Microscopic foundations of the vector meson dominance model and the analysis of ρ-ω mixing

We use a momentum-space analysis of a generalized Nambu–Jona-Lasinio (NJL) model to provide a microscopic foundation for the vector-meson-dominance model. (In our model the photon interacts with the constituent quarks rather than with the hadrons.) A novel feature of our model is the introduction of ${\mathrm{q}}^2$-dependent meson decay constants, ${\mathrm{g}}^{\mathrm{\rho }}$ ${(\mathrm{q}}^2$) and ${\mathrm{g}}^{\mathrm{\omega }}$ ${(\mathrm{q}}^2$), as well as ${\mathrm{q}}^2$-dependent meson-meson coupling constants, such as ${\mathrm{g}}_{\mathrm{\rho }\mathrm{\pi }\mathrm{\pi }}$ ${(\mathrm{q}}^2$). We discuss the values of ${\mathrm{g}}^{\mathrm{\rho }}$ ${(\mathrm{q}}^2$), ${\mathrm{g}}^{\mathrm{\omega }}$ ${(\mathrm{q}}^2$), and ${\mathrm{g}}_{\mathrm{\rho }\mathrm{\pi }\mathrm{\pi }}$ ${(\mathrm{q}}^2$) obtained using our generalized NJL model, considering different choices for the parameters of the model. We also provide a quark-based description of ρ-ω mixing including the effects of direct ω→${\mathrm{\pi }}^{+}$+${\mathrm{\pi }}^{\mathrm{-}}$ decay. The definition of momentum-dependent meson decay constants allows us to introduce current correlation functions for the ρ and ω mesons into the analysis in an unambiguous manner, when we start with an analysis of hadronic current correlators that are expressed in terms of quark fields. A good fit is obtained for the pion form factor in the region where ρ-ω mixing is important.