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

Abstract

We compute the matrix element of the four-quark operator ${\text{Op}}_S$ = $\bar{b}(1-{\gamma }_5)s\bar{b}(1-{\gamma }_5)s$ 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 ${\text{Op}}_S$, and the third represents unknown $1/m_b$ correction.

Comments: 17 pages, 6 figures, uses REVTeX, corrected typos, conservative systematic error