  The energy measurement of jets produced by b-quarks at hadron colliders
suffers from biases due to the peculiarities of the hadronization and decay of
the originating B hadron. The impact of these effects can be estimated by
reconstructing the mass of Z boson decays into pairs of b-quark jets. From a
sample of 584 pb-1 of data collected by the CDF experiment in 1.96 TeV
proton-antiproton collisions at the Tevatron collider, we show how the Z signal
can be identified and measured. Using the reconstructed mass of Z candidates we
determine a jet energy scale factor for b-quark jets with a precision better
than 2%. This measurement allows a reduction of one of the dominant source of
uncertainty in analyses based on high transverse momentum b-quark jets. We also
determine, as a cross-check of our analysis, the Z boson cross section in
hadronic collisions using the b-bbar final state as sigma x B(Z->b-bbar) = 1578
+636 -410 pb.
