Radiative leptonic decay $B\to \gamma \ell {\nu }_{\ell }$ with subleading power corrections

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 ${\varphi }_{+}\left(\omega \right)$ shows that the latter dominates. The radiative leptonic decay is therefore well suited to constrain the parameters of ${\varphi }_{+}\left(\omega \right)$, including the first inverse moment, $1/{\lambda }_B$, from the expected high-statistics data of the BELLE II experiment.