Constructing local composite operators for glueball states from a confining Gribov propagator

TL;DR

This paper constructs BRST invariant local operators for lightest glueball states using a confining Gribov gluon propagator, analyzing their correlation functions and mass ratios.

Contribution

It introduces a method to build local operators for glueballs within a confining gauge theory using a Gribov-type propagator, providing spectral analysis insights.

Findings

Correlation functions exhibit positive spectral densities.

Operators successfully encode quantum numbers of lightest glueballs.

Initial qualitative mass ratio analysis is presented.

Abstract

The construction of BRST invariant local operators with the quantum numbers of the lightest glueball states, $J^{PC}= 0^{++}, 2^{++}, 0^{-+}$, is worked out by making use of an Euclidean confining renormalizable gauge theory. The correlation functions of these operators are evaluated by employing a confining gluon propagator of the Gribov type and shown to display a spectral representation with positive spectral densities. An attempt to provide a first qualitative analysis of the ratios of the masses of the lightest glueballs is also discussed