Nonlinear iteration solution for the full gluon propagator as a function of the mass gap

TL;DR

This paper demonstrates that Quantum Chromodynamics (QCD) remains gauge invariant at a non-zero mass gap, and explores the structure of the gluon propagator with solutions indicating both massless and massive gluon states.

Contribution

It introduces a nonlinear iteration method to analyze the full gluon propagator as a function of the mass gap, revealing solutions with and without effective gluon mass.

Findings

Existence of two types of solutions for the gluon propagator.

Presence of a nonlinear iteration solution with massless gluons.

Demonstration of solutions with an effective gluon mass.

Abstract

We have explicitly shown that QCD is the color gauge invariant theory at non-zero mass gap as well. It has been defined as the value of the regularized full gluon self-energy at some finite point. The mass gap is mainly generated by the nonlinear interaction of massless gluon modes. All this allows one to establish the structure of the full gluon propagator in the explicit presence of the mass gap. In this case, the two independent general types of formal solutions for the full gluon propagator as a function of the regularized mass gap have been found. The nonlinear iteration solution at which the gluons remain massless is explicitly present. The existence of the solution with an effective gluon mass is also demonstrated.