Neutral<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>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 Cabibbo-Kobayashi-Maskawa matrix elements from experimental measurements of mass differences $\ensuremath{\Delta}{M}_{d}$ and $\ensuremath{\Delta}{M}_{s}$. We find $\ensuremath{\xi}\ensuremath{\equiv}{f}_{{B}_{s}}\sqrt{{\stackrel{^}{B}}_{{B}_{s}}}/{f}_{{B}_{d}}\sqrt{{\stackrel{^}{B}}_{{B}_{d}}}=1.258(33)$, ${f}_{{B}_{d}}\sqrt{{\stackrel{^}{B}}_{{B}_{d}}}=216(15)\text{ }\text{ }\mathrm{MeV}$, and ${f}_{{B}_{s}}\sqrt{{\stackrel{^}{B}}_{{B}_{s}}}=266(18)\text{ }\text{ }\mathrm{MeV}$. We also update previous results for decay constants and obtain ${f}_{{B}_{d}}=190(13)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}_{s}}=231(15)\text{ }\text{ }\mathrm{MeV}$, 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 $\mathrm{Br}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$ with reduced errors. We determine $|{V}_{td}|/|{V}_{ts}|=0.214(1)(5)$ and $\mathrm{Br}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})=3.19(19)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$.