# Subleading-power corrections to the radiative leptonic $B \to \gamma \ell \nu$ decay in QCD

## TL;DR

This paper calculates subleading-power QCD corrections to the $B o \gamma \ell
u$ decay using light-cone sum rules, revealing significant effects from hadronic photon contributions and providing predictions for branching fractions relevant to Belle II.

## Contribution

It introduces a detailed calculation of subleading-power corrections to $B o \gamma \ell
u$ decay, including higher-twist effects, using light-cone sum rules with photon distribution amplitudes.

## Key findings

- Hadronic photon effects can cause up to 30% correction to leading-power results.
- Higher-twist corrections are estimated to be around 3-5%.
- Predicted partial branching fractions aid in determining $B$-meson distribution amplitudes.

## Abstract

Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic $B \to \gamma \ell \nu$ decay, at next-to-leading order in QCD for the twist-two contribution and at leading order in $\alpha_s$ for the higher-twist contributions, induced by the hadronic component of the collinear photon. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two $B \to \gamma$ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking effect already at tree level in QCD. Using the conformal expansion of photon distribution amplitudes with the non-perturbative parameters estimated from QCD sum rules, the twist-two hadronic photon contribution can give rise to approximately 30\% correction to the leading-power "direct photon" effect computed from the perturbative QCD factorization approach. In contrast, the subleading-power corrections from the higher-twist two-particle and three-particle photon distribution amplitudes are estimated to be of ${\cal O} (3 \sim 5\%)$ with the light-cone sum rule approach. We further predict the partial branching fractions of $B \to \gamma \ell \nu $ with a photon-energy cut $E_{\gamma} \geq E_{\rm cut}$, which are of interest for determining the inverse moment of the leading-twist $B$-meson distribution amplitude thanks to the forthcoming high-luminosity Belle II experiment at KEK.