We compute the matrix element of the four-quark operator \OpS = bˉ(1−γ5)sbˉ(1−γ5)s in the Bs−Bˉs mixing on the lattice using NRQCD, which gives a leading contribution in the calculation of the width difference ΔΓs in the 1/mb expansion. Using the next-to-leading formula of Beneke \textit{et al.}, we obtain (ΔΓ/Γ)s = 0.151(37)(36)(17), where the the first error reflects the uncertainty of fBs = 245(30) MeV, the second error comes from our calculation of the matrix element of \OpS, and the third represents unknown 1/mb correction.
Cite
@article{arxiv.hep-ph/9912318,
title = {Width difference in the $B_s$-$\bar{B}_s$ system with lattice NRQCD},
author = {S. Hashimoto and K-I. Ishikawa and T. Onogi and N. Yamada},
journal= {arXiv preprint arXiv:hep-ph/9912318},
year = {2009}
}