# Three-quark potentials in an $SU(3)$ effective Polyakov loop model

## TL;DR

This paper investigates three-quark potentials in a three-dimensional SU(3) gauge theory at finite temperature, using a Polyakov loop model to compare numerical results with analytical predictions and explore confinement-deconfinement transition features.

## Contribution

It provides a detailed numerical analysis of three-quark potentials in the Polyakov loop model, comparing with analytical predictions and examining the confinement transition.

## Key findings

- Three-quark potentials follow $ riangle$ and $Y$ laws.
- The $3q$ string tension is comparable to the $qar{q}$ string tension.
- Critical behavior across the deconfinement transition is characterized.

## Abstract

Three-quark potentials are studied in great details in the three-dimensional $SU(3)$ pure gauge theory at finite temperature, for the cases of static sources in the fundamental and adjoint representations. For this purpose, the corresponding Polyakov loop model in its simplest version is adopted. The potentials in question, as well as the conventional quark--anti-quark potentials, are calculated numerically both in the confinement and deconfinement phases. Results are compared to available analytical predictions at strong coupling and in the limit of large number of colors $N$. The three-quark potential is tested against the expected $\Delta$ and $Y$ laws and the $3q$ string tension entering these laws is compared to the conventional $q\bar{q}$ string tension. As a byproduct of this investigation, essential features of the critical behaviour across the deconfinement transition are elucidated.