Light-cone distribution amplitudes of light mesons with QED effects

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 ${\Lambda }_{\mathrm{QCD}}$ 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 ${\alpha }_{\mathrm{em}}$, which resums large logarithms in QCD on top of a fixed-order expansion in ${\alpha }_{\mathrm{em}}$. 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.

Comments: 30 pages, 3 figures