Renormalization of the mass gap

TL;DR

This paper develops a renormalization procedure for the non-perturbative gluon propagator in QCD, clarifying how to handle infrared singularities and establishing gauge-invariant criteria for confinement.

Contribution

It provides a detailed renormalization framework for the intrinsically non-perturbative gluon propagator, enabling first-principles calculations in low-energy QCD.

Findings

Renormalization of the mass gap is precisely formulated.

Infrared singularities are correctly treated.

Gauge-invariant criteria for confinement are established.

Abstract

The full gluon propagator relevant for the description of the truly non-perturbative QCD dynamics, the so-called intrinsically non-perturbative gluon propagator has been derived in our previous work. It explicitly depends on the regularized mass gap, which dominates its structure at small gluon momentum. It is automatically transversal in a gauge invariant way. It is characterized by the presence of severe infrared singularities at small gluon momentum, so the gluons remain massless, and this does not depend on the gauge choice. In this paper we have shown how precisely the renormalization program for the regularized mass gap should be performed. We have also shown how precisely severe infrared singularities should be correctly treated. This allowed to analytically formulate the exact and gauge-invariant criteria of gluon and quark confinement. After the renormalization program is completed, one can derive the gluon propagator applicable for the calculation of physical observables processes, etc., in low-energy QCD from first principles.