Predicting the $B_s^0-{\bar{B}}_s^0$ width difference $\Delta {\Gamma }_s$ relies on the heavy quark expansion and on hadronic matrix elements of $\Delta B=2$ operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators $R_{2,3}$ and linear combinations ${\tilde{R}}_{2,3}$ using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC ensembles of gauge field configuations with $2+1+1$ flavors of sea quarks with the HISQ discretization, including lattices with physically light up/down quark masses. We discuss features unique to calculating matrix elements of these operators and analyze uncertainties from series truncation, discretization, and quark mass dependence. Finally we report the first Standard Model determination of $\Delta {\Gamma }_s$ using lattice QCD results for all hadronic matrix elements through $𝒪(1/m_b)$. The main result of our calculations yields the $1/m_b$ contribution $\Delta {\Gamma }_{1/m_b}=-0.022(10)p{s}^{-1}$. Adding this to the leading order contribution, the Standard Model prediction is $\Delta {\Gamma }_s=0.092(14)p{s}^{-1}$.

中文翻译：

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Bs0-B‾s0的宽度差超出前导阶的格子QCD矩阵元素

预测 ${乙}_s^0-{\stackrel{〜}{乙}}_s^0$ 宽度差 $\Delta {\Gamma }_s$ 依靠重夸克展开和强子矩阵元素 $\Delta 乙=2$操作员。我们展示了7维算子的矩阵元素的第一个晶格QCD结果${\mathrm{[R}}_{2，3}$ 和线性组合 ${\widetilde{\mathrm{[R}}}_{2，3}$对底部夸克使用非相对论性QCD，对奇异夸克使用高度改进的交错夸克（HISQ）动作。计算使用仪表场配置的MILC集成$2+\mathrm{1个}+\mathrm{1个}$带有HISQ离散化的海夸克口味，包括具有物理上点亮/滑下夸克质量的晶格。我们讨论了计算这些算子的矩阵元素所特有的功能，并分析了因序列截断，离散化和夸克质量依赖性而引起的不确定性。最后，我们报告第一个标准模型确定$\Delta {\Gamma }_s$ 通过所有强子矩阵元素使用晶格QCD结果 $𝒪（\mathrm{1个}/{米}_b）$。我们计算的主要结果是$\mathrm{1个}/{米}_b$ 贡献 $\Delta {\Gamma }_{\mathrm{1个}/{米}_b}=-0.022（10）p{s}^{-\mathrm{1个}}$。将其添加到领先订单中，标准模型预测为$\Delta {\Gamma }_s=0.092（14）p{s}^{-\mathrm{1个}}$。