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

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 $\mathcal{O}(3\sim 5\%)$ 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 $E_{\gamma }\ge E_{\mathrm{cut}}$, 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.

36 pages, 9 figures

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