A measurement of the $bjet$ production cross section is presented for events containing a $Z$ boson produced in $pbar{p}$ collisions at $sqrt{s}=1.96$ TeV, using data corresponding to an integrated luminosity of 2 fb$^{-1}$ collected by the CDF II detector at the Tevatron. $Z$ bosons are selected in the electron and muon decay modes. Jets are considered with transverse energy $E_T>20$ GeV and pseudorapidity $|eta|<1.5$ and are identified as $bjets$ using a secondary vertex algorithm. The ratio of the integrated $Z+bjet$ cross section to the inclusive $Z$ production cross section is measured to be $3.32 pm 0.53 {rm (stat.)} pm 0.42 {rm (syst.)}times 10^{-3}$. This ratio is also measured differentially in jet $E_T$, jet $eta$, $Z$-boson transverse momentum, number of jets, and number of $bjets$. The predictions from leading order Monte Carlo generators and next-to-leading-order QCD calculations are found to be consistent with the measurements within experimental and theoretical uncertainties.
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