Baryon masses in the three-state Potts field theory in a weak magnetic field

TL;DR

This paper calculates the masses of light baryons in the 3-state Potts field theory under weak magnetic fields, revealing how confinement leads to bound states of kinks in a two-dimensional lattice model.

Contribution

It introduces a method to compute light baryon masses in the weak confinement regime using a three-body quantum problem approach.

Findings

Masses of light baryons are obtained numerically.

Confinement causes kinks to form bound states.

Results enhance understanding of non-perturbative effects in lattice models.

Abstract

The 3-state Potts field theory describes the scaling limit of the 3-state Potts model on the two-dimensional lattice near its continuous phase transition point. In the presence of thermal and magnetic field perturbations, the 3-state Potts field theory in the ordered phase exhibits confinement of kinks, which allows both mesons and baryons. We calculate the masses of light baryons in this model in the weak confinement regime in leading order of the small magnetic field. In leading order of perturbation theory, the light baryons can be viewed as bound states of three quantum particles - the kinks, which move on a line and interact via a linear potential. We determine the masses of the lightest baryons by numerical solution of the associated non-relativistic one-dimensional quantum three-body problem.