# Hybrid static potential flux tubes from SU(2) and SU(3) lattice gauge theory

## TL;DR

This study computes and compares flux densities for hybrid static potentials in SU(2) and SU(3) lattice gauge theories, revealing unique flux tube structures that resemble vibrating strings with localized peaks.

## Contribution

First numerical analysis of flux densities for seven hybrid static potentials in SU(2) and SU(3), including five studied for the first time.

## Key findings

- Hybrid flux tubes differ significantly from ordinary static potential tubes.
- Flux densities show localized peaks indicative of valence gluons.
- Hybrid flux tubes resemble vibrating strings.

## Abstract

We compute chromoelectric and chromomagnetic flux densities for hybrid static potentials in SU(2) and SU(3) lattice gauge theory. In addition to the ordinary static potential with quantum numbers $\Lambda_\eta^\epsilon = \Sigma_g^+$, we present numerical results for seven hybrid static potentials corresponding to $\Lambda_\eta^{(\epsilon)} = \Sigma_u^+, \Sigma_g^-, \Sigma_u^-, \Pi_g, \Pi_u, \Delta_g, \Delta_u$, where the flux densities of five of them are studied for the first time in this work. We observe hybrid static potential flux tubes, which are significantly different from that of the ordinary static potential. They are reminiscent of vibrating strings, with localized peaks in the flux densities that can be interpreted as valence gluons.