Hadron Properties and Dyson-Schwinger Equations

TL;DR

This paper reviews the application of Dyson-Schwinger equations to understanding hadron properties, emphasizing nonperturbative QCD phenomena like confinement, mass generation, and nucleon structure, with insights into mesons and nucleons.

Contribution

It provides a comprehensive overview of Dyson-Schwinger equations in hadron physics, highlighting new exact results and insights into confinement, mass, and nucleon structure within a nonperturbative QCD framework.

Findings

Exact results for pseudoscalar mesons related to the U_A(1) problem

Calculated masses of lightest J=0,1 hadron states

Analysis of quark orbital angular momentum contributions to nucleon spin

Abstract

An overview of the theory and phenomenology of hadrons and QCD is provided from a Dyson-Schwinger equation viewpoint. Following a discussion of the definition and realisation of light-quark confinement, the nonperturbative nature of the running mass in QCD and inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass are described. Some exact results for pseudoscalar mesons are also highlighted, with details relating to the U_A(1) problem, and calculated masses of the lightest J=0,1 states are discussed. Studies of nucleon properties are recapitulated upon and illustrated: through a comparison of the ln-weighted ratios of Pauli and Dirac form factors for the neutron and proton; and a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest. Comments on prospects for the future of the study of quarks in hadrons and nuclei round out the contribution.