Measurement of the $t\overline{t}$ cross section in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using dilepton events with a lepton plus track selection

This paper reports a measurement of the cross section for the pair production of top quarks in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ at the Fermilab Tevatron. The data were collected from the CDF run II detector in a set of runs with a total integrated luminosity of $1.1{\mathrm{fb}}^{-1}$. The cross section is measured in the dilepton channel, the subset of $t\overline{t}$ events in which both top quarks decay through $t\to Wb\to \ell \nu b$, where $\ell =e$, $\mu$, or $\tau$. The lepton pair is reconstructed as one identified electron or muon and one isolated track. The use of an isolated track to identify the second lepton increases the $t\overline{t}$ acceptance, particularly for the case in which one $W$ decays as $W\to \tau \nu$. The purity of the sample may be further improved at the cost of a reduction in the number of signal events, by requiring an identified $b$ jet. We present the results of measurements performed with and without the request of an identified $b$ jet. The former is the first published CDF result for which a $b$-jet requirement is added to the dilepton selection. In the CDF data there are 129 pretag $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ candidate events, of which 69 are tagged. With the tagging information, the sample is divided into tagged and untagged subsamples, and a combined cross section is calculated by maximizing a likelihood. The result is ${\sigma }_{t\overline{t}}=9.6\pm 1.2(\mathrm{stat}{)}_{-0.5}^{+0.6}(\mathrm{sys})\pm 0.6(\mathrm{lum})\mathrm{pb}$, assuming a branching ratio of $\mathrm{BR}(W\to \ell \nu )=10.8\%$ and a top mass of $m_t=175\mathrm{GeV}/c^2$.

Figure 1

Leading order diagrams for top quark pair production at the Tevatron.

Figure 2

Corrected missing transverse energy from several $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ backgrounds, compared to the $t\overline{t}$ signal. The distribution for $WW$ events is similar to the $t\overline{t}$ distribution but slightly softer, and is omitted for legibility. Candidate events are required to have a fully reconstructed lepton and track and two or more jets, but no other event selection is applied. For the cross section measurements, we require events to have ${\mathrm{E̸}}_T>25\mathrm{GeV}$. Distributions taken from events generated with pythia and normalized to have unit area.

Figure 3

Drawing showing reconstructed secondary vertices, illustrating example cases where (a) $L_{xy}<0$ and (b) $L_{xy}>0$.

Figure 4

Leading diagrams for $W$ and $\gamma$ production with one associated jet at the Tevatron. Diagrams (a) and (b) are for $\gamma +1$ jet production, and (c) and (d) are for $W+1$ jet production. Diagrams (a) and (c) dominate because of the relative strength of the gluon PDF at low $x$.

Figure 5

The fraction of jets matched to a quark in simulated photon (filled circles), $W$ (filled squares), and multijet (open squares) events, as a function of jet $E_T$. The fraction is shown for events with any number of jets (a), and then separately for events with one (b), two (c), and at least three (d) jets.

Figure 6

Track lepton fake rates in simulation as a function of denominator jet $E_T$. (a) Fake rate for all jets in simulated $\gamma +\mathrm{\text{jets}}$, $W+\mathrm{\text{jets}}$, and multijet events. The fake rate in multijet events is lower than the fake rate in $W+\mathrm{\text{jets}}$ events, and both are lower than that in $\gamma +\mathrm{\text{jets}}$ events. Note that this $\gamma +\mathrm{\text{jets}}$ sample does not have the $E_{\gamma }>80\mathrm{GeV}$ requirement applied. (b) Fake rate for jets matched to quarks (“quark jets”) compared to the fake rate for jets matched to gluons (“gluon jets”), showing the disagreement between them. Fake rates are taken from the simulated multijet sample. (c) Fake rates for quark jets in the three samples. The agreement is better than that observed in (a). (d) The same, but for jets matched to gluons.

