Momentum-space analysis of relativistic two-body equations with confining interactions: Stability considerations

Quark-antiquark bound states are considered using a relativistic equal-time (ET) equation for two spin-1/2 particles that includes negative-energy components of wave functions. In the limit where either particle close-quote s mass tends to infinity, the ET equation reduces to the one-body Dirac equation. The use of a scalar confining interaction in the ET equation is found to produce imaginary eigenvalues for the bound-state energy, similar to the findings based on the Salpeter equation. Retardation effects predict a modified static interaction in which couplings to doubly negative components of the wave function vanish. This modified static interaction eliminates the imaginary eigenvalues. However, the modified analysis can produce abnormal solutions with a large relative momentum between the quark and antiquark when used with a scalar confining interaction. Anomalous negative-energy components of wave functions result when a timelike vector confining interaction is used for equal-mass quarks. In the one-body limit, the Klein instability occurs with timelike vector confinement. For stability without regard to the type of confinement, the negative-energy components of wave functions should be omitted. copyright 1999 The American Physical Society