Measurement of Single Top Quark Production in L=2.7 fb-1
of CDF Run II Data Using a Matrix Element Technique
 
Peter Dong, Bernd Stelzer, Rainer Wallny (UCLA)
Florencia Canelli (FNAL)


σsingle top = 2.7+0.8-0.7pb, (Mtop = 175 GeV/c2)
 

  • Abstract
  • Event selection
  • Analysis Method
  • Validation of the method
  • Systematic uncertainties
  • Results
  • Single Top Signal Features
  • References

  • Winter 2008 Evidence Result


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    Abstract

    We present a search for electroweak single top quark production using 2.7 fb-1 of CDF II data collected between February 2002 and April 2008 at the Tevatron in proton-antiproton collisions at a center-of-mass energy of 1.96 TeV. The analysis employs a matrix-element technique which calculates event probability densities for signal and background hypotheses. We combine the probabilities to form a discriminant variable which is evaluated for signal and background Monte Carlo events. The resulting template distributions are fit to the data using a binned likelihood approach. We search for a combined single top s- and t-channel signal and measure a cross section of 2.7+0.8-0.7pb, assuming a top quark mass of 175 GeV/c2. The probability that the observed excess originated from a background fluctuation (p-value) is 9×10-6 (4.2σ) and the expected (median) p-value in pseudo-experiments is 8×10-7 (4.8σ).

    Event Selection

    This analysis uses events from leptonic decay of the W boson. We require a single, well isolated high-transverse-energy lepton, large missing transverse energy (from the neutrino), and exactly two or three high-transverse-energy jets. Of these jets, we require at least one to be identified as originating from a b-quark by secondary vertex tagging. The secondary vertex tag identifies tracks associated with the jet originating from a vertex displaced from the primary vertex. We further require the missing transverse energy and the jets not to be collinear for low values of missing transverse energy. This requirement removes a large fraction of the non-W background while retaining most of the signal.
    Our major backgrounds come from W + heavy flavor jets, Wbb-bar, Wcc-bar, and Wc+jet; mistags which are W + light quark/gluon events that are mistakenly tagged as b-jets due to detector resolution effects; Non-W, which are mostly multijet events in which a jet is mistakenly identified as a lepton and jets are mismeasured, providing a false missing transverse energy signature; and top pair production events in which one lepton or two jets are lost due to detector acceptance.



    Predicted event yield with 2.7 fb-1
    Process Two-jet events Three-jet events
    s-channel 49.3 ± 7.0 16.3 ± 2.3
    t-channel 74.3 ± 10.9 22.3 ± 3.2
    Single top 123.6 ± 17.9 38.6 ± 5.5
    W+bottom 549.1 ± 165.5 169.8 ± 51.3
    W+charm 453.5 ± 139.9 126.7 ± 39.0
    W+light 410.7 ± 51.0 125.5 ± 15.8
    tt-bar 173.5 ± 24.8 410.5 ± 58.4
    Diboson/Z+jets 105.6 ± 12.1 39.0 ± 4.6
    Non-W 75.6 ± 30.2 27.4 ± 11.0
    Total background 1768.0 ± 311.9 898.9 ± 108.2
    Total prediction 1891.6 ± 312.4 937.5 ± 108.3
    Observed 1874 902


    Jet multiplicity distribution for signal and background processes. We compare the predicted number of events in each W+jet bin to the number of events observed in data. Uncertainty on the data are statistical; the hatch marks represent systematic errors in the background estimate.

    Analysis Method

    This analysis is based on a Matrix-Element method in order to maximize the use of information in the events [2,3]. We calculate event probability densities under the signal and background hypotheses as follows. Given a set of measured variables of each event (the 4-vectors of the lepton and the two jets), we calculate the probability densities that these variables could result from a given underlying interaction (signal and background). The probability is constructed by integrating over the parton-level differential cross-section, which includes the matrix element for the process, the parton distribution functions, and the detector resolutions. This analysis calculates probabilities for four different underlying processes: s-channel, t-channel, Wbb-bar, tt-bar, Wcc-bar, Wc+jet and Wgg.

    Transfer functions are used to include detector effects. Lepton quantities and jet angles are considered to be well measured. However, jet energies are not, and their resolution is parameterized from Monte Carlo simulation to create a jet resolution transfer function. We integrate over the quark energies and over the z-momentum of the neutrino to create a final probability density.

