Analysis of the instantaneous Bethe-Salpeter equation for bound states

Abstract

We investigate the structure of the instantaneous Bethe-Salpeter equation for qq-bound states in the general case of unequal quark masses and develop a numerical scheme for the calculation of mass spectra and Bethe-Salpeter amplitudes. In order to appreciate the merits of the various competing models beyond the reproduction of the mass spectra we present explicit formulas to calculate electroweak decays. The results for an explicit quark model will be compared to experimental data in a subsequent paper [1].

Stability of the spectator, Dirac, and Salpeter equations for mesons

“…[4], but disagree with the results obtained by Parramore and Piekarewicz [3], who found the Salpeter equation to be unstable once the vector strength dropped below one-half, regardless of quark mass. However, as stated above, we find that the Salpeter equation is stable for a vector strength 0.4, and is even stable for a pure scalar interaction provided the quark mass is sufficiently large.…”

“…This seemed counter intuitive to us, since it is well known that, because of the famous Klein paradox, the Dirac equation is stable only when the potential is predominately scalar. Their result also contradicted the work of another group [4] who found that the Salpeter equation was stable for a pure scalar confining interaction, provided the quark mass was sufficiently large. …”

“…Any eigenstate wave function which describes a meson in momentum space, ψ(p, t), can be written 4) where E = √ µ 2 + P 2 . The discussion is simplified if the particle is chosen to be at rest, P = 0.…”

K0form factor and charge radius in a covariant Salpeter model

“…Starting from the Bethe-Salpeter equation, we use a qq -interaction assumed instantaneous in the rest frame of the bound state and free effective quark propagators to arrive at the Salpeter equation, which is expressed as an eigenvalue problem for the bound state mass and solved numerically [6]. In addition to the calculation of mass spectra we have presented there a method to reconstruct the four-dimensional Bethe-Salpeter amplitude from the equal-time Salpeter amplitudes.…”

“…In two previous papers [6,7] we presented a covariant quark model based on the Salpeter equation and used it to compute (transition) form factors between the light pseudoscalar and vector mesons [8]. This brief report shall serve as an extension of the latter to the neutral strange meson.…”