$B0$ Mixing and Flavor Taggers in Exclusive $B$ Decays at CDF

Since May 2002 the CDF detector at Fermilab's Tevatron $p \bar{p}$ collider has collected around $360~pb^{-1}$ of physics quality data, about three times as much as the previous Run I data set. The new Silicon Vertex Trigger processor allows one to select events containing displaced tracks, opening up the collection of fully hadronic samples enriched in charm and beauty hadrons. In particular, it permits the measurement of the $B_s$ oscillation frequency on fully reconstructed hadronic samples. Measurement of the $B0$ mixing frequency is an important milestone towards a $B_s$ mixing analysis. Preliminary studies of $B0$ mixing using the {\it same-side} and {opposite-side} flavor tagging techniques are presented. For this analysis a large number of fully hadronic decays are combined.