Chiral symmetry breaking in the truncated Coulomb Gauge II. Non-confining power law potentials

TL;DR

This study investigates chiral symmetry breaking caused by non-confining power-law potentials, especially near the Coulomb potential, revealing that symmetry breaking is driven by the UV part of the potential without IR enhancement.

Contribution

It analytically solves the mass-gap equation for non-confining potentials near Coulomb, identifying the conditions for chiral symmetry breaking and contrasting it with confining potentials.

Findings

Chiral symmetry breaking occurs only in specific vacua.

Breaking is driven by UV, not IR, parts of the potential.

Two vacua: chiral invariant false vacuum and a non-trivial vacuum.

Abstract

In this paper we study the breaking of chiral symmetry with non-confining power-like potentials. The region of allowed exponents is identified and, after the previous study of confining (positive exponent) potentials, we now specialize in shorter range non-confining potentials, with a negative exponent. These non-confining potentials are close to the Coulomb potential, and they are also relevant as corrections to the linear confinement, and as models for the quark potential at the deconfinement transition. The mass-gap equation is constructed and solved, and the quarks mass, the chiral angle and the quark energy are calculated analytically with a exponent expansion in the neighbourhood of the Coulomb potential. It is demonstrated that chiral symmetry breaking occurs, but only the chiral invariant false vacuum and a second non-trivial vacuum exist. Moreover chiral symmetry breaking is led by the UV part of the potential, with no IR enhancement of the quark mass. Thus the breaking of chiral symmetry driven by non-confining potentials differs from the one lead by confining potentials.