Factorization and dispersion relations for radiative leptonic B decay

• Published in: The journal of high energy physics 2016-09, Vol.2016 (9), p.1-33, Article 159
• Main Author: Wang, Yu-Ming
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Dispersion; Elementary Particles; Factorization; Form factors; High energy physics; Inverse; Mathematical analysis; Mathematical models; Physics; Physics and Astronomy; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Texts
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2016)159

A bstract 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.