We study SU (3)-breaking effects in the neutral B d -B d and B s -B s systems with unquenched N f = 2 + 1 lattice QCD. We calculate the relevant matrix elements on the MILC collaboration's gauge configurations with asqtad-improved staggered sea quarks. For the valence light-quarks (u, d, and s) we use the asqtad action, while for b quarks we use the Fermilab action. We obtain ξ = f Bs B Bs /f B d B B d = 1.268 ± 0.063. We also present results for the ratio of bag parameters B Bs /B B d and the ratio of CKM matrix elements |V td |/|V ts |. Although we focus on the calculation of ξ, the strategy and techniques described here will be employed in future extended studies of the B mixing parameters ∆M d,s and ∆Γ d,s in the Standard Model and beyond. * megamiz@ugr.es