Theoretical update of Bs-s mixing

Abstract

We update the theory predictions for the mass difference ΔM s, the width difference ΔΓs and the CP asymmetry in flavour-specific decays, afss, for the B s-s 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 ≤ (49.79.4)10 -4 and ΔΓs ≤ (fBs/240MeV) 2[(0.1050.016)B+(0.0240.004)S′-0.0270.015]ps -1 in terms of the bag parameters B, S′ in the NDR scheme and the decay constant fBs. The improved result for Γ12s also permits the extraction of the CP-violating Bs-s phase from afss with better accuracy. We show how the measurements of ΔMs, ΔΓs, afss, ACPmix(BsJ/ψφ) and other observables can be efficiently combined to constrain new physics. Applying our new formulae to data from the D experiment, we find a 2σ deviation of the Bs- s phase from its Standard Model value. We also briefly update the theory predictions for the Bd-d system and find ΔΓd/ΔMd ≤ (52.6+11.5-12.8)10-4 and afsd ≤ (-4.8 +1.0-1.2)10-4 in the Standard Model. © SISSA 2007.