Two-loop QED corrections to the Altarelli-Parisi splitting functions

TL;DR

This paper calculates two-loop QED corrections to the Altarelli-Parisi splitting functions using an Abelianization approach, providing explicit results and analyzing their phenomenological impact.

Contribution

It introduces a novel method to derive QED corrections from QCD results and presents explicit two-loop QED splitting functions including leptonic distributions.

Findings

QED corrections significantly affect splitting functions

Explicit two-loop QED splitting kernels are provided

Phenomenological impact analyzed

Abstract

We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.