NeutralBmeson mixing in unquenched lattice QCD

We study $B_d$ and $B_s$ mixing in unquenched lattice QCD employing the MILC Collaboration gauge configurations that include $u$, $d$, and $s$ sea quarks based on the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence light quarks also with the AsqTad action and use the nonrelativistic NRQCD action for the valence $b$ quark. We calculate hadronic matrix elements necessary for extracting Cabibbo-Kobayashi-Maskawa matrix elements from experimental measurements of mass differences $\Delta M_d$ and $\Delta M_s$. We find $\xi \equiv f_{B_s}\sqrt{{\widehat{B}}_{B_s}}/f_{B_d}\sqrt{{\widehat{B}}_{B_d}}=1.258(33)$, $f_{B_d}\sqrt{{\widehat{B}}_{B_d}}=216(15)\mathrm{MeV}$, and $f_{B_s}\sqrt{{\widehat{B}}_{B_s}}=266(18)\mathrm{MeV}$. We also update previous results for decay constants and obtain $f_{B_d}=190(13)\mathrm{MeV}$, $f_{B_s}=231(15)\mathrm{MeV}$, and $f_{B_s}/f_{B_d}=1.226(26)$. The new lattice results lead to updated values for the ratio of Cabibbo-Kobayashi-Maskawa matrix elements $|V_{td}|/|V_{ts}|$ and for the standard model prediction for $\mathrm{Br}(B_s\to {\mu }^{+}{\mu }^{-})$ with reduced errors. We determine $|V_{td}|/|V_{ts}|=0.214(1)(5)$ and $\mathrm{Br}(B_s\to {\mu }^{+}{\mu }^{-})=3.19(19)\times {10}^{-9}$.