Light-cone distribution amplitudes of heavy mesons with QED effects

TL;DR

This paper derives and analyzes the QED-corrected light-cone distribution amplitudes of heavy mesons, providing analytical and numerical solutions for their scale evolution and electromagnetic effects in exclusive B decays.

Contribution

It introduces the first derivation of the one-loop anomalous dimension for QED-generalized soft functions and provides comprehensive solutions including electromagnetic corrections.

Findings

Exact solutions for soft functions in Laplace space.

Numerical estimates of QED corrections to inverse moments.

Analytical solutions to all orders in strong coupling and first order in QED.

Abstract

We discuss the QED-generalized leading-twist light-cone distribution amplitudes of heavy mesons, that appear in QCD$\times$QED factorization theorems for exclusive two-body $B$ decays. In the presence of electrically charged particles, these functions should be more appropriately regarded as soft functions for heavy-meson decays into two back-to-back particles. In this paper, we derive the one-loop anomalous dimension of these soft functions and study their behaviour under renormalization-scale evolution, obtaining an exact solution in Laplace space. In addition, we provide numerical solutions for the soft functions and analytical solutions to all orders in the strong and to first order in the electromagnetic coupling. For the inverse (and inverse-logarithmic) moments, we obtain an all-order solution in both couplings. We further provide numerical estimates for QED corrections to the inverse moments.