Glueballs, Constituent Gluons and Instantons

TL;DR

This paper develops a constituent two-gluon model for glueballs in pure Yang--Mills theory, incorporating instanton effects and confinement, and compares results with lattice data.

Contribution

It introduces a novel two-gluon framework with instanton-induced mass and forces, aligning with lattice results and explaining glueball properties.

Findings

The scalar $0^{++}$ glueball is very compact, about 1/3 fm in size.

The tensor $2^{++}$ glueball is more spatially extended due to centrifugal effects.

The model supports Regge behavior for excited states, consistent with lattice observations.

Abstract

We present a constituent two-gluon description of the lowest-lying glueball states in pure Yang--Mills theory, calibrated against quenched lattice results. The framework incorporates an instanton-induced dynamical gluon mass, Casimir-scaled adjoint confinement, the short-distance adjoint Coulomb interaction, and instanton-induced central and tensor forces. The scalar $0^{++}$ glueball is found to be exceptionally compact, with a radius of order the instanton size, $\rho \sim \frac 13\,\mathrm{fm}$, consistent with lattice indications. By contrast, the tensor $2^{++}$ state remains spatially extended due to the centrifugal barrier. We also discuss the role of $S$-$D$ mixing. A semiclassical analysis further supports Regge behavior for excited states, in agreement with lattice results.