# Ad Lucem: QED Parton Distribution Functions in the MMHT Framework

## TL;DR

This paper introduces the MMHT2015qed PDF set, incorporating QED corrections into parton distribution functions, including the photon PDF, and explores their implications for high-energy physics phenomenology.

## Contribution

It presents a new PDF set with QED effects, including the photon PDF, and details the methods for coupled QED and QCD evolution at various orders.

## Key findings

- Photon PDF consistent with recent sets
- QED corrections impact on other partons analyzed
- Photon-initiated processes affect high mass Drell-Yan fits

## Abstract

We present the MMHT2015qed PDF set, resulting from the inclusion of QED corrections to the existing set of MMHT Parton Distribution Functions (PDFs), and which contain the photon PDF of the proton. Adopting an input distribution from the LUXqed formulation, we discuss our methods of including QED effects for the full, coupled DGLAP evolution of all partons with QED at $\mathcal{O}(\alpha)$, $\mathcal{O}(\alpha\alpha_{S})$, $\mathcal{O}(\alpha^2)$. While we find consistency for the photon PDF of the proton with other recent sets, building on this we also present a set of QED corrected neutron PDFs and provide the photon PDF separated into its elastic and inelastic contributions. The effect of QED corrections on the other partons and the fit quality is investigated, and the sources of uncertainty for the photon are outlined. Finally we explore the phenomenological implications of this set, giving the partonic luminosities for both the elastic and inelastic contributions to the photon and the effect of our photon PDF on fits to high mass Drell-Yan production, including the photon--initiated channel.