$B^0_s - \bar{B^0_s}$ Mixing Parameters from Unquenched Lattice QCD

TL;DR

This paper calculates key hadronic matrix elements for $B_s$ meson mixing using unquenched lattice QCD with improved actions, providing essential inputs for Standard Model predictions of mass and width differences.

Contribution

It presents the first unquenched lattice QCD determination of $B_s$ mixing parameters using MILC configurations with improved staggered quarks and Nonrelativistic QCD for the $b$ quark.

Findings

Determined $f_{B_s} imes ext{sqrt}( ext{B}_{B_s})$ as 0.281(21) GeV.

Provided matrix elements for four-fermion operators relevant to $ ext{Δ} ext{Γ}_s$.

Supplied nonperturbative inputs for Standard Model calculations of $B_s$ mixing.

Abstract

We determine hadronic matrix elements relevant for the mass and width differences, $\Delta M_s$ & $\Delta \Gamma_s$ in the $B^0_s - \bar{B^0_s}$ 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.