On the validity of the reduced Salpeter equation

Abstract

We adapt a general method to solve both the full and reduced Salpeter equations and systematically explore the conditions under which these two equations give equivalent results in meson dynamics. The effects of constituent mass, angular momentum state, type of interaction, and the nature of confinement are all considered in an effort to clearly delineate the range of validity of the reduced Salpeter approximations. We find that for $J\ne 0$ the solutions are strikingly similar for all constituent masses. For zero angular momentum states the full and reduced Salpeter equations give different results for small quark mass especially with a large additive constant coordinate space potential. We also show that $\frac{1}{m}$ corrections to heavy-light energy levels can be accurately computed with the reduced equation.

arXiv commentLatex (uses epsf macro), 24 pages of text, 12 postscript figures included. Slightly revised version, to appear in Phys. Rev. D

References in corpus (3)

• On the instantaneous Bethe-Salpeter equation
• On the Lorentz structure of the confinement potential
• Weak Decays of Heavy Mesons in the Instantaneous Bethe Salpeter Approach

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• Stability in the instantaneous Bethe-Salpeter formalism: reduced exact-propagator bound-state equation with harmonic interaction
• Exact-propagator instantaneous Bethe-Salpeter equation for quark-antiquark bound states