Measurement of the $t\overline{t}$ production cross section in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ events with jet probability $b$-tagging

We present a measurement of the $t\overline{t}$ production cross section using events with one charged lepton and jets from $p\overline{p}$ collisions at a center-of-mass energy of 1.96 TeV. A $b$-tagging algorithm based on the probability of displaced tracks coming from the event interaction vertex is applied to identify $b$ quarks from top decay. Using $318{\mathrm{pb}}^{-1}$ of data collected with the CDF II detector, we measure the $t\overline{t}$ production cross section in events with at least one restrictive (tight) $b$-tagged jet and obtain ${8.9}_{-1.0}^{+1.0}(\mathrm{stat}{)}_{-1.0}^{+1.1}(\mathrm{syst})\mathrm{pb}$. The cross section value assumes a top quark mass of $m_t=178\mathrm{GeV}/c^2$ in the acceptance corrections. The dependence of the cross section on $m_t$ is presented in the paper. This result is consistent with other CDF measurements of the $t\overline{t}$ cross section using different samples and analysis techniques, and has similar systematic uncertainties. We have also performed consistency checks by using the $b$-tagging probability function to vary the signal-to-background ratio and also using events that have at least two $b$-tagged jets.