Semirelativistic potential model for three-gluon glueballs

TL;DR

This paper extends a semirelativistic potential model to study three-gluon glueballs, achieving good agreement with some lattice results and offering explanations for discrepancies in specific quantum sectors.

Contribution

It introduces a generalized potential model with three parameters for three-gluon glueballs, building on previous two-gluon models and addressing singularities in the potential.

Findings

Good agreement with lattice results for the odderon trajectory

Discrepancies with lattice in the $J^{+-}$ sector explained

Model parameters fixed from two-gluon glueball spectra

Abstract

The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Our results are in good agreement with other approaches and lattice calculation for the odderon trajectory but differ strongly from lattice in the $J^{+-}$ sector. We propose a possible explanation for this problem.