Proton and pion distribution functions in counterpoint

TL;DR

This paper presents a unified set of predictions for proton and pion distribution functions at a common hadron scale, highlighting similarities and differences in their internal parton structures within QCD.

Contribution

It introduces a consistent framework for calculating all types of parton distribution functions for proton and pion using an all-orders exact evolution scheme based on an effective charge.

Findings

Proton and pion share the same light-front momentum fractions for partons at any scale.

Pion distribution functions are more dilated due to emergent hadron mass.

All distributions adhere to QCD constraints on scaling behaviour.

Abstract

Working with proton and pion valence distribution functions (DFs) determined consistently at the same, unique hadron scale and exploiting the possibility that there is an effective charge which defines an evolution scheme for DFs that is all-orders exact, we obtain a unified body of predictions for all proton and pion DFs - valence, glue, and four-flavour-separated sea. Whilst the hadron light-front momentum fractions carried by identifiable parton classes are the same for the proton and pion at any scale, the pointwise behaviour of the DFs is strongly hadron-dependent. All calculated distributions comply with quantum chromodynamics constraints on low- and high-$x$ scaling behaviour and, owing to emergent hadron mass, pion DFs are the most dilated. These results aid in elucidating the sources of similarities and differences between proton and pion structure.