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

A measurement of the inclusive bottom jet cross section is presented for events containing a $Z$ boson in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using the Collider Detector at Fermilab. $Z$ bosons are identified in their electron and muon decay modes, and $b$ jets with $E_T>20\mathrm{GeV}$ and $|\eta |<1.5$ are identified by reconstructing a secondary decay vertex. The measurement is based on an integrated luminosity of about $330{\mathrm{pb}}^{-1}$. A cross section times branching ratio of $\sigma (Z+b\mathrm{\text{jets}})\times \mathcal{B}(Z\to {\ell }^{+}{\ell }^{-})=0.93\pm 0.36\mathrm{pb}$ is found, where $\mathcal{B}(Z\to {\ell }^{+}{\ell }^{-})$ is the branching ratio of the $Z$ boson or ${\gamma }^{*}$ into a single flavor dilepton pair ($e$ or $\mu$) in the mass range between 66 and $116\mathrm{GeV}/c^2$. The ratio of $b$ jets to the total number of jets of any flavor in the $Z$ sample, within the same kinematic range as the $b$ jets, is $2.36\pm 0.92\%$. Here, the uncertainties are the quadratic sum of statistical and systematic uncertainties. Predictions made with next-to-leading order QCD agree, within experimental and theoretical uncertainties, with these measurements.