Soft contribution to $B\to \gamma \ell \nu_\ell$ and the $B$-meson distribution amplitude

TL;DR

This paper analyzes the soft-overlap contribution to the $B\to \gamma \ell \nu_\ell$ decay at high photon energies, demonstrating its calculability via effective theories and its importance for constraining the $B$-meson distribution amplitude.

Contribution

It introduces a method to compute the soft-overlap contribution using heavy-quark expansion and soft-collinear effective theory, enhancing the understanding of $B$-meson decay processes.

Findings

Soft-overlap contribution can be calculated using effective theories.

This contribution is crucial for constraining the $B$-meson distribution amplitude.

The approach parallels the calculation for the $\,\gamma^* \gamma \to \pi$ transition form factor.

Abstract

The $B\to \gamma \ell \nu_\ell$ decay at large energies of the photon receives a numerically important soft-overlap contribution which is formally of the next-to-leading order in the expansion in the inverse photon energy. We point out that this contribution can be calculated within the framework of heavy-quark expansion and soft-collinear effective theory, making use of dispersion relations and quark-hadron duality. The soft-overlap contribution is obtained in a full analogy with the similar contribution to the $\gamma^* \gamma \to \pi$ transition form factor. This result strengthens the case for using the $B\to \gamma \ell \nu_\ell$ decay to constrain the $B$-meson distribution amplitude and determine its most important parameter, the inverse moment $\lambda_B$.