We compute next-to-next-to-leading order corrections to the decay width difference of mass eigenstates and the charge-parity (CP) asymmetry afs in flavour-specific decays of neutral B mesons. We include both current-current and penguin operators at three-loop order. All input integrals in the transition amplitude are reduced to a small set of master integrals which depend on the ratio of the charm and bottom quark masses. The latter are computed using semi-analytic methods which provide deep expansions around properly selected values of mc/mb. We provide numerical results for ∆Γ and ∆Γ/∆M, both for the Bd and Bₛ system, including a detailed uncertainty analysis. Using the experimental value for the mass difference ∆Mₛ we predict ∆Γₛ = (0. 078 ± 0. 015) ps^−1. For the CP asymmetries we find as fₛ = (2. 27 ± 0. 13) × 10^−5 and ad fs = − (5. 19 ± 0. 30) × 10^−4. Furthermore, we show that the ratios (∆Γₛ/∆Mₛ) / (∆Γd/∆Md) and ∆Γd/∆Γₛ can be predicted with high precision. The former quantity permits the prediction ∆Γd = (0. 00215 ± 0. 00013) ps−1 from the measurements of ∆M₃, ₒ and ∆Γₛ. We further discuss the impact of ∆Γd/∆Γₛ on the CKM unitarity triangle and present ready-to-use formulae which permit improved predictions once updated results for the operator matrix elements are available.
Nierste et al. (Thu,) studied this question.