Revisiting semileptonic $B$ meson decays at next-to-next-to-leading order

TL;DR

This paper calculates high-order quantum corrections to semileptonic B meson decays, providing analytic and semi-analytic formulas for arbitrary quark masses, which enhances precision in theoretical predictions.

Contribution

It extends existing NNLO calculations to include arbitrary quark masses and introduces a semi-analytic method for complex contributions, improving the accuracy of decay rate predictions.

Findings

Results agree with known expansions for specific decay channels.

Provides analytic expressions in terms of iterated integrals.

Introduces a semi-analytic approximation method for complex contributions.

Abstract

We compute next-to-next-to-leading order corrections to the semileptonic decay rate of $B$ mesons for arbitrary values of the final-state quark mass. For the contribution with one massive quark in the final state, we extend the literature result and obtain analytic expressions in terms of iterated integrals. For the complete contribution, which also includes contributions with three massive quarks in the final state, we present a semi-analytic method, which leads to a precise approximation formula for the decay rate. Our results agree with the expansions available for $b\to c\ell \bar{\nu}_\ell$ and $b\to u\ell \bar{\nu}_\ell$ in the literature. The main emphasize of this paper is on the technical aspects of the calculation which are useful for a wider range of applications.