Bound state in the vector channel of the extended Nambu–Jona–Lasinio model at fixed fπ

We show that, as a consequence of fixing fπ = 93 MeV: (1) a bound state pole in the the JP=1− scattering amplitude of the ENJL model exists for arbitrarily weak (positive) vector coupling G2 so long as the constituent quark mass is sufficiently large; (2) there is a bound state for any quark mass when G2≥0.6/(8fπ2); (3) this bound state becomes massless at G2=1/(8fπ2) and a tachyon for G2 exceeding it. We show by way of an example that the model has no trouble fitting the ρ meson mass simultaneously with other observables.