Top Quark Properties Measurements in the Hadronic Tau + Jets Channel in 2.2 fb-1 of data

Authors

Daryl Hare
Ian Laflotte
(Rutgers)

A complete description of the analysis method can be found here.

Abstract
We present a measurement of the ttbar cross section and the first measurement of the top quark mass in the hadronic tau + jets channel using the CDF detector at the Fermilab Tevatron. The ttbar cross section is derived from a Poisson likelihood function based on the number of observed and predicted events. The top quark mass is extracted using an unbinned maximum likelihood method with the probability density function evaluated for each event using leading-order ttbar and W + jets matrix elements and a set of parameterized jet-to-parton mapping functions. Using a total integrated luminosity of 2.2 fb-1, we measure the ppbar to ttbar cross section to be 8.8 ± 4.0 pb, and the top quark mass to be 172.7 ± 10.0 GeV.

Event Selection

We use events from the hadronic tau + 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 tau and neutrino. The tau identification selects taus decaying to hadrons. These decays look like well isolated narrow cone jets with 1 or 3 charged hadrons. We require a single, high transverse energy, well-isolated tau, large missing transverse energy from the neutrino and exactly four high transverse energy 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.

Event Selection Criteria
lepton Tau with Et > 25 GeV
jets Et > 20 GeV, |&eta| < 2.0
missing Et missing Et > 20 GeV
b-tag >= 1 jet coming from secondary vertex

The dominant background for this analysis is QCD mulitjet events when one of the jets fakes the signature of a tau lepton. To further reduce the QCD multijets background, we developed a neural network (NN) to distinguish between true ttbar to tau + jets events and QCD multijets events. First, we create a sample of QCD multijets events by applying the selection cuts to the data. However, we reverse one of the tau isolation cuts so that we identity jets faking taus rather than actual tau leptons. The NN is trained to distinguish between these selected QCD multijets events and ttbar events which are generated with the Pythia Monte Carlo (MC) generator. We use 8 variables to train the NN: missing ET, lead jet ET, sum ET of the jets and tau lepton, sum ET of the two lowest ET jets and the tau lepton, sum ET of the two highest ET jets, transverse momentum of the W which decays to a tau lepton, average eta-moment of all jets not identified as coming from a b quark, and the lowest ratio of dijet mass to trijet mass for any possible triplet of jets. The distributions for each of these 8 variables can be seen here. After training the NN, we find it provides good separation between QCD multijets and ttbar events, and we chose to remove all events which return a NN output below 0.85.

Output distribution from neural network for ttbar (signal) and QCD multijets (background). The cut is chosen at 0.85.(EPS)

With this neural network cut applied on top of the selection cuts above, we estimate the following number of expected signal and background events:

Estimated number of signal and background events after applying all selection criteria.(EPS)

A full set of validtion plots for measured variables in selected events with these contributions can be found
here.

Finally, we plot the acceptance with all selection criteria as a function of the top quark mass. This function is used to normalize the probability function for the top quark mass measurement.

Event Display

Here is an example of what a tau + jets event looks like. The tau is the single well isolated track in the upper right quadrant of the cross section view.
Et (GeV) Eta Phi
tau 65.6 0.8250.6
b-tagged jet 53.6 -0.69295.6
jet 59.6 1.13146.8
jet 47.6 1.70 37.3
jet 36.8 1.63 218.5

• Cross Section

As the background estimate (as described in detail in the note) is dependent on the top pair production cross section, we cannot simply measure the cross section as:

where Ndata and Nbkgd are the number of events observed in the data and the number of estimated background events, respectively. The geometric and kinematic acceptance of the ttbar events is A, ε is the product of all the event selection data/MC scale factors (trigger, lepton identification, and b-tagging), and L is the total luminosity.

Instead, we construct a Poisson likelihood function based on the number of events in the data and the background prediction.

where D is the denominator of the previous equation (A times ε times L) and Nbttbar) is the number of events from the background prediction for a given top pair production cross section σttbar. We calculate this likelihood for several different input top pair production cross sections ranging from 5 to 15 pb. We then fit a second order polynomial around the minimum of this function. The minimum value is taken to be the measured cross section, and the uncertainty is measured as the range of cross sections which return a likelihood result within 0.5 units of the minimum likelihood value.

• Mass

Our previous top quark mass result with 3.2 fb-1 selecting electron or muon + jet events can be found here.

The top quark mass measurement is derived from a likelihood function based on signal and background probabilities for each event. The signal probability is based on a ttbar leading order matrix element calculation and is calculated over 31 input mass values from 145 to 205 GeV for each event. The background probability for each event is calculated with a W + jets matrix element from the Vecbos Monte Carlo generator. Since there is no top quark mass dependence in the background probability, it is calculated only once for each event. To improve the statistical uncertainty on the top mass measurement, we add a Gaussian constraint on the background fraction (1-cs) to the likelihood function. The background fraction is constrained to be 0.498 ± 0.106 from the estimated number of signal and background events in the table above. The likelihood function is calculated as:

where P is:

where Ps and Pb represent properly normalized signal and background probability terms, mt is the top mass, cs is the fractional contribution to the signal probability of each event, Abkgd is a relative normalization term which account for differences between the signal and background probability calculation, and the vector x represents all detector measured quantities. cS ensures that as long as Ps and Pb are properly normalized, then their sum P will also be properly normalized.
The signal and background probability are both calculated by integrating over the differential cross section for the appropriate process:

where dσ is the differential cross section, f is the probability distribution function (pdf) for a quark with momentum \tilde{q}, the vector x refers to detector reconstructed quantities, the vector y refers to parton level quantities, and W(x,y) is the transfer function used to map x to y. After calculating the probabilities for each event, we evaluate a likelihood function for each of the 31 input top quark masses and fit the result with a second order polynomial to derive the central value and statistical uncertainty.

For each event, we evaluate the signal probability on a grid of 31 mass points (for signal MC with known mass we use a smaller grid of 21 mass points to reduce computation time). The grid has a step size of 2 GeV in mt. The full grid covers mt from 145 to 205 GeV. The natural log of the signal probability for a given grid point and of the background probability for all events can be seen below.

ln pbkg for all events.(EPS)

To obtain our result, we fit our likelihood function over a region centered at the minimum of the natural log of our likelihood function. The region first spans 8 GeV in mass on both sides of the minimum point. We then continue to expand the region in 2 GeV steps on both sides until the goodness of fit (represented by the chi2 of the fit worsens.

After calibrating our method on signal monte carlo, we obtain the following linearity plots for the top mass residual and pull width.

Top mass pull width vs input top mass(EPS)

We also check the expected uncertainty as a function of mass. Based on the fit of the plot below, we expect a statistical uncertainty of 6.0 GeV for our expected mass value of 172.5 GeV.