The Width Difference in the Bs − B̄s System ∗

We use the heavy quark expansion to investigate the width difference ∆Γ Bs between the B s mass eigenstates. The corrections of O(Λ QCD /m b) and 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 ∆Γ Bs 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 (∆Γ/Γ) Bs with particular emphasis on theoretical uncertainties. We find (∆Γ/Γ) Bs = 0.16 +0.11 −0.09 , where the large error is dominated by the uncertainty in hadronic matrix elements. An accuracy of about 10% in (∆Γ/Γ) Bs should be within reach, assuming continuing progress in lattice calculations. In addition we address phenomenological issues and implications of a ∆Γ Bs measurement for constraints on ∆M Bs and CKM parameters. We further consider in some detail the lifetime ratio τ (B s)/τ (B d) and estimate that, most likely, |τ (B s)/τ (B d) − 1| < 1%.