Bound state in the vector channel of the extended Nambu-Jona-Lasinio modelat fixed f(pi)

We show that, as a consequence of fixings f(pi) = 93 MeV: (1) a bound state pole in the the J(P) = 1(-) scattering amplitude of the ENJL model exists f or arbitrarily weak (positive) vector coupling G(2) so long as the constitu ent quark mass is sufficiently large; (2) there is a bound state for any qu ark mass when G(2) greater than or equal to 0.6/(8f(pi)(2)); (3) this bound state becomes massless at G(2) = 1/(8(pi)(2)) and a tachyon for G(2) excee ding it. We show by way of an example that the model has no trouble fitting the rho meson mass simultaneously with other observables. (C) 1999 Publish ed by Elsevier Science B.V. All rights reserved.