Observability of glueball spectrum in QCD and the width of $\sigma$ resonance

TL;DR

This paper proves a theorem in QCD showing that in the strong coupling limit, the observed glueball spectrum matches that of pure Yang-Mills theory, and it computes the width of the sigma resonance as the lowest glueball state.

Contribution

It establishes a theorem relating the glueball spectrum in QCD to pure Yang-Mills theory at strong coupling and provides a full effective theory including sigma resonance decay width.

Findings

Glueball spectrum matches pure Yang-Mills in strong coupling limit

Computed decay width of the sigma resonance

Calculated vacuum gluon condensate supporting glueball identification

Abstract

We prove a theorem in QCD stating that in the limit of strong coupling, $g\to\infty$, the observed spectrum of glueballs in QCD is the same of a pure Yang-Mills theory, being mixing effects due to the next-to-leading order. A full effective theory for QCD is obtained and the width of the $\sigma$ resonance decay is straightforwardly computed. This appears as the lowest glueball state. Vacuum gluon condensate is computed that consistently support studies on the identification of this meson as a glueball.