The Mass Gap Approach to QCD. II. The non-perturbative renormalization program for the massive gluon fields

TL;DR

This paper develops a non-perturbative renormalization method for massive gluon fields in QCD, revealing how gluons can acquire mass dynamically while remaining confined, and analyzing their propagator properties.

Contribution

It introduces a new non-perturbative renormalization approach within the mass gap framework, enabling gluons to gain mass dynamically and addressing gauge and confinement issues.

Findings

Gluons can acquire mass dynamically without appearing as physical on-shell particles.

The full gluon propagator's asymptotic and mass-shell properties are thoroughly analyzed.

The approach ensures consistency with the massless limit and confinement in QCD.

Abstract

We present a non-perturbative multiplicative renormalization program for the massive gluon fields. This has been done within the previously formulated the mass gap approach to QCD. It is based on a new insights into its ground state true dynamical and gauge structures. Our approach makes it possible for gluons to acquire mass dynamically. The corresponding full gluon propagator has been investigated in full details. Its asymptotic properties have been analysed, including the perturbation theory limit. The peculiarities of the mass-shell structure of the full massive gluon propagator has been discussed. The inconsistency of the canonical gauge in QCD is fixed. Our approach does not allow the massive gluons to be the mass-shell objects. This prevents them to appear in the physical spectrum (confinement of massive gluon states). The massive gluons may exist in the vacuum or inside hadrons only. Expressions in Euclidean metric for the lattice simulations are also present. We have also shown that the massive solution has a correct limit to the free massless gluon propagator, when the exactly defined gluon pole mass is to be formally put zero.