Patterns of Broken Chiral Symmetry in Quantum Chromodynamics

TL;DR

This paper investigates the realization of chiral symmetry modes in zero-temperature QCD, showing conditions under which different symmetry patterns occur and ruling out certain modes without specific beta function behavior.

Contribution

It clarifies the conditions for chiral symmetry realization in QCD, including the vector mode and the screening of axial-vector charges, based on the behavior of the beta function.

Findings

SU_(L+R)(N_F) exhibits the vector mode as conjectured by Georgi.

SU_(L-R)(N_F) is realized in Nambu-Goldstone or screened mode.

Wigner-Weyl mode is excluded unless the beta function has an infrared stable zero.

Abstract

We establish that in Quantum Chromodynamics (QCD) at zero temperature, SU_(L+R)(N_F) exhibits the vector mode conjectured by Georgi and SU_(L-R)(N_F)is realized in either the Nambu-Goldstone mode or else the axial-vector charge is also screened from view at infinity. The Wigner-Weyl mode is ruled out unless the beta function in QCD develops an infrared stable zero.