QED corrections to parton distributions and Altarelli-Parisi splitting functions in the polarized case

Abstract

We discuss the effect of QED corrections in the evolution of polarized parton distributions. We solve the corresponding evolution equations exactly to $\mathcal{O}(\alpha )$ and $\mathcal{O}({\alpha }_s^2)$ in Mellin $N$-space, extending the available techniques for pure QCD evolution. To accomplish this, we introduce, for the first time, the Altarelli-Parisi polarized kernels at LO in QED. Furthermore, we perform a phenomenological analysis of the QED effects on polarized parton distributions (pPDFs), proposing different scenarios for the polarized photon density. Finally, we quantify the impact of the corresponding QED contributions to the polarized structure function $g_1$. We show that the relative corrections to both the pPDFs and the $g_1$ structure function are approximately at the few percent level, which is the order of magnitude expected considering the value of $\alpha$.

23 pages, 3 figures

References in corpus (15)

• Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs
• The Path to Proton Structure at One-Percent Accuracy
• Extraction of Spin-Dependent Parton Densities and Their Uncertainties
• A first unbiased global determination of polarized PDFs and their uncertainties
• How bright is the proton? A precise determination of the photon parton distribution function
• Evidence for polarization of gluons in the proton
• Global Analysis of Helicity Parton Densities and Their Uncertainties
• The Photon Content of the Proton
• The PDF4LHC21 combination of global PDF fits for the LHC Run III
• QCD Analysis of the Polarized World Data
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• Determination of gluon polarization from deep inelastic scattering and collider data
• Photon-initiated processes at high mass
• Analytical solutions of the QCD$\otimes$QED DGLAP evolution equations based on the Mellin transform technique in NLO approximation

Cited by in corpus (2)

• Probing the polarized photon content of the proton in $ep$ collisions at the EIC
• The polarized photon distribution function