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

Abstract

We compute next-to-next-to-leading order QCD corrections to the partonic processes $b\to c\bar{u}d$ and $b\to c\bar{c}s$, 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 $O_1$ and $O_2$ in the $\Delta B=1$ 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 $b\to u\bar{c}s$ and $b\to u\bar{u}d$.

v2: ref. added; numerical values in CKM-suppressed contribution and fig.10 updated; conclusions unchanged