Width difference in theBs−B¯ssystem

We use the heavy quark expansion to investigate the width difference $\Delta {\Gamma }_{B_s}$ between the $B_s$ mass eigenstates. The corrections of $O\left(\frac{{\Lambda }_{\mathrm{QCD}}}{m_b}\right)$ and $O\left(\frac{m_s}{m_b}\right)$ to the leading-order expression in the operator product expansion are derived and estimated to yield a sizable reduction of the leading result for $\Delta {\Gamma }_{B_s}$ by typically 30%. For completeness we also quantify small effects due to penguin operators and CKM-suppressed contributions. Based on our results we discuss the prediction for ${\left(\frac{\Delta \Gamma }{\Gamma }\right)}_{B_s}$ with particular emphasis on theoretical uncertainties. We find ${\left(\frac{\Delta \Gamma }{\Gamma }\right)}_{B_s}={0.16}_{-0.09\mathrm{}}^{+0.11\mathrm{}}$, where the large error is dominated by the uncertainty in hadronic matrix elements. An accuracy of about 10% in ${\left(\frac{\Delta \Gamma }{\Gamma }\right)}_{B_s}$ should be within reach, assuming continuing progress in lattice calculations. In addition, we address phenomenological issues and implications of a $\Delta {\Gamma }_{B_s}$ measurement for constraints on $\Delta M_{B_s}$ and CKM parameters. We further consider in some detail the lifetime ratio $\frac{\tau \left(B_s\right)}{\tau \left(B_d\right)}$ and estimate that, most likely, $|\frac{\tau \left(B_s\right)}{\tau \left(B_d\right)}-1|<\mathrm{}1\%$.