Pion loop contribution toρ-ωmixing and mass splitting

Abstract

We study the self-energy amplitudes for the $\ensuremath{\rho}$-$\ensuremath{\omega}$ 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 ${m}_{u}\ensuremath{-}{m}_{d}.$ Dynamical effects associated with confinement and dressing of quarks and the finite size of the produced $\mathrm{q\ifmmode\bar\else\textasciimacron\fi{}}q$ meson modes are treated. Parameters of this approach, previously constrained by soft pion physics, are here supplemented in a minimal way to reproduce ${m}_{\ensuremath{\omega}}$ and ${g}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}.$ Calculations are carried out up to the one-pion-loop level and the predictions for ${\ensuremath{\rho}}^{0}$-$\ensuremath{\omega}$ mixing, mass splitting, the $\ensuremath{\rho}$ width and the symmetry breaking $\ensuremath{\omega}\ensuremath{\pi}\ensuremath{\pi}$ coupling constant and form factor are presented. The contribution of the direct $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ process relative to the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ process is discussed within this model.