Born-Oppenheimer Potentials for $SU(3)$ Gauge Theory

TL;DR

This paper develops parameterizations of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons in SU(3) gauge theory, fitting lattice results and capturing correct small and large separation behaviors.

Contribution

It introduces parameterizations of the lowest Born-Oppenheimer potentials for quarkonium hybrids based on lattice gauge theory data, with correct limiting behaviors.

Findings

Parameterizations match lattice data for SU(3) gauge theory.

Potentials exhibit correct small and large r limiting behaviors.

Identifies a narrow avoided crossing in the small-r region.

Abstract

We develop parameterizations of 8 of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation $r$ of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure $SU(3)$ lattice gauge theory. The parameterizations have the correct limiting behavior at small $r$, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large $r$, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-$r$ region between two potentials with the same Born-Oppenheimer quantum numbers.