Pion Loop Contribution to Rho-Omega Mixing and Mass Splitting

Abstract

We study the self-energy amplitudes for the rho-omega meson system produced by an effective field theory model at the quark level characterized by a finite range quark-quark interaction and an isospin breaking bare quark mass difference $m_u-m_d$. Dynamical effects associated with confinement and dressing of quarks and the finite size of the produced $\bar{q}q$ meson modes are treated. Parameters of this approach, previously constrained by soft pion physics, are here supplemented in a minimal way to reproduce $m_{\omega }$ and $g_{\rho \pi \pi }$. Calculations are carried out up to the one pion loop level and the predictions for rho-omega mixing, mass splitting, the rho width and the symmetry breaking omega-pi-pi coupling constant and form factor are presented. The contribution of the direct $\omega \to \pi \pi$ process relative to the $\omega \to \rho \to \pi \pi$ process is discussed within this model.

Comments: 30 pages, 10 figures, RevTeX document with PostScript figures, uuencoded