Off-shell ρ-ω mixing through quark loops with a nonperturbative meson vertex and quark mass functions

Abstract

The momentum dependence of the off-shell ρ-ω mixing amplitude is calculated through a two-quark loop diagram, using nonperturbative meson-quark vertex functions for the ρ and ω mesons, as well as nonperturbative quark propagators. Both these quantities are generated self-consistently through an interlinked Bethe-Salpeter equation (BSE) cum Schwinger- Dyson equation (SDE) approach with a 3D support for the BSE kernel with two basic constants that are prechecked against a wide cross section of both meson and baryon spectra within a common structural framework for their respective 3D BSE's. With the precalibration, the on-shell strength works out at -2.434 δ(m_q²) in units of the change in "constituent mass squared," which is consistent with the e⁺e^- to π⁺π^- data for a u-d mass difference of 4 MeV, while the relative off-shell strength (0.99±0.01) lies midway between quark-loop and QCD-SR results. We also calculate the photon-mediated ρ-ω propagator whose off-shell structure has an additional pole at q²=0. The implications of these results vis-a-vis related investigations are discussed.