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

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.