Off-Shell Rho-Omega Mixing Through Quark Loops With Non-Perturbative Meson Vertex And Quark Mass Functions

The momemtum dependence of the off-shell $\rho$-$\omega$ mixing amplitude is calculated through a two-quark loop diagram, using non-perturbative meson-quark vertex functions for the $\rho$ and $\omega$ mesons, as well as non-perturbative quark propagators. Both these quantities are generated self-consistently through an interlinked BSE-cum-SDE approach with a 3D support for the BSE kernel with two basic constants which are pre- checked against a wide cross section of both meson and baryon spectra within a common structural framework for their respective 3D BSE's. With this pre-calibration, the on-shell strength works out at -2.434$\delta(m_q^2)$ in units of the change in "constituent mass squared", which is consistent with the $e^+e^-$ to $\pi^+\pi^-$ data for a u-d mass difference of ~4 MeV ,while the relative off-shell strength (0.99 $\pm$ 0.01) lies midway between quark-loop and QCD-SR results. We also calculate the photon-mediated $\rho$-$\omega$ propagator whose off-shell structure has an additional pole at $q^2$=0. The implications of these results vis-a-vis related investigations are discussed.