Abstract
In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist B-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors in the decay at leading power in . Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by and ), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data.
Highlights
The radiative leptonic decay of the B meson is of interest as it is the most important channel to extract the parameters of the B-meson light-cone distribution amplitudes (LCDAs) and to test the factorization theorem when the emitted photon is energetic
The radiative leptonic decay mode B → γν is interesting both theoretically and experimentally. It plays an irreplaceable role in the determination of parameters of the B-meson LCDA
The factorizationscale dependence of the B-meson LCDA is governed by the LN evolution equation, which is an integro-differential equation and is not solved
Summary
The radiative leptonic decay of the B meson is of interest as it is the most important channel to extract the parameters of the B-meson light-cone distribution amplitudes (LCDAs) and to test the factorization theorem when the emitted photon is energetic. At leading power in Λ/mb, the QCD factorization formula has been derived for the B → γ form factors FA,V [3, 4] and was confirmed under the framework of soft-collinear effective theory (SCET) [5, 6]. Morevoer, based on transverse-momentum-dependent factorization, the power corrections to B → γ ν decay were investigated in [18] All these studies indicate that the power-suppressed contribution is sizable and should not be neglected in the determination of the first inverse moment of the B-meson LCDA. We derive the scale-independent factorization formula of the B → γ form factors and discuss the power-suppressed contributions; this is followed by the phenomenological analysis.
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