Abstract
Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic B → γℓν decay from the twist-two hadronic photon contribution at next-to-leading order in QCD; and further evaluate the higher-twist “resolved photon” corrections at leading order in αs, up to twist-four accuracy. QCD factorization for the vacuum-to-photon correlation function with an interpolating current for the B-meson is established explicitly at leading power in Λ/mb employing the evanescent operator approach. Resummation of the parametrically large logarithms of mb2/Λ2 entering the hard function of the leading-twist factorization formula is achieved by solving the QCD evolution equation for the light-ray tensor operator at two loops. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two B → γ 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}left(3sim 5%right) with the light-cone sum rule approach. We further predict the partial branching fractions of B → γℓν with a photon-energy cut Eγ ≥ Ecut, 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.
Highlights
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
Employing the technique of lightcone sum rules (LCSR) with the two-particle photon DAs, the power suppressed “resolved photon” contribution was computed at twist-four accuracy and at leading-order (LO) in αs [9,10,11], and was further updated [12] by including the NLO correction to the leadingtwist hadronic photon DA contribution and by calculating the higher-twist correction from the three-particle photon DAs at tree level
We will apply the standard perturbative matching procedure including the evanescent SCET operators to establish QCD factorization formulae for the vacuum-to-B-meson correlation function with the Dirac matrix γ5 defined in naive dimensional regularization (NDR)
Summary
To obtain the sum rules for the form factors FV (n · p) and FA(n · p), we construct the vacuum-to-photon correlation function with an interpolating current for the B-meson. Where q = p + pν refers to the four-momentum of the lepton-neutrino pair. QCD factorization for the correlation function (3.1) can be demonstrated with the technique of the light-cone OPE at (p + q) m2b and q2 m2b. We will employ the following power counting scheme n · p ∼ O(mb), |n · (p + q) − mb| ∼ O(Λ). The primary task of this section is to compute the perturbative matching coefficient entering the leading-twist factorization formula for (3.1) at NLO, with the evanescent operator approach
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