Evolution of the $B$-Meson Light-Cone Distribution Amplitude in Laplace Space

TL;DR

This paper analyzes the evolution of the $B$-meson light-cone distribution amplitude in Laplace space, deriving its RG equation, solving it exactly, and applying it to improve the theoretical description of certain $B$ decay processes.

Contribution

It introduces the Laplace transform of the $B$-meson distribution amplitude, derives its RG evolution, and provides a scale-independent factorization theorem for $B$ decays.

Findings

Exact solution to the RG equation for the Laplace-transformed distribution amplitude

Scale-independent formulation of the $B$ decay amplitude

Unbiased parameterization of the distribution amplitude in terms of hadronic parameters

Abstract

The $B$-meson light-cone distribution amplitude is a central quantity governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in $\Lambda_{\rm QCD}/m_b$ is most directly contained in its Laplace transform $\tilde\phi_+(\eta)$. We derive the renormalization-group (RG) equation satisfied by this function and present its exact solution. We express the RG-improved QCD factorization theorem for the decay $B^-\to\gamma\ell^-\bar\nu$ in terms of $\tilde\phi_+(\eta)$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of $\tilde\phi_+(\eta)$ in terms of a small set of uncorrelated hadronic parameters.