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

TL;DR

This paper calculates advanced quantum chromodynamics corrections to key B-meson decay processes, reducing theoretical uncertainties and improving the precision of lifetime predictions within the Standard Model.

Contribution

It provides the first complete next-to-next-to-leading order QCD corrections to dominant B-meson decay channels, including novel semi-analytic results for relevant master integrals.

Findings

Reduced renormalization scale dependence after NNLO corrections

Enhanced accuracy in B-meson lifetime predictions

First NNLO calculations for specific suppressed decay channels

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 $b \to u \bar u d$.