Revisiting radiative leptonic $B$ decay

TL;DR

This paper revisits the theoretical calculations of radiative leptonic B decay, focusing on resummation techniques, power corrections, and their impact on form factors and branching ratios, aiding future experimental comparisons.

Contribution

It introduces a Mellin space factorization formula with NLL resummation for B decay form factors and analyzes power and soft contributions at two-loop level.

Findings

Resummation and power corrections significantly reduce form factors.

Numerical results suggest notable effects on decay rates.

Provides predictions for future experimental validation.

Abstract

In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist $B$-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors $F_{A,V}$ in the $B \to \gamma \ell\nu$ decay at leading power in $\Lambda/m_b$. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by $1/E_\gamma$ and $1/m_b$), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data.