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

A bstract We compute next-to-next-to-leading order corrections to the decay width difference of mass eigenstates and the charge-parity (CP) asymmetry a fs 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 m c /m b . We provide numerical results for ∆Γ and ∆Γ / ∆ M , both for the B d and B s system, including a detailed uncertainty analysis. Using the experimental value for the mass difference ∆ M s we predict ∆Γ s = (0 . 078 ± 0 . 015) ps − 1 . For the CP asymmetries we find afsˢ=(2.27± 0.13)× 10⁻⁵ a fs s = 2.27 ± 0.13 × 10 − 5 and afsᵈ=-(5.19± 0.30)× 10⁻⁴ a fs d = − 5.19 ± 0.30 × 10 − 4 . Furthermore, we show that the ratios (∆Γ s / ∆ M s ) / (∆Γ d / ∆ M d ) and ∆Γ d / ∆Γ s can be predicted with high precision. The former quantity permits the prediction ∆Γ d = (0 . 00215 ± 0 . 00013) ps − 1 from the measurements of ∆ M d,s and ∆Γ s . We further discuss the impact of ∆Γ d / ∆Γ s 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.