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

Abstract

We use a momentum-space analysis of a generalized Nambu{endash}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 {ital q{sup 2}}-dependent meson decay constants, {ital g{sup {rho}}(q{sup 2})} and {ital g{sup {omega}}(q{sup 2})}, as well as {ital q{sup 2}}-dependent meson-meson coupling constants, such as {ital g{sub {rho}{pi}{pi}}(q{sup 2})}. We discuss the values of {ital g{sup {rho}}(q{sup 2})}, {ital g{sup {omega}}(q{sup 2})}, and {ital g{sub {rho}{pi}{pi}}(q{sup 2})} obtained using our generalized NJL model, considering different choices for the parameters of the model. We also provide a quark-based description of {rho}-{omega} mixing including the effects of direct {omega}{r_arrow}{pi}{sup +}+{pi}{sup {minus}} decay. The definition of momentum-dependent meson decay constants allows us to introduce current correlation functions for the {rho} and {omega} 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 {rho}-{omega} mixing is important. {copyright} {ital 1997} {ital The American Physical Society}