Measurement of the W-Boson Helicity Fractions in t&rarr Wb Decays using the Matrix Element Analysis Technique in 2.7 pb-1 of CDF Data
 
Florencia Canelli1, Mousumi Datta2, Ricardo Eusebi2, Douglas Glenzinski2
1) Fermilab and U.Chicago, 2) Fermilab


f0 =   0.88 ± 0.11 (stat) ± 0.06 (syst)
f+ = -0.15 ± 0.07 (stat) ± 0.06 (syst)
&rho0+ = -0.59.
 

  • Abstract
  • Motivation
  • Method
  • Event Selection
  • Calibration of the Method
  • Systematic Uncertainties
  • Results
  • Data and Monte Carlo comparisons
  • Reference

  • Conference Note
    		•
     


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     Abstract
     
    We present several measurements of the fraction of longitudinally (f0) and right-handed (f+) polarized W bosons from top-quark decay using ttbar events in the lepton+jets final state. The analysis is based on a matrix element method where a likelihood function is calculated for each event from the leading order ttbar and W+jets differential cross-sections with parameterized parton showering. Using 2.7 fb-1 of CDF RunII data and assuming a top-quark mass of 175 GeV/c2 three measurements are performed. A simultaneous determination of (f0,f+) yields the model-independent results
    f0 =   0.88 ± 0.11 (stat) ± 0.06 (syst)
    f+ = -0.15 ± 0.07 (stat) ± 0.06 (syst)
    with a linear correlation coefficient of &rho0+=0.XX. A determination of f0 constraining f+ to its SM value of 0 yields f0 =   0.70 ± 0.07 (stat) ± 0.04 (syst), while a determination of f+ constraining f0 to its SM value of 0.7 yields f+ = -0.01 ± 0.02 (stat) ± 0.05 (syst). All these results are consistent with Standard Model expectations.
     
     
     Motivation
     

    The top quark was discovered in 1995 by the CDF and D0 experiments at the Fermilab Tevatron during the Run I operation. The mass of the top quark mt is much larger than the masses of all the other quarks and is in the same order of magnitude as the masses of W and Z bosons. Due to the large mass, unlike any other quark, the top quark in the Standard Model (SM) decays before hadronization; and provides us with the unique opportunity to study the properties of a ``bare'' quark.

    Top quark decays to a W boson and a b quark most of the time. In the SM the coupling at the Wtb vertex is purely left-handed and can be used to test the V-A structure of weak interaction. Different helicity states of the W bosons: longitudinal, right-handed and left-handed, are reflected in the angular distribution of the decay products. The differential decay rate for unpolarized top quark is given by:

    (1/&Gamma) (d&Gamma/dcos&theta*) = f- (3/8) (1- cos&theta*)2 + f0 (3/4) ( 1 - cos&theta*2 ) + f+ (3/8) ( 1 + cos&theta* )2 ,


    where cos&theta* is the angle between the momentum of the charged lepton (or down type quark) in the W rest frame and the momentum of the W boson in the top quark rest frame; f-, f0, and f+ are the fractions for left-handed, longitudinal, and right-haded helicity states, respectively, and (f-+f0+f+)=1 . The three terms in the equation above corresponds to three different helicity states. At the tree level, f0 = 0.703, f- = 0.297 and f+ = 3.4 × 10-4, for mt = 175 GeV/c2, MW = 80.4 GeV/c2 and mb = 4.7 GeV/c2 [1]. In many new physics scenarios deviations from the SM expectation are possible due to the presence of anomalous couplings [1].

    The helicity of the W boson from top decay has been measured by the CDF and D0 collaborations [2, 3] however all the measurements were limited by small sample statistics. We perform measurements of f0 and f+ using a matrix element technique, which provides ~20% better statistical sensitivity compared to existing CDF analyses on the same dataset.

    A previous version of this analysis fixed f+ to zero in the likelihood. The present analysis has extended the matrix element technique to simultaneously measure all three W helicity fractions in a model independent manner (with the constraint that their sum equals one). With the increasing data sample at the Tevatron these W helicity fractions should be measured with considerable precision.

     
     
     Method
     

    The Matrix Element method employed here is adapted from [4] to include the dependence on the W-boson helicity fractions. The likelihood for each event is created based on the leading order matrix element expressions for signal (ttbar) and for the dominant background (W+jets). The likelihood L for a sample of N events is reconstructed by taking the product of the per event likelihood. Probability density of observing an event Pevt,i is expressed in terms of a set of event variables X and measurable quantity f0:

    Pevt,i ( X; Cs f0 f+ ) = Cs Pttbar,i ( X; f0 f+ ) + ( 1 - Cs ) PW+jets, i (X)

    L( X; Cs f0 f+ ) = &prodi=1Nevents Pevt,i ( X; Cs f0 f+)



    Here Pttbar,i ( X; f0 f+) and PW+jets, i (X) are the probabilities of ttbar and W+jets production for an event, respectively; and Cs is the signal purity of the selected event sample.

