The spin structure of the qq interaction and the mass spectra of bound q(q)over-bar systems: different versions of the 3-dimensional reductions of the Bethe-Salpeter equation

摘要

Bound q-systems are considered in the framework of three different versions of the 3-dimensional reduction of the Bethe-Salpeter equation, all having the correct one-body limit when one of the constituent quark masses tends to infinity. The same systems are treated also in the framework of the Salpeter equation. The spin structure of confining qq interaction potential is taken in the form x gamma(1)(0) gamma(1)(0) + (1 - x)I1I2, with 0 less than or equal to x less than or equal to 1. The problem of existence (nonexistence) of stable solutions of 3-dimensional relativistic equations for bound q systems is investigated for different values of x from this interval. Some related aspects of this problem are discussed. (C) 1998 Published by Elsevier Science B.V. All rights reserved. References: 12