# Symmetry, symmetry breaking, and pion parton distributions

## TL;DR

This paper calculates pion parton distribution functions using a symmetry-preserving continuum approach, revealing how dynamical chiral symmetry breaking influences the distributions and aligning with lattice QCD results.

## Contribution

It introduces a continuum framework that accurately captures pion parton distributions, incorporating symmetry preservation and dynamical chiral symmetry breaking effects.

## Key findings

- Valence-quark distribution hardens due to chiral symmetry breaking.
- Predicted momentum fractions at 2 GeV: valence 0.48, glue 0.41, sea 0.11.
- Results agree with lattice QCD calculations at 5.2 GeV.

## Abstract

Pion valence, glue and sea distributions are calculated using a continuum approach to the two valence-body bound-state problem. Since the framework is symmetry preserving, physical features of the distributions are properly expressed. The analysis reveals that the emergent phenomenon of dynamical chiral symmetry breaking causes a hardening of the valence-quark distribution function, ${q}^\pi(x)$. Nevertheless, this distribution exhibits the $x\simeq 1$ behaviour predicted by quantum chromodynamics (QCD). At the scale $\zeta_2:=2\,$GeV, the following momentum fractions are predicted: $\langle x_{\rm valence} \rangle = 0.48(3)$, $\langle x_{\rm glue} \rangle = 0.41(2)$, $\langle x_{\rm sea} \rangle = 0.11(2)$. Evolving to $\zeta=5.2\,$GeV, the result for ${q}^\pi(x)$ agrees with that computed using lattice QCD. These outcomes should both spur improved analyses of existing experiments and stimulate efforts to obtain new data on the pion distribution functions using available and envisioned facilities.