Parton distributions incorporating QED contributions

TL;DR

This work integrates O(α_QED) corrections into global parton analyses by modifying DGLAP evolution and introducing photon PDFs for the proton and neutron. The authors adopt a practical isospin-violating input at the initial scale, enabling a consistent NLO/NNLO fit that reveals small but significant effects on isospin symmetry and the NuTeV sin^2θ_W anomaly. They demonstrate that photon distributions can be generated and, in principle, measured at HERA via ep → eγX, with current data already providing consistency checks. The NNLO results show slight improvements and confirm that QED effects are non-negligible for precision phenomenology, particularly in electroweak corrections to hadron collider processes.

Abstract

We perform a global parton analysis of deep inelastic and related hard-scattering data, including ${\cal O}(α_{\rm QED})$ corrections to the parton evolution. Although the quality of the fit is essentially unchanged, there are two important physical consequences. First, the different DGLAP evolution of u and d type quarks introduces isospin violation, i.e. $u^p \neq d^n$, which is found to be unambiguously in the direction to reduce the NuTeV $\sin^2θ_W$ anomaly. A second consequence is the appearance of photon parton distributions $γ(x,Q^2)$ of the proton and the neutron. In principle these can be measured at HERA via the deep inelastic scattering processes $e N \to eγX$; our predictions are in agreement with the present data.

Figures (5)

• Figure 1: The ratio of valence quarks in the neutron and proton at the starting scale, $Q_0^2 = 1$ GeV$^2$, in the NLO global analysis, incorporating the isospin violation described by Eq. (\ref{['nstarting']}).
• Figure 2: The parton distributions in the proton at $Q^2=20\;\rm GeV^2$ obtained from the NLO pQCD $+$ LO QED global fit. The curves for the sea quarks correspond to the $\bar{u}$, $\bar{d}$, $s$, $c$ and $b$ distributions.
• Figure 3: The parton distributions in the neutron at $Q^2=20\;\rm GeV^2$ obtained from the NLO pQCD $+$ LO QED global fit. The curves for the sea quarks correspond to the $\bar{u}$, $\bar{d}$, $s$, $c$ and $b$ distributions.
• Figure 4: The difference between the isospin exchanged valence quarks in the proton and the neutron at $Q^2=20\;\rm GeV^2$.
• Figure 5: Schematic diagram for the deep inelastic scattering process $ep \to e\gamma X$, which displays the convolution of $\gamma^p$ and $\hat{\sigma}(e\gamma \to e\gamma)$ of (\ref{['sigamma1']}). Besides the $s$-channel diagram for $e\gamma \to e\gamma$ that is shown, there is also a contribution from the diagram with a virtual $u$-channel electron.