QED corrections to the Altarelli-Parisi splitting functions

Abstract

We discuss the combined effect of QED and QCD corrections to the evolution of parton distributions. We extend the available knowledge of the Altarelli-Parisi splitting functions to one order higher in QED, and provide explicit expressions for the splitting kernels up to ${\cal O}(\alpha \, \alpha_{\mathrm{S}})$. The results presented in this article allow to perform a parton distribution function analysis reaching full NLO QCD-QED combined precision.Comment: 11 pages, 1 figure. References added, improved discussion. Final version published in EPJC. Typo corrected in Eq. (22