The muon parton distribution functions

TL;DR

This paper calculates the unpolarised muon parton distribution functions, addressing scale evaluation issues and establishing a formalism that can be extended to higher logarithmic accuracy in QED and QCD.

Contribution

It introduces a novel approach for computing muon PDFs, handling scale issues, and setting up a formalism for higher-order accuracy in QED and QCD.

Findings

Computed muon PDFs for leptons, photon, quarks, and gluons.

Compared new approach with existing literature.

Framework ready for next-to-leading logarithmic accuracy.

Abstract

We compute the Parton Distribution Functions (PDFs) of the unpolarised muon for the leptons, the photon, the light quarks, and the gluon. We discuss in detail the issues stemming from the necessity of evaluating the strong coupling constant at scales of the order of the typical hadron mass, and compare our novel approach with those currently available in the literature. While we restrict our phenomenological results to be leading-logarithmic accurate, we set up our formalism in a way that renders it straightforward to achieve next-to-leading logarithmic accuracy in the QED, QCD, and mixed QED$\times$QCD contributions.