Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments

Abstract

A large number of treatments of the meson spectrum have been tried that consider mesons as quark - anti quark bound states. Recently, we used relativistic quantum "constraint" mechanics to introduce a fully covariant treatment defined by two coupled Dirac equations. For field-theoretic interactions, this procedure functions as a "quantum mechanical transform of Bethe-Salpeter equation". Here, we test its spectral fits against those provided by an assortment of models: Wisconsin model, Iowa State model, Brayshaw model, and the popular semi-relativistic treatment of Godfrey and Isgur. We find that the fit provided by the two-body Dirac model for the entire meson spectrum competes with the best fits to partial spectra provided by the others and does so with the smallest number of interaction functions without additional cutoff parameters necessary to make other approaches numerically tractable. We discuss the distinguishing features of our model that may account for the relative overall success of its fits. Note especially that in our approach for QCD, the resulting pion mass and associated Goldstone behavior depend sensitively on the preservation of relativistic couplings that are crucial for its success when solved nonperturbatively for the analogous two-body bound-states of QED.

arXiv comment75 pages, 6 figures, revised contents

References in corpus (12)

• Observation of a Narrow Meson Decaying to Ds+pi0 at a Mass of 2.32 GeV/c^2
• q\bar q$ bound states in the Bethe-Salpeter formalism
• The relativistic two-body potentials of constraint theory from summation of Feynman diagrams
• Understanding the success of nonrelativistic potential models for relativistic quark-antiquark bound states
• Two-Body Dirac Equations for Nucleon-Nucleon Scattering
• A Tale of Three Equations: Breit, Eddington-Guant, and Two-Body Dirac
• How to obtain a covariant Breit type equation from relativistic Constraint Theory
• Relativistic Meson Spectroscopy and In-Medium Effects
• Singularity-Free Breit Equation from Constraint Two-Body Dirac Equations
• Covariant Quark-Representation of Composite Meson Systems and Chiral Symmetry
• Reduction of relativistic three-body kinematics
• Gauge transformations in relativistic two-particle constraint theory

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