$B_s^0-\overline{B_s^0}$ Mixing Parameters from Unquenched Lattice QCD

Abstract

We determine hadronic matrix elements relevant for the mass and width differences, $\Delta M_s$ & $\Delta {\Gamma }_s$ in the $B_s^0-\overline{B_s^0}$ meson system using fully unquenched lattice QCD. We employ the MILC collaboration gauge configurations that include $u$, $d$ and $s$ sea quarks using the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence $s$ quark also with the AsqTad action and use Nonrelativistic QCD for the valence $b$ quark. For the nonperturbative QCD input into the Standard Model expression for $\Delta M_s$ we find $f_{B_s}\sqrt{{\hat{B}}_{B_s}}=0.281(21)$GeV. Results for four-fermion operator matrix elements entering Standard Model formulas for $\Delta {\Gamma }_s$ are also presented.

Comments: 5 pages, version to appear in Physical Review D (Rapid Communications), short section on the width difference $\Delta {\Gamma }_s$ added