First study of the three-gluon static potential in lattice QCD

Abstract

We estimate the potential energy for a system of three static gluons in lattice QCD. This is relevant for the different models of three-body glueballs that have been proposed in the literature, either for gluons with a constituent mass, or for massless ones. A Wilson loop adequate to the static hybrid three-body system is developed. We study different spacial geometries, to compare the starfish model with the triangle model, for the three-gluon potential. We also study two different color structures, symmetric and antisymmetric, and compare the respective static potentials. A first simulation is performed in a ${24}^{3}\ifmmode\times\else\texttimes\fi{}48$ periodic Lattice, with $\ensuremath{\beta}=6.2$ and $a\ensuremath{\sim}0.072\text{ }\text{ }\mathrm{fm}$.