Yang-Mills Propagators and QCD

TL;DR

This paper develops a strong coupling expansion method to analyze the infrared behavior of quantum field theories, specifically applying it to Yang-Mills theory and QCD, resulting in insights into the gluon propagator and low-energy spectrum.

Contribution

It introduces a novel strong coupling expansion approach for infrared quantum field theory and applies it to Yang-Mills and QCD, deriving the gluon propagator and low-energy effective Lagrangian.

Findings

Gluon propagator matches lattice results

Spectrum analysis supports glueball interpretation of $\sigma$ resonance

Derived low energy QCD Lagrangian reduces to a Nambu-Jona-Lasinio model

Abstract

We present a strong coupling expansion that permits to develop analysis of quantum field theory in the infrared limit. Application to a quartic massless scalar field gives a massive spectrum and the propagator in this regime. We extend the approach to a pure Yang-Mills theory obtaining analogous results. The gluon propagator is compared satisfactorily with lattice results and similarly for the spectrum. Comparison with experimental low energy spectrum of QCD supports the view that $\sigma$ resonance is indeed a glueball. The gluon propagator we obtained is finally used to formulate a low energy Lagrangian for QCD that reduces to a Nambu-Jona-Lasinio model with all the parameters fixed by those of the full theory.