Theoretical update of Bs mixing

Abstract

We update the theory predictions for the mass difference ΔMs, the width difference ΔΓs and the CP asymmetry in flavour-specific decays, afss, for the Bs−bar Bs system. In particular we present a new expression for the element Γ12s of the decay matrix, which enters the predictions of ΔΓs and afss. To this end we introduce a new operator basis, which reduces the troublesome sizes of the 1/mb and αs corrections and diminishes the hadronic uncertainty in ΔΓs/ΔMs considerably. Logarithms of the charm quark mass are summed to all orders. We find ΔΓs/ΔMs = (49.7±9.4)bold dot10−4 and ΔΓs = (fBs/240 MeV)2[(0.105±0.016) B + (0.024±0.004) tilde BS' − 0.027±0.015] ps−1 in terms of the bag parameters B, tilde BS' in the NDR scheme and the decay constant fBs. The improved result for Γ12s also permits the extraction of the CP-violating Bs−bar Bs phase from afss with better accuracy. We show how the measurements of ΔMs, ΔΓs, afss, ACPmix(Bs→J/ψphgr) and other observables can be efficiently combined to constrain new physics. Applying our new formulae to data from the DØ experiment, we find a 2σ deviation of the Bs−bar Bs phase from its Standard Model value. We also briefly update the theory predictions for the Bd−bar Bd system and find ΔΓd/ΔMd = (52.6+11.5−12.8) bold dot10−4 and afsd = (−4.8+1.0−1.2) bold dot10−4 in the Standard Model.