On the role of dynamical quark mass generation in chiral symmetry breaking in QCD

TL;DR

This paper investigates how dynamical quark mass generation influences chiral symmetry breaking in QCD, establishing exact relationships and solving the problem explicitly in two-dimensional QCD at large N_c.

Contribution

It introduces a gauge invariant formalism linking quark Green's functions and bound state equations, providing new insights into massless pseudoscalar solutions and chiral symmetry breaking.

Findings

Established an exact relationship between quark Green's function and bound state equations.

Identified a nontrivial solution indicating massless pseudoscalar states.

Explicitly solved the problem in 2D QCD at large N_c.

Abstract

The phenomenon of dynamical quark mass generation is studied in QCD within the framework of a gauge invariant formalism. An exact relationship is established between the equation satisfied by the scalar part of the two-point gauge invariant quark Green's function and the quark-antiquark bound state equation in the chiral limit. A possible nontrivial solution of the former yields a massless pseudoscalar solution of the bound state equation with vanishing total momentum. The result is also corroborated by the corresponding Ward-Takahashi identity. The problem is explicitly solved in two-dimensional QCD in the large-$N_c$ limit.