Measurement of $b$ jet Production in Events with a $Z$ Boson in $p\overline{p}$ Collisions at $\sqrt{s}$ = 1.96 TeV

A measurement of the single inclusive bottom jet cross section is presented for events containing a $Z$ boson in $p\overline{p}$ collisions at $\sqrt{s}$ = 1.96 TeV with the Collider Detector at Fermilab. $Z$ bosons are identified in their electron and muon decay modes, and $b$ jets with $E_T$ $>$ 20~GeV and $|\eta| < 1.5$ are identified by reconstructing a secondary decay vertex. The measurement is based on an integrated luminosity of 337 pb$^{-1}$ for the electron decay mode and 324 pb$^{-1}$ for the muon decay mode. We find a cross section of $\sigma$($Z + b$ jet, $Z \rightarrow l^+ l^-$) = 0.96~$\pm$~0.35~pb and the fraction of $b$-jets to the total number of jets in this sample is (2.39 $\pm$ 0.86)\%. This measurement is in agreement with NLO QCD predictions.