Width difference in the $B_s$-$\bar{B}_s$ system with lattice NRQCD

TL;DR

This paper calculates the width difference in the $B_s$-$ar{B}_s$ system using lattice NRQCD, providing a key theoretical input for understanding meson mixing and decay properties.

Contribution

It presents the first lattice NRQCD computation of the matrix element of a four-quark operator relevant to $B_s$ mixing, improving the precision of $ riangle ext{Gama}_s$ predictions.

Findings

Calculated $( riangle ext{Gama}/ ext{Gama})_s$ = 0.151(37)(36)(17)

Quantified uncertainties from decay constant, matrix element, and $1/m_b$ corrections

Provides a benchmark for future lattice and phenomenological studies.

Abstract

We compute the matrix element of the four-quark operator $\Op_S$ = $\bar{b}(1-\gamma_5) s \bar{b} (1-\gamma_5) s$ in the $B_s-\bar{B}_s$ mixing on the lattice using NRQCD, which gives a leading contribution in the calculation of the width difference $\Delta\Gamma_s$ in the $1/m_b$ expansion. Using the next-to-leading formula of Beneke \textit{et al.}, we obtain $(\Delta\Gamma/\Gamma)_s$ = 0.151(37)(36)(17), where the the first error reflects the uncertainty of $f_{B_s}$ = 245(30) MeV, the second error comes from our calculation of the matrix element of $\Op_S$, and the third represents unknown $1/m_b$ correction.