Selected highlights from the study of mesons

TL;DR

This paper reviews recent advances in meson studies using Dyson-Schwinger equations, highlighting exact results, nonperturbative methods, and implications for understanding QCD phenomena like confinement and chiral symmetry breaking.

Contribution

It introduces a nonperturbative, symmetry-preserving Bethe-Salpeter kernel and demonstrates how dressed-quarks acquire momentum-dependent anomalous moments, advancing meson spectrum understanding.

Findings

Resolved the rho-a1 mass splitting as parity partners.

Demonstrated large infrared anomalous moments for dressed-quarks.

Provided insights into meson electromagnetic form factors and quark distribution functions.

Abstract

We provide a brief review of recent progress in the study of mesons using QCD's Dyson-Schwinger equations. Along the way we touch on aspects of confinement and dynamical chiral symmetry breaking but in the main focus upon: exact results for pseudoscalar mesons, including aspects of the eta-eta' problem; a realisation that the so-called vacuum condensates are actually an intrinsic, localised property of hadrons; an essentially nonperturbative procedure for constructing a symmetry-preserving Bethe-Salpeter kernel, which has enabled a demonstration that dressed-quarks possess momentum-dependent anomalous chromo- and electromagnetic moments that are large at infrared momenta, and resolution of a longstanding problem in understanding the mass-splitting between rho- and a1-mesons such that they are now readily seen to be parity partners in the meson spectrum; features of electromagnetic form factors connected with charged and neutral pions; and computation and explanation of valence-quark distribution functions in pseudoscalar mesons. We argue that in solving QCD, a constructive feedback between theory and extant and forthcoming experiments will enable constraints to be placed on the infrared behaviour of QCD's beta-function, the nonperturbative quantity at the core of hadron physics.