Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance

TL;DR

This paper develops a non-local gauge theory framework that reproduces key features of QCD, including confinement and chiral symmetry breaking, by deriving a non-local NJL model and analyzing its spectrum and gap equations.

Contribution

It introduces a novel non-local gauge theory approach with a complete Dyson--Schwinger equation set, extending previous techniques and demonstrating confinement and chiral symmetry breaking.

Findings

Spectrum aligns with lattice local results at large non-locality mass

Non-locality induces confinement and mass gap in the fermionic sector

The model reproduces key QCD features like chiral symmetry breaking

Abstract

We derive a Nambu--Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories, providing a set of Dyson--Schwinger equations in differential form. In the local case, we obtain closed form solutions in the simplest case of the scalar field and extend it to the Yang--Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang--Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson--Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive the gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g.,\ for quantum chromodynamics at lower energies.