W Boson Helicity Fractions Measurement using the Matrix Element Analysis Technique

 
Florencia Canelli, Mousumi Datta, Ricardo Eusebi, Douglas Glenzinski (Fermilab)


f0 = 0.637 ± 0.084 (stat) ± 0.069 (syst)
 

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

  • Conference Note
    		•
     


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     Abstract
     
    We present a measurement of the fraction of longitudinally polarized W boson from top quark decay (f0) using ttbar events in the lepton+jets channel. The analysis is based on matrix element method where a likelihood function is calculated for each event from the leading order ttbar and W+jets differential cross sections and parameterized parton showering. In the likelihood function the fraction of right-handed polarized W boson from top decay f+ is kept fixed to the Standard Model predicted value (f+~0). Using 468 events observed in 1.9 fb-1 data collected at the CDF II detector we find f0 = 0.637 ± 0.084 (stat) ± 0.069 (syst), for top-quark mass of 175 GeV/c2.
     
     
     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 the beyond the SM 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, 4] however all the measurements were limited by small statistics of the sample. We perform a measurement of f0 using a matrix element technique, which provides ~20% better statistical sensitivity compared to existing CDF analyses on the same dataset.

    For the current measurement the value f+ has been fixed to zero in the likelihood. The analysis can be extended to simultaneously measure all three W helicity fractions. With the increasing data sample at the Tevatron the W helicity fractions will be measured with considerable precision.

     
     
     Method
     

    The Matrix Element method was first used by D0 Collaboration during Run I [4,5]. The likelihood for each event is created based on the leading order matrix elements for signal ttbar and 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 ) = Cs Pttbar,i ( X; f0 ) + ( 1 - Cs ) PW+jets, i (X)

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



    Here Pttbar,i ( X; f0 ) and PW+jets, i (X) are the probabilities of ttbar and W+jets production for an event, respectively; and Cs is the relative ttbar fraction.

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

     
     
     Event Selection
     

    We use events with at least four high jets with large transverse energy, 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. Event selection and background estimation procedure can be found in [6]. The expected sample composition is listed in Table below, where ttbar event yield is estimated using the CDF measured top pair production cross section in the lepton+jets decay channel [6].

    Number of expected and observed events: CDF Run II Preliminary (1.9 fb-1)

    Sample Events with 4 jets Events with 5 or more jets
    W+Light 13.77 ± 3.59 2.86 ± 1.09
    Non-W 13.12 ± 11.49 4.66 ± 4.73
    W+Bottom 13.65 ± 5.69 3.03 ± 1.36
    W+Charm 10.81 ± 4.53 2.33 ± 1.05
    Electro-weak 8.97 ± 5.26 2.06 ± 1.47
    Total Background 60.33 ± 16.40 14.94 ± 5.56
    Signal ttbar (8.2 pb) 311.54 ± 42.12 105.80 ± 14.64
    Total Expected 371.87 ± 46.13 120.74 ± 15.66
    Data (Observed) 356 112

    The signal acceptance varies based on the W helicity fractions. The average signal acceptance as a function of f0 is determined from Monte Carlo (MC) events and is parameterized using an analytical function:

     
     
     Calibration of the Method
     

    The MC ttbar events and various background events are used for determining the response and sensitivity of the measurement. To determine the response curve we look at the output f0 as a function of the input f0 value. The output f0 is determined using ensembles of signal and background pseudo experiments constructed using the expected sample composition. The results are shown in the following plot:

    A linear fit to these points, which has a slope less than unity, is used to correct the obtained f0 value from the -lnL(X;f0) curve. That the slope of the response curve is less than unity is due to the events which are not completely described by the signal and background matrix elements. For example, the signal probability is based on leading order ttbar matrix element, which does not include effects like initial- and final state radiation or the four-jets not corresponding to the four-quarks from ttbar decay.

    We use the pseudo-experiments described above to determine whether or not the width of the -lnL(X;f0) curve provides an accurate estimate of the statistical uncertainty by studying the pull width as a function of f0. The average pull width is found to be 0.93 independent of f0. The statistical uncertainty will be scaled by this average pull width.

     
     
     Systematic Uncerttainties
     

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

    Systematic Uncertainties: CDF Run II Preliminary (1.9 fb-1)

    Sources Uncertainty on f0
    Generator 0.050
    Initial state radiation 0.026
    Final state radiation 0.020
    Parton distribution functions 0.023
    Jet energy scale 0.019
    b-tagging 0.002
    Background composition and modeling 0.009
    Method 0.012
    Total 0.069
     
     
     Results
     

    We apply the method to the 468 events selected in 1.9 fb-1 CDF data. The obtained f0 from the negative log likelihood (NLL) curve for the data events is corrected by the response curve. The NLL value as a function of corrected f0 is shown in Figure below:

    Using the minimum of the NLL curve and after using all the corrections we determine:

    f0 = 0.637 ± 0.084 (stat.)± 0.069 (syst.) for mt=175 GeV/c2 and f+=0.

    We check the expected statistical uncertainty and pull distributions from pseudo experiments for ttbar MC with input f0 same as the measured f0 value from data, as shown below. The blue line in the upper plot indicates the statistical uncertainty obtained from data.

     
     
     Data and Monte Carlo Comparisons
     

     
     
     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, A. Abulencia et al., Measurement of W Boson Helicity Fractions in Top Quark Decays Using cosThetaStar, CDF Public Note 8971 (2007); CDF Collaboration, A. Abulencia et al., Measurement of the W Helicity in Fully Reconstructed Top Anti-Top Events using 1.7 fb-1, CDF Public Note 8938 (2007); 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] D0 Collaboration, V.M. Abazov et al., Helicity of the W boson in lepton + jets t anti-t events, Phys. Lett. B617, 1 (2005); M. F. Canelli, Helicity of the W Boson in Single-Lepton ttbar Events, Ph.D. thesis (fermilab-thesis-2003-22), University of Rochester (2003).
      [5] D0 Collaboration, V.M. Abazov et al., A Precision Measurement of the Mass of the Top Quark, Nature 429, 638 (2004).
      [6] CDF Collaboration, A. Abulencia et al., Measurement of the Top Pair Production Cross Section in the Lepton+Jets Decay Channel, CDF Public Note 8795 (2007).