String Baryon Model "Triangle": Hypocycloidal Solutions

TL;DR

This paper presents exact analytic solutions for a baryon model with three quarks connected by relativistic strings forming hypocycloidal shapes, classifying different rotational states and applying them to baryon Regge trajectories.

Contribution

It introduces new analytic solutions for a relativistic three-quark baryon model with string connections, describing hypocycloidal rotating configurations and their topological classifications.

Findings

Solutions describe hypocycloidal rotating curves for baryons.

Different topologies correspond to various baryon states.

Application to Regge trajectories links solutions to experimental baryon spectra.

Abstract

The considered model of baryon consists of three pointlike masses (quarks) bounded pairwise by relativistic strings forming a curvilinear triangle. Classic analytic solutions for this model corresponding to a planar uniform rotation about the system center of mass are found and investigated. These solutions describe a rotating curve composed of segments of a hypocycloid. The curve is a curvilinear triangle or --- a more complicated configuration with a set of internal massless points moving at the speed of light. Different topological types of these motions are classified in connection with different forms of hypocycloids in zero quark mass limit. An application of these solutions to description of baryon states on the Regge trajectories is considered.