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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 BSEs. 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.
An improved quark mass density- dependent model with the non-linear scalar sigma field and the $omega$-meson field is presented. We show that the present model can describe saturation properties, the equation of state, the compressibility and the eff
We construct the two loop Greens functions for a quark bilinear operator inserted at non-zero momentum in a quark 2-point function for the most general off-shell configuration. In particular we consider the quark mass operator, vector and tensor curr
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