Complete next-to-next-to-leading order QCD corrections to the decay matrix in B-meson mixing at leading power

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 ∆Md,s 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.