Light-cone distribution amplitudes of light mesons with QED effects

TL;DR

This paper extends the concept of light-cone distribution amplitudes for light mesons to include QED effects, analyzing their evolution and impact on meson decay processes, with analytical solutions and numerical estimates provided.

Contribution

It introduces a generalized evolution framework for meson distribution amplitudes incorporating QED effects, highlighting differences from pure QCD evolution and providing analytical solutions.

Findings

QED effects alter the endpoint behavior of meson distribution amplitudes.

Analytical solutions to the evolution equations are obtained to first order in m.

Numerical estimates show significant QED corrections to Gegenbauer coefficients.

Abstract

We discuss the generalization of the leading-twist light-cone distribution amplitude for light mesons including QED effects. This generalization was introduced to describe virtual collinear photon exchanges above the strong-interaction scale $\Lambda_{\rm QCD}$ in the factorization of QED effects in non-leptonic $B$-meson decays. In this paper we study the renormalization group evolution of this non-perturbative function. For charged mesons, in particular, this exhibits qualitative differences with respect to the well-known scale evolution in QCD only, especially regarding the endpoint-behaviour. We analytically solve the evolution equation to first order in the electromagnetic coupling $\alpha_{\rm em}$, which resums large logarithms in QCD on top of a fixed-order expansion in $\alpha_{\rm em}$. We further provide numerical estimates for QED corrections to Gegenbauer coefficients as well as inverse moments relevant to (QED-generalized) factorization theorems for hard exclusive processes.