A measurement of the b jet production cross section is presented for events containing a Z boson produced in p anti-p collisions at s**(1/2) 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 pseudorapi+dity |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+/-0.53(stat)+/-0.42(syst)x10-3. 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.
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