Figure 7

Track lepton fake rates as a function of $E_T$ (a) and $|\eta |$ (b) of the faking jet. The fake rate is the probability for a jet to pass the track lepton identification requirements, including the track isolation. The fake rate is measured in jets from $\mathrm{\text{photon}}+\mathrm{\text{jets}}$ data, and includes $Z+1$ jet events in the one-jet fake rate. The uncertainty is statistical only. See Sec. 7a3 for details.

Figure 8

Predicted and observed numbers of fake track leptons in simulated $W+\mathrm{\text{jets}}$ events, as a function of jet $E_T$. The comparison is made for events with zero (a), one (b), and at least two (c) jets, in addition to the one that is reconstructed as an isolated track. One prediction, shown as solid squares, is made using the fake rate derived from simulated $\gamma +\mathrm{\text{jets}}$ and $Z+\mathrm{\text{jets}}$ events, exactly as the fake rate is constructed from the observed data. The other, shown as open circles, is made using a fake rate derived from simulated QCD multijet events. Uncertainties on the predictions are statistical only.

Figure 9

Predicted and observed numbers of isolated tracks observed in CDF $Z+\mathrm{\text{jets}}$ data, as a function of jet $E_T$. The comparison is made for events with zero (a), one (b), and at least two (c) jets, in addition to the one that is reconstructed as an isolated track. The fake rate used is derived from $\gamma +\mathrm{\text{jets}}$ data, and the uncertainty on it is statistical only.

Figure 10

Fully reconstructed lepton fake rates as a function of $E_T$ (a) and $|\eta |$ (b) of the jet in the denominator. The fake rate is the probability for a jet to pass the lepton identification requirements and is measured in jets from $\mathrm{\text{photon}}+\mathrm{\text{jets}}$ data. The shown uncertainty is statistical only.

Figure 11

Pull distribution from pseudoexperiments run with the likelihood used to find the combined cross section.

Figure 12

Number of predicted pretag $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ events compared to the number observed in the CDF data. The cross-hatched areas show the combined statistical and systematic uncertainties (1 standard deviation) on the prediction.

Figure 13

Missing transverse energy of pretag $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ candidate events with two or more jets, compared to the predicted distribution. The highest bin shown includes all events which would be past the right edge of the plot.

Figure 14

Summed transverse energy ($H_T$) of pretag $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ candidate events with two or more jets, compared to the predicted distribution. The sum includes the fully reconstructed lepton, the track lepton, the ${\mathrm{E̸}}_T$, and all jets passing the analysis selection. The highest bin shown includes all events which would be past the right edge of the plot.

Figure 15

Distribution of lepton transverse momenta in pretag $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ candidate events with two or more jets, compared to the predicted distribution. There are two entries for each event: one each for the fully reconstructed lepton and the isolated track. For fully reconstructed electrons, the $E_T$ is used to estimate the $p_T$. The highest bin shown includes all events which would be past the right edge of the plot.

Figure 16

Reconstructed invariant mass of the fully reconstructed lepton and isolated track pair in pretag candidate events with two or more jets, compared to the predicted distribution. The highest bin shown includes all events which would be past the right edge of the plot.

Figure 17

Summed scalar energy ($H_T$) of the fully reconstructed lepton, the isolated track, the ${\mathrm{E̸}}_T$, and all jets in the tagged candidate sample, compared to the combined signal and background predictions.

Figure 18

Missing transverse energy of the $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ tagged candidate sample, compared to the combined signal and background predictions.

Figure 19

Transverse momentum of the fully reconstructed lepton in the tagged $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ candidate sample, compared to the combined signal and background predictions. The $E_T$ is used as an estimate of the lepton $p_T$ for fully reconstructed electron candidates.

Figure 20

Transverse momentum of the track lepton (isolated track) in the tagged $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ candidate sample, compared to the combined signal and background predictions.

Figure 21

Distance along the jet axis to the reconstructed secondary vertex in tagged jets in the $\mathrm{\text{lepton}}+\mathrm{\text{track}}$ candidate sample, compared to the combined signal and background predictions.

Figure 22

Measured cross section as a function of the assumed top quark mass, compared to theoretical predictions for the cross section.