Pion loop contribution to ? - ? 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 $\mathrm{q¯}q$ 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 ${\rho }^0$-$\omega$ 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.