Factorization in leptonic radiative B -> gamma eνdecays

TL;DR

The paper tackles factorization for exclusive radiative B decays with an energetic photon using soft-collinear effective theory (SCET). It derives an all-orders factorization formula that splits the amplitude into a hard Wilson coefficient, a jet function, and a soft B-meson light-cone wavefunction, connected by a single light-cone convolution. A key result is that the leading B→γ form factors f_V and f_A are equal at leading power due to chiral symmetry, with the nonperturbative physics contained in Ψ_B and the jet dynamics in J and the subleading J_ell contributions; one-loop jet functions are computed, and resummation can be performed via RG evolution of the Wilson coefficients. The framework clarifies the structure of radiative B decays, reconciles previous one-loop results with a rigorous all-orders factorization, and provides a pathway for applying SCET to a broader class of radiative heavy-to-light processes.

Abstract

We discuss factorization in exclusive radiative leptonic B->γeνdecays using the soft-collinear effective theory. The form factors describing these decays can be expanded in a power series in Lambda/E_γwith E_γthe photon energy. We write down the most general operators in the effective theory which contribute to the form factors at leading order in Lambda_QCD/E_γ, proving their factorization into hard, jet and soft contributions, to all orders in alpha_s.

Figures (2)

• Figure 1: One-loop effective theory graphs contributing to the T-product (\ref{['Aeff']}). Only the collinear graphs are shown; the topology of the usoft graphs is identical to that of the QCD graphs. The graphs (a)-(d) are produced by the first term in (\ref{['Aeff']}), and (e)-(g) by the second term. The lower vertex in (a)-(d) denotes the $\bar{\xi} \varepsilon\!\!\!\slash_\perp^* Wq$ operator; in (e)-(g) the photon attaches to the circled cross vertex, denoting the ${\cal J}_g$ operator, and the lower vertex is the ${\cal L}^{(1)}_{\xi q}$ subleading Lagrangian.
• Figure 2: Collinear graphs for photon emission from a light quark in the effective theory. The wiggly line denotes the photon. The graph (a) corresponds to the local operator in the matching, and the remaining two (b), (c) come from the nonlocal term. The blob in (a) denotes the $\bar{\xi} \varepsilon\!\!\!\slash_\perp^* Wq$ operator; in (b), (c) the shaded blob denotes the ${\cal L}^{(1)}_{\xi q}$ subleading Lagrangian and the circled cross is the insertion of ${\cal J}_g$.