  A search for Z boson decays to pairs of b-quark jets has been performed in
the full dataset collected with the CDF detector at the Tevatron
proton-antiproton collider. After the selection of a pure sample of bb events
by means of the identification of secondary vertices from b-quark decays, we
have used two kinematic variables to further discriminate the electroweak bb
production from QCD processes, and sought evidence for the Z decay in the dijet
invariant mass distribution. An absolute background prediction allows the
extraction of an excess of events inconsistent with the background predictions
by 3.23 sigma but in good agreement with the amount and characteristics of the
expected signal. We then fit the mass distribution with an unbinned likelihood
technique, and obtain a Z -> bb signal amounting to 91+-30+-19 events.
