Width Difference in the $B_s-\overline{B_s}$ System

Abstract

We use the heavy quark expansion to investigate the width difference $\Delta {\Gamma }_{B_s}$ between the $B_s$ mass eigenstates. The corrections of $\mathcal{O}({\Lambda }_{QCD}/m_b)$ and $\mathcal{O}(m_s/m_b)$ 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 $(\Delta \Gamma /\Gamma {)}_{B_s}$ with particular emphasis on theoretical uncertainties. We find $(\Delta \Gamma /\Gamma {)}_{B_s}=0.16_{-0.09}^{+0.11}$, where the large error is dominated by the uncertainty in hadronic matrix elements. An accuracy of about $10\%$ in $(\Delta \Gamma /\Gamma {)}_{B_s}$ 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 $\tau (B_s)/\tau (B_d)$ and estimate that, most likely, $|\tau (B_s)/\tau (B_d)-1|<1\%$.

24 pages, LaTeX, 1 figure as uudecoded file

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