The stability of the spectator, Dirac, and Salpeter equations for mesons

Abstract

Mesons are made of quark-antiquark pairs held together by the strong force. The one channel spectator, Dirac, and Salpeter equations can each be used to model this pairing. We look at cases where the relativistic kernel of these equations corresponds to a time-like vector exchange, a scalar exchange, or a linear combination of the two. Since the model used in this paper describes mesons which cannot decay physically, the equations must describe stable states. We find that this requirement is not always satisfied, and give a complete discussion of the conditions under which the various equations give unphysical, unstable solutions.

References in corpus (3)

• A Bethe-Salpeter model for light mesons: spectra and decays
• Analysis of the instantaneous Bethe-Salpeter equation for \(q\bar{q}\)-bound-states
• On the Lorentz structure of the confinement potential

Cited by in corpus (8)

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• Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions
• Covariant Spectator Theory of heavy-light and heavy mesons and the predictive power of covariant interaction kernels
• Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation
• Stability in the instantaneous Bethe-Salpeter formalism: reduced exact-propagator bound-state equation with harmonic interaction
• Relativistic phenomenology of meson spectra with a covariant quark model in Minkowski space