Glueball-glueball scattering and the glueballonium

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.