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.

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

References in corpus (5)

• Parton distributions in the LHC era: MMHT 2014 PDFs
• Delineating parton distributions and the strong coupling
• On the Impact of Lepton PDFs
• Triple collinear splitting functions at NLO for scattering processes with photons
• Polarized triple-collinear splitting functions at NLO for processes with photons

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