Vector mesons from tensor couplings in the NJL model

We propose to describe vector mesons in a pure quark model such as the one of Nambu and Jona-Lasinio by means of four point tensor interactions, but with vanishing vector and axial couplings. This becomes possible due to tensor-vector mixing at the one quark loop level. As a consequence a bound particle with ρ quantum numbers is generated. This has the advantage of avoiding the A−π mixing which is known to generate a wrong off-shell pion wave function renormalization. In addition, there is no A1 meson. We make our arguments quantitative by computing Euclidean correlators via dispersion relations and comparing with lattice QCD and random instanton model results.