QED corrections to the Altarelli–Parisi splitting functions

Daniel De Florian,Germán Rodrigo,Germán F R Sborlini

doi:10.1140/epjc/s10052-016-4131-8

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.

Highlights

With the advent of the Run II of the Large Hadron Collider (LHC), a large number of processes will be probed within a formidable accuracy
We discussed the computation of the NLO mixed QCD–QED corrections to the Altarelli–Parisi evolution kernels
In order to reach that accuracy, we analyzed the colour structure of each diagram contributing to these corrections and evaluated their modification after a gluon is transformed into a photon

Summary

Introduction

With the advent of the Run II of the Large Hadron Collider (LHC), a large number of processes will be probed within a formidable accuracy. The splitting functions that run the evolution of parton distributions are known at NNLO in QCD [1,2,3,4]. Modern analysis, performed up to NNLO in QCD and LO in QED show that the photon PDF contribution is not negligible and needs to be carefully studied for precise predictions at the LHC, and even more for higher energies as the FCChh [16,17,18,19]. Concerning hadronic cross-sections, a full NNLO contribution in the context of QCD + QED requires the knowledge of the kernels presented in this paper to perform the subtraction of IR singularities and define the corresponding factorization scheme at this order.

Splitting kernels and parton distribution basis

QCD–QED splitting kernels

C A eq2 2

Conclusions