Neutral Vector Mesons and the Hadronic Electromagnetic Current

The question of whether the entire hadronic electromagnetic current operator can be identical with a linear combination of the renormalized field operators for the known neutral vector mesons ${\rho }^0$, ${\phi }^0$, and ${\omega }^0$ is investigated in the context of a Lagrangian field theory. It is found that such an identity is completely consistent with gauge invariance, provided that these mesons are coupled only to conserved currents. The general renormalization problem of the strong interactions of these vector mesons is discussed. It is shown that the proposed identity between the hadronic electromagnetic current and the renormalized meson fields can be related to the possible identity between the unrenormalized currents generating the neutral vector mesons and those generating the photon; furthermore, this proposed identity leads to an exact relation between the entire $O\left(e^2\right)$ hadronic contribution to the photon propagator and the renormalized propagators of the neutral vector mesons, and such a relation implies, among other consequences, that to $O\left(e^2\right)$ and neglecting leptonic contributions, the ratio of the unrenormalized charge $e_0$ and the renormalized charge $e$ is finite. Various experimental applications are given. In particular, the analysis of $\phi -\omega$ mixing and their leptonic decay rates is made independently of the approximate validity of the $S{U}_3$ symmetry.