Factorization in B->V gamma Decays

TL;DR

This work establishes a robust leading-power factorization theorem for exclusive B -> V gamma decays using soft-collinear effective theory, expressing amplitudes as a universal B->V form factor at zero momentum transfer plus calculable hard-scattering kernels convolved with light-cone distribution amplitudes. The authors implement a two-step QCD -> SCET_I -> SCET_II matching, enabling resummation of large logarithms across hard and hard-collinear scales and clarifying how soft-collinear messenger modes affect factorization. They apply the formalism to B -> K^* gamma, incorporating nonperturbative inputs from sum rules, and demonstrate that the soft and hard contributions combine to yield predictions with controlled perturbative uncertainties, while highlighting NP sensitivity via spectator emission and flavor-singlet effects. The analysis also discusses the limitations of factorization in flavor-singlet cases and the impact of light-quark masses, providing a framework for constraining New Physics through exclusive radiative B decays and related observables.

Abstract

The factorization properties of the radiative decays B->V gamma are analyzed at leading order in 1/m_b using the soft-collinear effective theory. It is shown that the decay amplitudes can be expressed in terms of a B->V form factor evaluated at q^2=0, light-cone distribution amplitudes of the B and V mesons, and calculable hard-scattering kernels. The renormalization-group equations in the effective theory are solved to resum perturbative logarithms of the different scales in the decay process. Phenomenological implications for the B->K* gamma branching ratio, isospin asymmetry, and CP asymmetries are discussed, with particular emphasis on possible effects from physics beyond the Standard Model.

Figures (7)

• Figure 1: Three QCD Feynman diagrams for the contributions of $Q_8$ and their leading-order representation in the effective theory. The double line denotes the heavy-quark field. The dashed lines denote hard-collinear fields in SCET$_{\rm I}$ and collinear fields in SCET$_{\rm II}$. Solid lines in the effective-theory diagrams denote soft fields and the dotted line denotes a soft-collinear field.
• Figure 2: Example of an exceptional momentum configuration giving rise to an interaction in SCET$_{\rm I}$ involving $hc$ and $\overline{hc}$ fields.
• Figure 3: Example of a SCET$_{\rm I}$ diagram relevant for $B\to V\gamma$ decay with an offshell-collinear gluon. The same contribution is also depicted in the second line of Figure \ref{['fig:matching']}.
• Figure 4: Leading-order QCD diagrams for the matching of $Q_1$ and $Q_8$ onto $J^B_i$. Other diagrams are power suppressed or vanish.
• Figure 5: Leading-order QCD diagrams for the matching of $Q_{1,2}^p$ and $Q_8$ onto $J^C_i$.