Measurement of the top quark mass using the Matrix Element Analysis Technique in the lepton+jets channel with 680pb-1
 
Florencia Canelli, Jay Hauser, Brian Mohr, Rainer Wallny
UCLA


Mtop = 174.09 ± 2.54 (stat+JES) ± 1.35 (syst) GeV/c2
= 174.09 ± 2.87 GeV/c2
 

  • Abstract
  • Event selection
  • Method
  • Validation of the method
  • Systematic uncertainties
  • Results
  • Data and Monte Carlo comparisons
  • References

  • Winter 2006 Conference Note
  • CDF internal page (password protected)

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     Abstract
     
    We present a measurement of the mass of the top quark from ppbar collisions at 1.96 TeV from CDF Run II at the Fermilab Tevatron. We use events from ppbar to ttbar in the lepton plus jets channel and require at least one jet to be identified as coming from a b-quark. The jet energy scale (JES) systematic uncertainty is convoluted with the statistical error using an in-situ measurement of the hadronic W boson mass. A likelihood is calculated for each event using a leading-order ttbar and W+jets differential cross-section and parameterized parton showering. The final measured top quark mass and JES systematic is extracted from a joint likelihood of the product of the individual event likelihoods. From the 118 events observed with 680 pb-1 of data we extract a top quark mass of 174.09 ± 2.54 (stat+JES) ± 1.35 (syst) GeV/c2.


     
     
     Event Selection
     
    We use events from the lepton+jets decay channel of the ttbar system, where each of the top quarks decays into a W boson and b-quark, and one of the W bosons subsequently decays hadronically into two jets and the other leptonically into a lepton (electron or muon) and neutrino. We require a single, high-transverse energy, well-isolated lepton, large missing transverse energy from the neutrino and exactly four high-transverse energy and central jets (two from the b-quarks and two from the hadronic W). Of these jets, we require at least one to be identified as originating from a b-quark using a secondary vertex tag. The secondary vertex tag identifies tracks associated with the jet originating from a vertex displaced from the primary vertex. We further require the angle between missing transverse energy and leading jet, &Delta&phi, not be collinear for the lowest values of missing transverse energy passing our selection. This requirement removes a large fraction of the non-W background while retaining most of the signal.


    Details of event selection requirements.


    Fraction of events passing selection as a function of top quark mass and JES.

     
     
     Method
     
    We create a likelihood for each event by combining a signal probability with a background probability. This method has been developed by the D0 collaboration during Run I (see references). This likelihood is minimized for three variables: the top quark mass, JES and the fraction of events consistent with our signal hypothesis.



    The extracted top quark mass is obtained from a 2-dimensional fit in top quark mass and JES where Cs is minimized via MINUIT. The signal probability measures how well an event describes the ttbar to lepton plus jets hypothesis, and the background probability indicates how well an event describes the largest contributing background hypothesis, leptonically decaying W + extra jets. The background probability uses the different matrix-elements of W+4 jets of the Vecbos Monte Carlo routine. The signal probability only uses the leading order matrix-element of the qqbar-to-ttbar process. These probabilities are constructed by integrating over the appropriate parton-level differential cross-section, parton distribution functions and include the detector resolution effects.



    The angles of the measured jets and leptons, as well as the momentum of the leptons are considered to well known. The jet energy resolution is parametrized from the Monte Carlo. We call this resolution transfer function - the mapping between jet energies and parton energies (Wjet(x, y)). Signal and background probabilities are evaluated for all the possible permutations among jets and partons. Moreover, the signal probability also considers all the kinematically possible longitudinal momenta of the unmeasured neutrino and the different values of the pT of the ttbar system.

    We are sensitive to the JES through the hadronically decaying W boson. We constrain the invariant mass of 2 untagged jets to be the value of the world average of the W mass, 80.4 GeV/c2. We define JES to be the multiplicative scale factor applied to the energies of the two untagged jets inside the transfer function.



