Gauge invariant bound state equations for quark-antiquark systems in QCD

TL;DR

This paper develops gauge invariant bound state equations for quark-antiquark systems in QCD using path-ordered phase factors and Wilson loop averages, providing insights into chiral symmetry breaking.

Contribution

It introduces two compatible Dirac-type bound state equations for quark-antiquark pairs with kernels defined via Wilson loops, advancing gauge invariant formulations in QCD.

Findings

Derived bound state equations using gauge invariant Green's functions.

Established a criterion linking chiral symmetry breaking to the quark Green's function.

Connected Goldstone boson wave functions with the scalar part of the quark Green's function.

Abstract

Using gauge invariant quark Green's functions, defined with path-ordered gluon field phase factors along polygonal lines, and functional relations among them, two compatible bound state equations of the Dirac type are established for quark-antiquark systems, each relative to the quark or to the antiquark of the system. The kernels of the bound state equations are defined through a series of Wilson loop averages along closed polygonal contours and their functional derivatives on them. A sufficient criterion for spontaneous chiral symmetry breaking is derived, relating the Goldstone boson wave function in the zero total momentum limit with the scalar part of the gauge invariant quark two-point Green's function.