.
Inserting Eq. 4 into Eq. 5, the likelihood, becomes: The above integrals are calculated using MC methods. In this case the acceptance A(x)  Fig. 1) indicate that a response correction must be applied to the data. Studies using resolution-smeared partons (rather than jets) indicate that the reason the response correction differs from unity may have origin in gluon radiation, which is not included in our definition of probabilities. We apply the correction from Fig. 1 to the data, and Fig. 2a shows the result for the final sample of 22 events. For m t =175 GeV/c 2 , we find F 0 =0.60±0.30(stat), and obtain a signal background ratio that is compatible with the value of 0.54 found in the mass analysis [5].
When a probability density represents the data accurately, no systematic bias is expected in the extraction of any parameter through the maximum likelihood method. The current uncertainty in the top-quark mass is large enough to affect the value of F 0 . For sufficiently high statistics, the likelihood can be maximized as a function of the two variables (F 0 ,m t ), which can then correctly take account of any correlations between the two parameters and the fact that F 0 is bounded between 0 and 1. Given our limited statistics, the next best way to account for the uncertainty in m t is by projecting the two-dimensional likelihood onto the F 0 axis. In this way, the systematic uncertainty in F 0 from the uncertainty in m t can be obtained by integrating the probability over the mass, which we do from 165 to 190 GeV/c 2 , in steps of 2.5 GeV/c 2 , using no other prior knowledge of the mass. Figure 3 shows the 2-dimensional probability density as a function of F 0 and m t for the data, after applying the response correction from Fig. 1. Figure 2b shows the probability density from Fig. 3, after integration over m t . The probability in Fig. 2b is fitted to a 5 th -order polynomial as a function of F 0 . We use the most probable output value (at the maximum) to define the extracted F 0 . The uncertainty in F 0 (shaded region in Fig. 2b) is defined by the most narrow interval within which the integral of the normalized probability function contains 68.27% of the area, and reflects the statistical error convoluted with the uncertainty on the mass of the top quark: This is the only uncertainty we are able to treat in this manner. The other systematic uncertainties are quite small, and were calculated by varying their impact in the Monte Carlo or data, and added in quadrature (see Table I). The final result is F 0 = 0.56 ± 0.31(stat&m t ) ± 0.07(sys).
After combining the two errors in quadrature, the final result is F 0 =0.56±0.31, which is consistent with expectations of the SM, as well as with the result obtained by the CDF Collaboration of 0.91±0.39 [3].