Radiative leptonic decay $B\to \gamma \ell \nu_\ell$ with subleading power corrections

TL;DR

This paper refines QCD predictions for the radiative decay $B\to \gamma \ell \nu_\ell$ by including subleading power corrections, highlighting the decay's potential to constrain $B$-meson light-cone distribution amplitudes with upcoming experimental data.

Contribution

It incorporates power-suppressed corrections from higher-twist $B$-meson LCDAs into decay predictions, emphasizing the importance of the leading-twist LCDA in form factor analysis.

Findings

The decay form factors are mainly sensitive to the leading-twist LCDA $\phi_+(\omega)$.

Soft contributions are estimated via dispersion relations and QCD sum rules.

The decay can constrain the parameter $\lambda_B$ from future high-statistics data.

Abstract

We reconsider the QCD predictions for the radiative decay $B\to \gamma \ell \nu_\ell$ with an energetic photon in the final state by taking into account the $1/E_\gamma, 1/m_b$ power-suppressed hard-collinear and soft corrections from higher-twist $B$-meson light-cone distribution amplitudes (LCDAs). The soft contribution is estimated through a dispersion relation and light-cone QCD sum rules. The analysis of theoretical uncertainties and the dependence of the decay form factors on the leading-twist LCDA $\phi_+(\omega)$ shows that the latter dominates. The radiative leptonic decay is therefore well suited to constrain the parameters of $\phi_+(\omega)$, including the first inverse moment, $1/\lambda_B$, from the expected high-statistics data of the BELLE II experiment.