Hybrid static potentials in SU(3) lattice gauge theory at small quark-antiquark separations

TL;DR

This study computes hybrid static potentials in SU(3) lattice gauge theory at very small quark-antiquark separations, providing data and parametrizations useful for predicting heavy hybrid mesons.

Contribution

It presents the first lattice data for hybrid static potentials at separations as small as 0.08 fm, with systematic errors carefully analyzed and parametrizations provided for future applications.

Findings

Hybrid static potentials computed at separations down to 0.08 fm.

Systematic errors from topological freezing, finite volume, and glueball decays are analyzed and excluded.

Parametrizations of potentials suitable for Born-Oppenheimer predictions are provided.

Abstract

We compute the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials in SU(3) lattice gauge theory using four different lattice spacings ranging from $a = 0.040\,\text{fm}$ to $a = 0.093\,\text{fm}$. We provide lattice data points for quark-antiquark separations as small as $0.08\, \text{fm}$, where the $a$-dependent self-energy as well as lattice discretization errors at tree-level of perturbation theory and at leading order in $a^2$ have been removed. We also investigate and exclude possibly present systematic errors from topological freezing, due to the finite spatial lattice volume and from glueball decays. Moreover, we provide corresponding parametrizations of the potentials, which can e.g. be used for Born-Oppenheimer predictions of heavy hybrid mesons.