Current-current operator contribution to the decay matrix in B-meson mixing at next-to-next-to-leading order of QCD

A bstract We compute next-to-next-to-leading order perturbative corrections to the decay width difference of mass eigenstates and the charge-parity asymmetry a fs in flavour-specific decays of neutral B mesons. In our calculation we take into account the full dependence on the charm and bottom quark masses for the current-current operator contributions up to three-loop order. Special emphasis is put on the proper construction of the so-called |∆ B | = 2 theory such that Fierz symmetry is preserved. We provide updated phenomenological predictions, for ∆Γ, ∆Γ/∆ M and a fs for the B d and B s system, including a detailed analysis of the uncertainties of our predictions. The calculated NNLO correction reduce the perturbative uncertainty of the leading term of the 1/ m b expansion of the width difference ∆Γ s in the B s system to the level of the current experimental error. The uncertainty of our prediction ∆Γ s = (0.077 ± 0.016) ps − 1 is dominated by the sub-leading term of this expansion. We further illustrate how better future measurements of ∆Γ d and $${a}_{\text{fs}}^{d}$$ will help to gain a better understanding of $${B}_{d}{\text -}{\overline{B} }_{d}$$ mixing.