Neutral B Meson Mixing in Unquenched Lattice QCD

Abstract

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 CKM matrix elements from experimental measurements of mass differences $\Delta M_d$ and $\Delta M_s$. We find $\xi =f_{B_s}\sqrt{{\hat{B}}_{B_s}}/f_{B_d}\sqrt{{\hat{B}}_{B_d}}=1.258(33)$, $f_{B_d}\sqrt{{\hat{B}}_{B_d}}=216(15)$ MeV and $f_{B_s}\sqrt{{\hat{B}}_{B_s}}=266(18)$ MeV. We also update previous results for decay constants and obtain $f_{B_d}=190(13)$ MeV, $f_{B_s}=231(15)$ MeV and $f_{B_s}/f_{B_d}=1.226(26)$. The new lattice results lead to updated values for the ratio of CKM matrix elements $|V_{td}|/|V_{ts}|$ and for the Standard Model prediction for $Br(B_s\to {\mu }^{+}{\mu }^{-})$ with reduced errors. We determine $|V_{td}|/|V_{ts}|=0.214(1)(5)$ and $Br(B_s\to {\mu }^{+}{\mu }^{-})=3.19(19)\times 10^{-9}$.

Comments: 12 pages, 10 postscript figures, version to appear in Phys.Rev.D. Two new figures, Fig.6 and Fig.10, added. Result on branching fraction Br(B_s \rightarrow mu^+, mu^-) added. Other results on decay constants and on \xi unchanged