    We assume the JES determined for the W-jets also applies to b-jets and assign an additional systematic uncertainty for difference between this JES and the b-jets energy scale.


     
     
     Validation of the Method
     
    Many tests of the performance of the analysis are done using simulated (Monte Carlo) samples generated with different top quark masses. The extracted top quark mass against the top quark mass of the input events is found to be unbiased. Similar tests are performed for the JES output. In this case, we find a slope different than one. The origin of this bias is understood coming from an non-perfect parametrization of the transfer function. This bias does not affect our measurement of the top quark mass, but we correct for it so that we properly interpret the output of the JES. A mapping function to convert the output of Cs is used to interpret its value as the signal fraction. This mapping rises from all the assumptions made in the construction of the signal and background probability to describe our events. The evaluation of the errors on the extracted top quark mass is tested calculating pull distributions. We find that the RMS of the pull distribution to be 1.06 on average. Thus, the statistical plus JES systematic error is inflated by 6% after the top mass measurement is made.

    Output top quark mass of likelihood vs. top quark mass of input events. We see no bias or offset. In the left plot, we expect p0 = 0. In the right plot, we expect p0 = 172.5 and p1 = 1.

    Output JES of likelihood vs.JES of input events before mapping, we expect p0 = 1 and p1 = 1.
    Output JES of likelihood vs. top quark mass of input events after mapping (right). The three input JES values for the plot on right are 1.06, 1.00 and 0.94, and we expect the p0 values to reflect this.



    Comparison of partons from ttbar events (red), jets (black) and partons smeared with transfer functions (blue). We expect the smeared partons to match closely the jets. Plot on left is before application of JES mapping and plot on right is after. This demonstrates the JES mapping corrects problems with the transfer functions and we observe no bias as a function of &eta or pT.




    Output signal fraction vs. input signal fraction. We use this mapping as a consistency check with the measured cross-section from other analyses.



    Pull RMS of distribution of pseudo-experiment results in coverage tests as a function of pole mass in input events. We inflate our error by 6% to obtain proper coverage. The pseudo-experiments were constructed with 0.83 signal events and 118 total number of events.



    Statistical plus JES systematic expected error after inflation by 6%. These pseudo-experiments were done with a total of 118 events and 83% ttbar events. The red line indicates our measured error in the data after inflation.

     
     
     Systematic Uncertainties
     
    Listed below are systematic uncertainties estimated from various Monte Carlo samples. To first order, we fit the JES systematic in our likelihood, but we also apply a residual systematic to cover any higher order effects such as variations in the expected &eta or pT distribution. This higher order effect is estimated by fluctuating the jet energies up and down by one sigma as defined by the CDF Jet Energy and Resolution (JER) group. The generator systematic takes into account differences in the fragmentation and showering comparing the different output masses obtained with two different Monte Carlo models PYTHIA and HERWIG. Possible biases originating from differences in the amount of radiation between the data and the Monte Carlo are estimated using PYTHIA samples generated with different amount of initial and final state radiation. The uncertainty on the parton distribution functions (PDF) is evaluated as the sum in quadrature of the difference between MRST and CTEQ parton distribution functions, between MRST with &LambdaQCD = 228 MeV and &LambdaQCD = 300 MeV, and the variation in the 20 CTEQ eigenvectors. Systematic effects from the dependence of the b-tagging with pT are evaluated changing the dependence by one sigma. The background composition and modeling systematic error is the sum in quadrature of three effects: largest variation when fluctuating by 100% individual background sample contribution to total background, variation to adjusting background fraction in total sample by plus or minus 10%, and the largest variation due to changing the Q2 scale in W + jet production. To understand the effects of limited statistics in the background sample, we divide the smallest sample in half and compare the results using each half separately. This experiment is repeated several times dividing the sample in different ways and we take one-half the RMS of the distribution of the differences as a systematic error.



