Nonleptonic B-meson decays to next-to-next-to-leading order

We compute next-to-next-to-leading order QCD corrections to the partonic processes b→ c ū d and b→ c c̄ s, which constitute the dominant decay channels in standard model predictions for B-meson lifetimes within the heavy quark expansion. We consider the contribution from the four-quark operators O₁ and O₂ in the Δ B =1 effective Hamiltonian. The decay rates are obtained from the imaginary parts of four-loop propagator-type diagrams. We compute the corresponding master integrals using the ``expand and match'' approach which provides semi-analytic results for the physical charm and bottom quark masses. We show that the dependence of the decay rate on the renormalization scale is significantly reduced after including the next-to-next-to-leading order corrections. Furthermore, we compute next-to-next-to-leading order corrections to the Cabibbo-Kobayashi-Maskawa-suppressed decay channels b → u c s and b → u u d.