NOVEL FEATURE OF THE VECTOR-MESON SOLUTION IN THE NAMBU-JONA-LASINIO MODEL

Based on the extended Nambu-Jona-Lasinio model, we study the meson spectrum, in particular, the vector-meson masses (1) by solving the Bethe-Salpeter equation and (2) by using a spectral-function method which has been recently proposed by several authors. The two approaches give very different behaviors of the vector mesons when the vector-channel attraction becomes too weak to support bound-state solutions. The solution of the Bethe-Salpeter equation changes smoothly from a bound state to a "virtual-state" solution reminiscent of an s-wave virtual state in the nonrelativistic potential problem. We discuss why this behaviour is missing in a spectral-function method used recently in the literature.