    Systematic uncertainties (GeV/c2)
    JES residual 0.42
    Initial state radiation 0.72
    Final state radiation 0.76
    Generator 0.19
    Background composition and modeling 0.21
    Parton distribution functions 0.12
    b-JES 0.60
    b-tagging 0.31
    Monte Carlo statistics 0.04
    Total 1.35




     
     
     Results
     
    The output likelihood is an unbinned simultaneous fit to three parameters: top quark mass, JES and Cs. In the extraction of the top quark mass we do not use any prior knowledge of the JES or Cs. The data used in this analysis corresponds to the period of Feb-02 to Sep-05 with a total integrated luminosity of 680 pb-1 where 118 events are observed. The plots below show the fits to the data and different divisions of the data depending on the lepton flavor and the amount of b-tagging in the sample. Although, the contours in &Delta ln L were not adjusted by 6% from the RMS of the pull distributions the reported top quark mass uncertainty are inflated. Only statistical uncertainties are reported on JES and Cs. The uncertainty on JES error is inflated by the RMS of the pull distribution (10%).


     

    Results from full dataset (118) events.
    Mtop = 174.09 ± 2.54 (stat+JES) ± 1.35 (syst) GeV/c2
    JES = 1.019 ± 0.021 (stat)
    Cs = 0.67 ± 0.06 (stat) (S/(S+B) = 0.83)


    Results from events with 1 b-tag. Results from events with 2 b-tags.
    Mtop = 169.52 ± 3.44 (stat+JES) GeV/c2 Mtop = 180.29 ± 3.97 (stat+JES) GeV/c2
    JES = 1.00 ± 0.03 (stat) JES = 1.05 ± 0.03 (stat)
    Cs = 0.62 ± 0.07 (stat) (S/(S+B) = 0.77) Cs = 0.78 ± 0.09 (stat) (S/(S+B) = 0.99)


    Results from events with electrons. Results from events with muons.
    Mtop = 172.55 ± 3.33 (stat+JES) GeV/c2 Mtop = 177.11 ± 3.91 (stat+JES) GeV/c2
    JES = 0.98 ± 0.02 (stat) JES = 1.08 ± 0.03 (stat)
    Cs = 0.64 ± 0.07 (stat) (S/(S+B) = 0.80) Cs = 0.72 ± 0.08 (stat) (S/(S+B) = 0.90)


     
     
     Data and Monte Carlo Comparisons
     
    In this section we compare between data and Monte Carlo various kinematical distributions and distributions related to our signal and background probability. When constructing Monte Carlo histograms, we add background according to our expected values to ttbar events (83%) and normalize the total Monte Carlo to the number of observed events in the data (118). The background Monte Carlo samples were generated from HERWIG. For ttbar events, we use PYTHIA Monte Carlo with a mass of 178 GeV/c2 in the kinematical comparisons and HERWIG Monte Carlo with a mass of 175 GeV/c2 in the comparisons of quantities related to the probabilities. The Monte Carlo in the kinematical comparisons is set to have the same JES as what we measure in data (JES = 1.02). A Kolmogorov-Smirnov (KS) probability is given for all of the kinematic distributions. The comparisons are done at the particle-jet level (jets energies were corrected by the calorimeter response).


    Probability Distributions

    Signal probability evaluated at Mtop = 174.5 GeV/c2 and JES = 1 (left). Background probability evaluated at JES = 1 (right).

    Most probable JES as determined from maximum of signal probability for various bins of top mass.

    Most probable top mass as determined from maximum of signal probability for various bins of JES.

    Kinematic Distributions




     
     
     References
     
    • D&empty Collaboration, V.M. Abazov, et, al., Nature 429 (2004); D&empty Collaboration, V.M. Abazov, et. al., Phys. Lett. B 617 (2005); F. Canelli, PhD thesis, University of Rochester (2003).
    • CDF Dynamical Likelihood Method Page