    By minimizing Cs via MINUIT at each (f0, f+) an optimized curve of -lnL(X;f0 f+) is obtained. The minimum of the parameterized -lnL curve provides the measured value and changes of 0.5 units with respect of the curve's minimum are assigned as the statistical uncertainty on the measurement.

     
     
     Event Selection
     

    We use events with at least four jets with large transverse energy (ET > 20 GeV, | &eta |<2), one isolated electron (muon) candidate with large transverse energy (momentum), large missing transverse energy. At least one of the jets is required to satisfy tight secondary vertex b-tag selection. Relative to the previous version of this analysis we have increased the signal acceptance by about 40% by including events collected on additional trigger paths. The event selection and background estimation procedure can be found in [5]. The expected sample composition given in the Table below assumes a ttbar production cross section of 6.7 pb.

    Number of expected and observed events: CDF Run II Preliminary (2.7 fb-1)

    Process Central Forward met+Jets
    e, &mu e &mu
    ttbar (6.7 pb) 478 ± 66 58 ± 8 134 ± 19
    W+hf 71 ± 22 13 ± 9 19 ± 6
    W+lf 23 ± 6 5 ± 7 6 ± 2
    EWK 17 ± 10 3 ± 1 5 ± 3
    QCD 28 ± 22 46 ± 37 1 ± 1
    Total expected 616 ± 74 125 ± 40 165 ± 20
    Observed 650 136 178

    The signal acceptance varies as a function of the W helicity fractions. The average signal acceptance as a function of (f0 f+) is determined from Monte Carlo (MC) events and is parameterized using a second order polynomial:

     
     
     Calibration of the Method
     

    Pseudo-experiments are used to determine the response and sensitivity of the measurements. They are constructed using MC ttbar events while the background is modelled with a mix of data and MC events. The sample composition is taken from the Table above. Individual contributions are allowed to Poisson fluctuatefrom pseudo-experiment to pseudo-experiment. For the ttbar contribution we use a range of samples each generated with different values of (f0 f+).

    To determine the response curve we look at the mean fitted f0(+) as a function of the input f0(+) value. The mean fitted f0(+) is determined using ensembles of pseudo-experiments while the input f0(+) corresponds to the helicity fractions used to generate the corresponding ttbar MC sample. For the model independent fit we have a family of f0(+) response curves in slices of input f+(0). Linear fits to these curves are used to derive the final calibration functions which include small (f0 f+) cross-dependencies for the model-independent fit.

    We also use these ensembles of pseudo-experiments to study the width of the pull distribution as a function of the input (f0 f+). We find that the pull widths are largely independent of the input helicity fractions except near the physical boundaries of 1 and 0 where they can get as large as 1.3.

    After all corrections the expected statistical uncertainty for the model independent fit is ± 0.12 and ± 0.07 for f0 and f+, respectively. When constraining f+ to its SM value the expected statistical uncertainty on the fitted f0 is 0.06 after all corrections. When constraining f0 to its SM value the expected statistical uncertainty on the fitted f+ is 0.03 after all corrections.

    Calibration curves of measured f0 versus input f0 in slices of input f+ for the model independent fit.

    Calibration curves of measured f+ versus input f+ in slices of input f0 for the model independent fit.

     
     
     Systematic Uncertainties
     

    Various sources of systematic uncertainties effecting the measurement are summarized in following Table:

    Systematic Uncertainties: CDF Run II Preliminary (2.7 fb-1)

    Sources &Delta f0(f+ fixed) &Delta f+(f0 fixed) &Delta f0(model indep) &Delta f+(model indep)
    Parton Shower ± 0.012 ± 0.008 ± 0.031 ± 0.017
    ISR / FSR ± 0.020 ± 0.018 ± 0.020 ± 0.021
    PDF ± 0.024 ± 0.013 ± 0.009 ± 0.016
    Jet Energy Scale ± 0.018 ± 0.017 ± 0.004 ± 0.012
    Background ± 0.009 ± 0.038 ± 0.042 ± 0.039
    Method ± 0.010 ± 0.005 ± 0.024 ± 0.024
    Total Systematic ± 0.041 ± 0.048 ± 0.062 ± 0.057
     
     
     Results
     

    For the model-independent fit the events from forward electron trigger are exluded as this significantly reduces the bakground modeling uncertainty. We apply the method to the 828 events selected in 2.7 fb-1 CDF data using central electron and muon, and MET+Jets triggers. For the model dependent fit we use 964 events collected by central electron and muon, forward electron, and MET+Jets triggers. The fitted helicity fractions from the -lnL contour/curve for the data events is corrected by the calibration functions discussed above. The -lnL value as a function of the helicity fractions is shown in the Figures below for the three separate fits.

