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 $\mathcal{O}(\alpha {\alpha }_{\mathrm{S}})$. The results presented in this article allow to perform a parton distribution function analysis reaching full NLO QCD-QED combined precision.

Comments: 11 pages, 1 figure. References added, improved discussion. Final version published in EPJC. Typo corrected in Eq. (22)