Glueballs from the Bethe-Salpeter equation

TL;DR

This paper develops a continuum framework using the Bethe-Salpeter equation to calculate glueball masses in Landau gauge Yang-Mills theory, incorporating ghost effects and matching Dyson-Schwinger approximations.

Contribution

It introduces a novel Bethe-Salpeter approach for glueball mass calculation that includes ghost effects and aligns with Dyson-Schwinger equation approximations.

Findings

Scalar glueball mass agrees with lattice results

Framework successfully incorporates ghost effects

Provides a continuum method for glueball mass estimation

Abstract

We formulate a framework to determine the mass of glueball states of Landau gauge Yang-Mills theory in the continuum. To this end we derive a Bethe-Salpeter equation for two gluon bound states including the effects of Faddeev-Popov ghosts. We construct a suitable approximation scheme such that the interactions in the bound state equation match a corresponding successful approximation of the Dyson-Schwinger equations for the Landau gauge ghost and gluon propagators. Based upon a recently obtained solution for the propagators in the complex momentum plane we obtain results for the mass of the scalar and pseudoscalar glueballs. In the scalar channel we find a mass value in agreement with lattice gauge theory.