# Short distance potential and the thick center vortex model

## TL;DR

This paper enhances the thick center vortex model to accurately describe short and long distance potentials between heavy SU(3) and SU(4) sources, capturing Coulombic, linear, and N-ality dependent behaviors.

## Contribution

It introduces vortex flux fluctuations and core size variations to the model, enabling a unified description of potentials across all distance regimes.

## Key findings

- Achieves Coulombic potential consistent with Casimir scaling.
- Restores linear potential in agreement with Casimir scaling.
- Reproduces large distance N-ality dependence.

## Abstract

The short distance potentials between heavy SU(3) and SU(4) sources are calculated by increasing the role of vortex fluxes piercing Wilson loops with contributions close to the trivial center element and by fluctuating the vortex core size in the model of thick center vortices. By this method, a Coulombic potential consistent with Casimir scaling is obtained. In addition, all other features of the potential including a linear intermediate potential in agreement with Casimir scaling and a large distance potential proportional to the $N$-ality of the representation are restored. Therefore, the model of thick center vortices may be used as a phenomenological model, which is able to describe the potential for all regimes.