# An improved covariant treatment of the light mesons

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## Abstract

In an earlier paper a covariant version of the two-particle Dirac equation-employing a potential which was a function of the (invariant) proper separation-was used to fit the light meson quark-anti-quark bound states. This paper improves upon that work by introducing a better separation of the equation into internal and external coordinates, and a better separation into angular and radial coordinates. The new eigenvalue which arises from the introduction of hyperspherical harmonics is related to the meson energy in a more rigorous manner than before. As a result, the light meson trajectories can be better fit with fewer free parameters. In particular, the potential now has only Coulomb and linear terms, with no constant term, and current masses are used for the quarks rather than constituent masses. The reduction of the equation to Schrödinger form is discussed. It is shown how the non-relativistic reduction of the linear potential can lead to a constant term in the Schrödinger equation potential, as well as an enhancement of the Coulomb term. The resulting non-relativistic potential is similar to potentials used in successful fits of the charmonium spectrum.

## Keywords

Constant Term Linear Term Particle Acceleration Good Separation Covariant Treatment## Preview

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## References

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