Hadron Correlators and the Structure of the Quark Propagator

TL;DR

This paper proposes an Ansatz for the quark propagator in QCD, linking it to hadron correlators and exploring implications for confinement, symmetries, and lattice QCD calculations.

Contribution

It introduces a novel Ansatz for the quark propagator and analyzes its implications for hadron correlators and confinement mechanisms in QCD.

Findings

Exotic components of the propagator can lead to symmetry violations if not vanishing.

Restrictions on gauge field configurations are derived from symmetry considerations.

Lattice QCD can be used to analyze the microscopic structure of confinement.

Abstract

The structure of the quark propagator of $QCD$ in a confining background is not known. We make an Ansatz for it, as hinted by a particular mechanism for confinement, and analyze its implications in the meson and baryon correlators. We connect the various terms in the K\"allen-Lehmann representation of the quark propagator with appropriate combinations of hadron correlators, which may ultimately be calculated in lattice $QCD$. Furthermore, using the positivity of the path integral measure for vector like theories, we reanalyze some mass inequalities in our formalism. A curiosity of the analysis is that, the exotic components of the propagator (axial and tensor), produce terms in the hadron correlators which, if not vanishing in the gauge field integration, lead to violations of fundamental symmetries. The non observation of these violations implies restrictions in the space-time structure of the contributing gauge field configurations. In this way, lattice $QCD$ can help us analyze the microscopic structure of the mechanisms for confinement.