Vector meson dominance and ρ-ω mixing

Abstract

The scale of a phenomenologically successful charge-symmetry-violating nucleon-nucleon interaction, that attributed to meson exchange with a ∆I = 1 rho-omega transition, is set by the Coleman-Glashow SU (2) breaking tadpole mechanism. A single tadpole scale has been obtained from symmetry arguments, electromagnetic meson and baryon measured mass splittings, and the observed isospin violating (∆I = 1) decay ω → π + π − . The hadronic realization of this tadpole mechanism lies in the I = 1 a 0 scalar meson. We show that measured hadronic and two-photon widths of the a 0 meson, with the aid of the Vector Meson Dominance model, recover the universal Coleman-Glashow tadpole scale.

The u–d quark mass difference and nuclear charge symmetry breaking

“…(8,9,10) which is close to the fitted baryon tadpole scale (H 3 tad ) p−n ≈ −2.5 MeV in (3). Both of these latter scales are reproduced in the alternative quark-loop scheme, and again result in the universal quark-loop ∆I = 1 transitions in eqs.…”

“…where g ρ ≈ 5.03 and g ω ≈ 17.05 (for e = √ 4πα ≈ 0.30282) follow from electron-positron decay rates [10,13]. The ω is 97% nonstrange and 3% strange so the ∆I = 1 transition between the physical particles is well described by the difference of the u − d polarization function…”

“…It was shown in Ref. [10] that the measured decays of the a • meson with the aid of the vector dominance model lead to g a•ρω = g a•πη NS . Then the tadpole term for the ρω transition is the same as the second term of (14), and the ρ • − ω effective Hamiltonian becomes …”

The contribution of the $ρ^0 - ω$ interference to the violation of the isospin invariance in the $πN$ system

“…In a 1997 review article on the ρ 0 −ω interference, O'Connell, Pearce, Thomas, and Williams [11], elaborating on their earlier ideas, established the 'mixedpropagator approach' as the means to determine the contributions of the ρ 0 −ω interference to the scattering amplitudes. However, the approach was criticised by Coon and Scadron [12], after they discovered that the violation of the charge symmetry, obtained in such an approach, is not consistent with the experimental results. The mixed-propagator approach was re-examined in a subsequent paper [14] and also found to be inconsistent, both in terms of the compatibility with effective Lagrangian models, as well as of the reproduction of the experimental data.…”

“…Since then, the interference between the two states has been investigated in a multitude of studies, e.g., see Refs. [7,8,9,10,11,12,13,14,15,16] (this list is not exhaustive).…”