    We use the probabilities to construct a discriminant variable for each event. The two single-top channels are combined to form a single signal probability. We also introduce extra non-kinematic information by using the output (b) of a neural network b-tagger which assigns a probability (0 < b < 1) for each b-tagged jet to originate from a b quark. The event probability discriminant variable (EPD) is then constructed as:


    We evaluate the event probability discriminant in the W+2jets sample and W+3jets sample. The corresponding templates (normalized to unit area) are shown below for W+2jet events (left) and W+3jets events (right).


    To quantify the single top content in the data, we perform a binned maximum likelihood fit to the data. We fit a linear combination of signal and background shapes of the event probability discriminant to the data. The background normalization are Gaussian constraint in the fit. The fit determines the most probable value of the single-top cross section. All sources of systematic uncertainty are included as nuisance parameters in the likelihood function. Sources of systematic uncertainties can affect the normalization and shape for a given process. Correlations between both are taken into account through a common nuisance parameter (δi). The likelihood function is reduced through a standard Bayesian marginalization technique.


    Here βj; is the template fit parameter for each process, indexed by j; δi; are the nuisance parameters for each systematic effect, with (relative) normalization uncertainty εji; and (relative) shape uncertainty κjik;, indexed by ji;k indexes the bins of the event probability discriminant. H(δi) denotes the Heavyside function to treat asymmetric uncertainties properly. The plot below shows the linearity scan for various assumed multiples (beta) of the SM single top quark cross-sections. Each point corresponds to 1500 pseudo-experiments.


    Validation of the Method

    Several tests have been performed for this analysis. We compare the distribution of many kinematic variables predicted by Monte Carlo simulation for signal and background to the data. In particular, we compare the distributions of the input variables to ensure the data matches the Monte Carlo prediction. We evaluate the event probability discriminant in the untagged W + 2 jets sample, a high-statistics control sample with very little single-top content (<0.5%). We also evaluate the event probability discriminant in the tagged dipleton + 2 jets sample (using only the most energetic lepton) and in tagged lepton + 4 jets sample (using only the two most energetic jets as input to the discriminant), which should agree well with tt-bar Monte Carlo. In all control samples, the data agrees well with the Monte Carlo prediction.


    Evaluation of the event probability discriminant in the high statistics taggable but untagged W + 2 jets control sample.




    The discriminants evaluated in the tagged lepton + 4 jets sample (2.7 fb-1), control sample which is mainly composed of tt-bar events.



    The input variables to the signal and background event probability calculations in the b-tagged W + 2 jet data sample.


    Systematic Uncertainties

    Each source of systematic uncertainty can posses a normalization uncertainty and a shape uncertainty. The normalization uncertainty includes changes to the event yield due to the systematic effect, and the shape uncertainty includes changes to the template histograms. Both of these effects are included in the likelihood function as shown above.

    Listed below are systematic uncertainties estimated from various Monte Carlo samples.

    • The jet energy scale systematic is obtained by changing the jet energy scale by 1 standard deviation (SD) and recalculating the event yield and the discriminant template histograms. This affects both normalization and shape.
    • We increase or decrease the amount of initial state radiation in the Monte Carlo to assign a systematic from this effect.
    • We increase or decrease the amount of final state radiation in the Monte Carlo to assign a systematic from this effect.
    • We vary the eigenvectors in the CTEQ parton distribution function tables to determine the uncertainty from this effect. We also include the effect of using different versions of CTEQ and of using MRST with different values of ΛQCD.
    • We include a systematic error to account for the modeling of the single top sample (MadEvent).
    • We include an uncertainty on event detection efficiency due to the scale factors that we apply to our Monte Carlo samples (mainly b-tagging and lepton ID scale factors)
    • We include a 6% uncertainty on our measured luminosity.
    • We include a systematic which accounts for systematic variation of the neural network b tagger output.
    • We use an alternative model for our mistag model and use the difference to the default model as a systematic uncertainty.
    • We use an alternate model to model our non-W background. We also assign a systematic effect to the flavor composition of the background, which is necessary to include for the neural-net b tagger to run.
    • We vary the factorization and renormalization scele (Q2) in the Monte Carlo samples that have been created with the ALPGEN Monte Carlo program.

