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 slving the Bethe-Sapleter 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. (orig.)