Glueball-glueball scattering and the glueballonium

TL;DR

This paper investigates glueball-glueball scattering and the potential formation of a stable bound state called glueballonium using a dilaton potential model, predicting its properties and suggesting lattice tests for validation.

Contribution

It introduces a unitarization approach to predict glueball scattering and bound states within a dilaton potential framework, providing testable lattice predictions.

Findings

A stable glueballonium can form if the parameter $\\Lambda_G$ is sufficiently small.

The predicted glueballonium mass is approximately 3.4 GeV for parameters consistent with the gluon condensate.

The study offers a way to test the dilaton potential model through lattice calculations.

Abstract

The scalar glueball $G$ is the lightest particle of the Yang-Mills sector of QCD, with a lattice predicted mass of about $m_{G}\simeq1.7$ GeV. It is natural to investigate glueball-glueball scattering and the possible emergence of a bound state, that we call glueballonium. We perform this study in the context of a widely used dilaton potential, that depends on a single dimensionful parameter $\Lambda_G$. We consider a unitarization prescription that allows us to predict the lowest partial waves in the elastic window. These quantities can be in principle calculated on the lattice, thus offering possibility for testing the validity of the dilaton potential and an independent determination of its parameter. Moreover, we also show that a stable glueballonium exists if $\Lambda_{G}$ is small enough. In particular, for $\Lambda_{G}$ compatible with the expectations from the gluon condensate, the glueballonium has a mass of about $3.4$ GeV.