Baryon Spectrum Analysis using Dirac's Covariant Constraint Dynamics

TL;DR

This paper develops a relativistically covariant three-body framework using Dirac's constraint dynamics to analyze the baryon spectrum, incorporating two-body potentials and comparing results with experimental data.

Contribution

It introduces a novel three-body relativistic formalism for baryons based on Dirac's constraint dynamics, integrating two-body interactions into a covariant three-body equation.

Findings

Accurate baryon energy spectra obtained using the formalism.

Good agreement with experimental baryon spectra.

Effective use of multiple algorithms for parameter fitting.

Abstract

The energy spectrum of the baryons is determined by treating each of them as a three-body system with the interacting forces coming from a set of two-body potentials that depend on both the distance between the quarks and the spin and orbital angular momentum coupling terms. Constraint dynamics is first reviewed for a relativistic two-body system in order to assemble the necessary two body framework for the three-body problem and then we review the different types of covariant two-body interactions involved in constraint dynamics, including vector and scalar, and solve the problem of energy eigenstates using constraint dynamics. The Two Body Dirac equations of constraint dynamics derived by Crater and Van Alstine, matched with the quasipotential formalism of Todorov as the underlying two-body formalism are used, as well as the three-body constraint formalism of Sazdjian to integrate the three two-body equations into a single relativistically covariant three body equation for the bound state energies. The results are analyzed and compared to experiment using a best fit method and several different algorithms, including a gradient approach, and Monte Carlo method.