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

A determination of the B_s^0 and B_d^0 mixing parameters in 2+1 lattice QCD