Mixed QCD-QED corrections to DGLAP equations

TL;DR

This paper extends the DGLAP evolution equations to include mixed QCD and QED corrections at higher order, improving the accuracy of parton distribution functions and accounting for charge separation effects crucial for photon distribution analysis.

Contribution

It introduces the first calculation of mixed QCD-QED corrections to the DGLAP equations at ${\cal O}(\alpha \alpha_S^2)$, incorporating charge separation effects for the first time.

Findings

Extended splitting functions to higher order in QED.

Inclusion of charge separation effects in DGLAP equations.

Enhanced accuracy in photon distribution modeling.

Abstract

We study the mixed effect of QCD and QED corrections to the evolution of parton distribution functions (PDFs). The Altarelli-Parisi splitting functions are extended to one order higher in QED, reaching ${\cal O}(\alpha \, \alpha_S^2)$ accuracy. This also involves extending DGLAP equations to include charge separation effects, that are ignored for pure QCD corrections. Besides that, these effects are crucial for the determination of the photon distribution, which plays an increasingly important role in nowadays phenomenological analysis.