    Using the minimum of the -lnL curves and after all the corrections we determine from the model independent fit

    f0 =   0.88 ± 0.11 (stat) ± 0.06 (syst)
    f+ = -0.15 ± 0.07 (stat) ± 0.06 (syst)

    with a linear correlation coefficient of &rho0+=-0.59.

    The resulting -lnL contour for the model-independent fit.

    As the measurement is close to the physical boundary, to ensure coverage we have applied the Feldman-Cousins method to obtain the confidence level (CL) intervals as shown below.

    Contours in the (f0,f+) plane indicating 68% and 90% CL intervals determined using Feldman Cousins (FC) method. The FC method obtained from the likelihood does not eliminate the residual bias. Therefore the contours are not centered at the measured (f0, f+) value obtained after calibration. However the contours will still provide proper coverage.

    A determination of f0 constraining f+ to its SM value of 0 yields f0 =   0.70 ± 0.07 (stat) ± 0.04 (syst). Constraining f0 to its SM value of 0.7 we measure f+ = -0.01 ± 0.02 (stat) ± 0.05 (syst). and f+ < 0.12 at 95% CL.

    The resulting -lnL curves for the fit to f0 with f+ fixed to 0.0 (left), and for the fit to f+ with f0 fixed to 0.7 (right).

    All these results are consistent with Standard Model expectations.

     
     
     Data and Monte Carlo Comparisons
     

    We made many comparisons between the data and Monte Carlo predictions for events in the signal region. Some of these comparisons are shown in the plots below. In general the MC describes the data well.

    CEM, CMUP, CMX leptons

    Extended Muons

    PHX electrons

     
     
     References
     
      [1] J. Aguilar-Saavedra et al., Probing Anomalous Wtb Couplings in Top Pair Decays, Eur. Phys. J. C50, 519 (2007); J. Cao et al., Supersymmetric Effects in Top Quark Decay into Polarized W Boson, Phys. Rev. D68, 054019 (2003); F. del Aguila et al., Precise Determination of the Wtb Couplings at LHC, Phys. Rev. D67, 014009 (2003); G. Kane et al., Using the Top Quark for Testing Standard Model Polarization and CP Predictions, Phys. Rev. D45, 124 (1992).
      [2] CDF Collaboration, T. Aaltonen et al., Measurement of W-Boson Helicity Fractions in Top-Quark Decays Using cos theta*, arXiv:0811.0344v1 [hep-ex]; CDF Collaboration, A. Abulencia et al., Search for V+A current in top quark decay in p anti-p collisions at s**(1/2) = 1.96-TeV., Phys. Rev. Lett. 98, 072001 (2007); CDF Collaboration, A. Abulencia et al., Measurement of the helicity fractions of W bosons from top quark decays using fully reconstructed t anti-t events with CDF II, Phys. Rev. D 75, 052001 (2007); CDF Collaboration, A. Abulencia et al., Measurement of the helicity of W bosons in top-quark decays, Phys. Rev. D 73, 111103 (2006); CDF Collaboration, D. Acosta et al., Measurement of the W boson polarization in top decay at CDF at s**(1/2) = 1.8-TeV, Phys. Rev. D 71, 031101 (2005).
      [3] D0 Collaboration, V.M. Abazov et al., Model-independent Measurement of the W Boson Helicity in Top Quark Decays, arXiv:0711.0032v1[hep-ex] (2007); D0 Collaboration, V.M. Abazov et al., Measurement of the W boson helicity in top quark decay at D0, Phys. Rev. D 75, 031102 (2007).
      [4] CDF Collaboration, T. Aaltonen et al., Precise Measurement of the top quark mass in the lepton+jets topology at CDF II, Phys.Rev.Lett. 99 182002 (2007); CDF Collaboration, A. Abulencia et al., Measurement of the Top Quark Mass using the Matrix Element Analysis Technique in the Lepton+Jets Channel with In-situ W&rarr jj Calibration, CDF Public Note 8375 (2006).
      [5] CDF Collaboration, T. Aaltonen et al., Measurement of the Top Pair Production Cross Section in the Lepton Plus Jets Decay Channel with 2.7 fb-1, CDF Public Note 9462 (2008).