Neutral $B$-meson mixing from three-flavor lattice quantum chromodynamics: Determination of the $SU(3)$-breaking ratio $\xi$

Abstract

We study SU(3)-breaking effects in the neutral Bd−B―d and Bs−B―s systems with unquenched Nf=2+1 lattice quantum chromodynamics (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=fBsBBs/fBdBBd=1.268±0.063. We also present results for the ratio of bag parameters BBs/BBd and the ratio of Cabibbo-Kobayashi-Maskawa matrix elements |Vtd|/|Vts|. 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 △Md,s and △Γd,s in the standard model and beyond.