On the Lorentz structure of the confining potential in the instantaneous BetheSalpeter equation
Abstract
We investigate the Lorentz structure of the confining potential through a study of the meson spectrum using Salpeter's instantaneous approximation to the BetheSalpeter equation. The equivalence between Salpeter's and a randomphaseapproximation (RPA) equation enables one to employ the same techniques developed by Thouless, in his study of nuclear collective excitations, to test the stability of the solutions. The stability analysis reveals the existence of imaginary eigenvalues for a confining potential that transforms as a Lorentz scalar. Moreover, we argue that the instability persists even for very large values of the consitituent quark mass. In contrast, we find no evidence of imaginary eigenvalues for a timelike vector potential — even for very small values of the constituent mass.
 Publication:

Nuclear Physics A
 Pub Date:
 February 1995
 DOI:
 10.1016/03759474(94)00722Y
 arXiv:
 arXiv:nuclth/9402019
 Bibcode:
 1995NuPhA.585..705P
 Keywords:

 Nuclear Theory;
 High Energy Physics  Phenomenology
 EPrint:
 18 pages using RevTeX 3.0, with 8 figures available upon request, FSUSCRI9415