    Systematic uncertainty Rate Shape
    Jet energy scale 0...16% X
    Initial state radiation 0...11% X
    Final state radiation 0...15% X
    Parton distribution functions 2...3% X
    Monte Carlo generator 1...5%
    Event detection efficiency 0...9%
    Luminosity 6.0%
    Neural-net b tagger N/A X
    Mistag model N/A X
    Non-W model N/A X
    Q2 scale in Alpgen MC N/A X
    Monte Carlo mismodeling N/A X
    W+bottom normalization 30%
    W+charm normalization 30%
    Mistag normalization 17...29%
    tt-bar normalization 23%
    Systematic uncertainties. The numbers here are given for the combined single-top channel. Jet energy scale and neural network b tagger systematics are applied to all processes (not shown here).


    Results

    1. Cross Section Measurement
      The result of the binned maximum likelihood fit is shown below. All sources of systematic uncertainties (normalization and shape) are included in the result.

      Results from full dataset (all W+2/3 jets candidate events):

      σsingle top =2.7+0.8-0.7pb




      Event probability discriminant distribution for signal and background processes. All templates are normalized to the prediction. The inset shows the most sensitive bins of the analysis (EPD>0.7).


    2. Vtb Measurement:
      We use the measured single top cross section to directly measure the CKM matrix element |Vtb| that describes the strength of the Wtb vertex. |Vtb| is directly proportional to (&sigmasingle top)2 so we can extract Vtb from the posterior probability density. This measurement assumes |Vtd|2 +|Vts|2 ≪ |Vtb|2. The theory uncertainties arrise from the cross-section dependence on the top quark mass, the Factorization and Renormalization scales, parton distribution functions and alpha_s [1].

      |Vtb| = 0.97 ± 0.13experiment ± 0.07theory



    3. Hypothesis Test:

      We have calculate the signal significance of this result using a standard likelihood ratio technique [4]. In this approach, pseudo-experiments are generated from background only events. The likelihood ratio is used as the test statistic. We then calculate the p-value which is the probability of the background only hypothesis (b) to fluctuate to the observed result in data. We estimate the expected p-value, by taking the median of the test hypothesis (signal + background) distribution as the 'observed' value (dashed red line).


    Single Top Signal Features

    We enrich the sample with signal events by making increasing cuts on our event probability discriminant (EPD) and look for characteristic changes in these sensitive variables. Although the uncertainties are large, there is a good agreement between data and the Monte Carlo simulation. For shape comparisons, the predicted Monte Carlos shapes are normalized to the data.


    Increasing cuts on the EPD for the product of the lepton charge and the pseudo-rapidity of the untagged jet, a variable known to be sensitive to t-channel (left) and the invariant mass of the W and the b-tagged jet, a quantity which is close to the top quark mass. The top row includes data with discriminant scores (EPD>0.8) and the bottom row includes with discriminant scores (EPD>0.95).

    Conclusions

    We have updated our search for single top using a Matrix-Element based analysis and applied it to 2.7 fb-1 of data taken by the CDF experiment. We include rate and shape systematic uncertainties in our analysis method. We measure a single top cross-section of σsingle top =2.7+0.8-0.7pb. We use a likelihood ratio method to calculate the signal significance. The observed p-value in 2.7 fb-1 of CDF data is 9×10-6 (4.2σ). The expected (median) p-value in pseudo-experiments is 8×10-7 (4.8σ). The cross section measurement is used to directly determine the CKM matrix element Vtb and we measure |Vtb| = 0.97±0.13experiment ± 0.07theory. The 95% confidence lower limit on |Vtb| is 0.71.

    References

    1. Understanding single-top-quark production, Z. Sullivan, Phys. Rev. D 70, 114012 (2004)
    2. B. Stelzer, PhD Thesis, University of Toronto, FERMILAB-THESIS-2005-79
    3. D∅ Collaboration, V.M. Abazov, et, al., Nature 429 (2004); D∅ Collaboration, V.M. Abazov, et. al., Phys. Lett. B 617 (2005); P. Dong, Ph.D. thesis, University of California, Los Angeles (2008); F. Canelli, Ph.D. thesis, University of Rochester (2003);
    4. T. Junk, Nucl. Instrum. Meth. A 434, 435 (1999), L. Read, J.Phys.G 28, 2693 (2002), Website