Charge symmetry breaking via ϱω mixing from model quark-gluon dynamics

Abstract

The quark-loop contribution to the ρ 0 − ω mixing self-energy function is calculated using a phenomenologically successful QCD-based model field theory in which the ρ 0 and ω mesons are compositeqq bound states. In this calculation the dressed quark propagator, obtained from a model Dyson-Schwinger equation, is confining. In contrast to previous studies, the meson-qq vertex functions are characterised by a strength and range determined by the dynamics of the model; and the calculated off-mass-shell behaviour of the mixing amplitude includes the contribution from the calculated diagonal meson self-energies. The mixing amplitude is shown to be very sensitive to the small isovector component of dynamical chiral symmetry breaking. The spacelike quark-loop mixing-amplitude generates an insignificant charge symmetry breaking nuclear force.

Vector meson dominance and ρ-ω mixing

“…The data analysis of Ref. [18] suggests G ≈ 0.10, the coupled Dyson-Schwinger equations approach [20] finds a value five times smaller (G ≈ 0.017), and the generalized Nambu-Jona-Lasinio model [19] predicts a value which is a further factor of four smaller (G ≈ 0.004). The last very small ratio would make direct ω decay a relatively unimportant contribution to the calculation of ρ • −ω mixing from the data.…”

“…Furthermore, such a large value of ρ • |H em |ω is not consistent with the ∆I = 1 universal tadpole scale obtained in (17) with the aid of the Vector Meson Dominance (VMD) model. In view of the inconsistency with the global Coleman-Glashow picture and the limited support from quark based models [19,20] for a contact ω → 2π which violates G-parity, it is instructive to look at the analogue four-point contact term in the strong decay ω → 3π. This term was introduced on general grounds some time after the suggestion [35] that ω → ρπ → 3π will dominate the ω → 3π transition.…”

Model gluon propagator and pion and ρ-meson observables

“…This improves upon the results of Refs. [2][3][4][5], in which the quark propagator was parametrised and illustrates the connection, suggested in these articles, that may be made between hadronic observables and the quark-quark interaction.…”

“…This approach is reviewed in Ref. [1] and has recently been applied to the study of π-π scattering [2], the electromagnetic pion form factor [3], ρ-ω mixing [4] and the anomalous γ * π 0 → γ-transition form factor. [5] It is possible to obtain information about such Schwinger functions via a numerical simulation of a lattice-QCD action.…”

πandρmesons, and their diquark partners, from a contact interaction

“…Unsurprisingly, these are the just the circumstances under which a shift in integration variables is permitted, an operation required in order to prove Eq. (14).…”