QED corrections to the evolution of parton distributions

TL;DR

Problem: precisely predicting hadronic observables requires including electroweak (QED) corrections in the scale evolution of parton distributions. Approach: derive a QCD+QED DGLAP framework with an enlarged parton basis, separate kernels into QCD and QED parts, use Mellin-space evolution, and implement two bases to limit mixing. Contributions: show mixing among Delta_UD, Sigma, g, gamma, and Sigma_l, and quantify QED effects in a four-flavor toy model, finding corrections up to ~1% at large x that grow with Q. Impact: demonstrates that QED corrections are competitive with NNLO QCD in precision regimes and should be included in global fits with realistic initial conditions.

Abstract

We study the systematic inclusion of QED corrections in the evolution of parton distributions. O(alpha) corrections modify the evolution equation for parton distributions. They introduce additional parton distributions, like the photon distribution in the nucleon, and lead to additional mixing effects. We discuss the modifications for a realistic model of N_f,up up-type flavours and N_f,down down-type flavours. We have implemented these corrections into a numerical program and we quantify the size of these effects in a toy model. The corrections reach the order of 1%.

Figures (1)

• Figure 1: Difference in per cent due to QED effects of the $u$-quark, $d$-quark and gluon parton distributions as a function of $x$ for $Q=100{\,\mathrm{GeV}}$ (l.h.s.) and as a function $Q$ for $x=0.1$ (r.h.s.).