Hadron Mass Spectra

Hadrons are universally considered quantum bound states of quarks. Employing the language of the direct product of O(3), SU(2), and SU(3) we can obtain an understanding of this spectra. Even though O(3) is not Lorentz-invariant, the little group for massive particle is locally isomorphic to O(3). Indeed, O(3) of the quark model is a manifestly relativistic concept. We shall start with non-relativistic models in the Lorentz frame in which the hadron is at rest. Among those models, the three-dimensional isotropic harmonic oscillator serves many useful purposes, as the harmonic oscillator formalism is mathematically simple, can be made relativistic, and the formalism readily accommodates three-particle kinematics and symmetry properties. The formalism contains the O(3) symmetry. Here, we see whether there is evidence in the mass spectrum data for the existence of the harmonic oscillator excitations. Specifically, we study the (mass) \(^2\) spectrum. The harmonic oscillator excitations should create an equal-spaced spectrum. To examine this linearity, at least three levels, including the ground state are needed. This is possible for non-strange baryons which are bound states of three quarks. Therefore, we go through the process of three-particle symmetry classification. We study mesons and conclude with a short summary of particles which are not hadrons.