Electromagnetic transitions in an effective chiral Lagrangian with the $\eta^{{\prime}}_{}$ and light vector mesons

Abstract

We consider the chiral Lagrangian with a nonet of Goldstone bosons and a nonet of light vector mesons. The mixing between the pseudoscalar mesons $\eta$ and $\eta^{\prime}$ is taken into account. A novel counting scheme is suggested that is based on hadrogenesis, which conjectures a mass gap in the meson spectrum of QCD in the limit of a large number of colors. Such a mass gap would justify to consider the vector mesons and the $\eta^{\prime}$ meson as light degrees of freedom. The complete leading-order Lagrangian is constructed and discussed. As a first application it is tested against electromagnetic transitions of light vector mesons to pseudoscalar mesons. Our parameters are determined by the experimental data on photon decays of the $\omega$ , $\phi$ and $\eta^{\prime}$ mesons. In terms of such parameters we predict the corresponding decays into virtual photons with either dielectrons or dimuons in the final state.