Measurement of cross sections for $b$ jet production in events with a $Z$ boson in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$

A measurement of the $b$ jet production cross section is presented for events containing a $Z$ boson produced in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$, using data corresponding to an integrated luminosity of $2{\mathrm{fb}}^{-1}$ 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 $E_T>20\mathrm{GeV}$ and pseudorapidity $|\eta |<1.5$ and are identified as $b$ jets using a secondary vertex algorithm. The ratio of the integrated $Z+b$ jet cross section to the inclusive $Z$ production cross section is measured to be $3.32\pm 0.53(\mathrm{stat})\pm 0.42(\mathrm{syst})\times {10}^{-3}$. This ratio is also measured differentially in jet $E_T$, jet $\eta$, $Z$-boson transverse momentum, number of jets, and number of $b$ jets. 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.