Factorization and dispersion relations for radiative leptonic B decay

Author(s)
Yu-Ming Wang
Abstract

Applying the dispersion approach we compute perturbative QCD corrections to the power suppressed soft contribution of B → γℓν at leading twist. QCD factorization for the B → γ

* form factors is demonstrated explicitly for the hard-collinear transverse polarized photon at one loop, with the aid of the method of regions. While the one-loop hard function is identical to the matching coefficient of the QCD weak current ūγ

μ ⊥(1 − γ

5)b in soft-collinear effective theory, the jet function from integrating out the hard-collinear fluctuations differs from the corresponding one entering the factorization formula of B → γℓν, due to the appearance of an additional hard-collinear momentum mode. Furthermore, we evaluate the sub-leading power contribution to the B → γ form factors from the three-particle B-meson distribution amplitudes (DAs) at tree level, with the dispersion approach. The soft contribution to the B → γ form factors from the three-particle B-meson DAs is shown to be of the same power compared with the corresponding hard correction, in contrast to the two-particle counterparts. Numerically the next-to-leading-order QCD correction to the soft two-particle contribution in B → γ form factors will induce an approximately (10 ∼ 20)% shift to the tree-level contribution at λ

B(μ

0) = 354 MeV. Albeit of power suppression parametrically, the soft two-particle correction can decrease the leading power predictions for the B → γ form factors by an amount of (10 ∼ 30)% with the same value of λ

B(μ

0). Employing the phenomenological model of the three-particle B-meson DAs inspired by a QCD sum rule analysis, the three-particle contribution to the B → γ form factors is predicted to be of O(1%), at leading order in α

s, with the default theory inputs. Finally, we explore theory constraints on the inverse moment of the leading-twist B-meson DA λ

B from the recent Belle measurements of the partial branching fractions of B → γℓν, taking into account the newly computed contributions to the B → γ form factors at subleading power.

Organisation(s)
Particle Physics
External organisation(s)
Nankai University
Journal
Journal of High Energy Physics
Volume
2016
No. of pages
33
ISSN
1029-8479
DOI
https://doi.org/10.1007/JHEP09(2016)159
Publication date
09-2016
Peer reviewed
Yes
Austrian Fields of Science 2012
103012 High energy physics
Keywords
ASJC Scopus subject areas
Nuclear and High Energy Physics
Portal url
https://ucris.univie.ac.at/portal/en/publications/factorization-and-dispersion-relations-for-radiative-leptonic-b-decay(4c3750f9-91b7-4e83-8ca0-b60ebe25a89f).html