  We report on the advances in our unquenched calculation of the matrix
elements relevant for the analysis of B^0-\bar B^0 mixing using the Asqtad
(light quark) and Fermilab (heavy quark) actions. We have calculated the
hadronic parameters for the mass and width differences in the neutral B meson
system. Preliminary results are presented for f_{B_q}^2 B_q as well as for the
ratio \xi^2=f_{B_s}^2 B_{B_s}/f_{B_d}^2 B_{B_d}.
