On the Mixed Propagator Approach to $\rho -\omega$ Mixing

Abstract

Mixed Propagator (MP) approach to $\rho-\omega$ mixing is discussed. It is found that under the pole-approximation assumption the results of MP approach is not compatible both with the effective Lagrangian theory and with the experiment measurement criterion. To overcome these inconsistent, we propose a new MP approach in which the physical states of $\rho$ and $\omega$ are determined by the requirement of experimental measurement to meson resonance. In terms of this new MP approach, the EM pion form factor $F_\pi$ and form factors of $\rho^0 \to \pi^0 \gamma$ and of $\omega \to \pi^0 \gamma$ are derived. The results of $F_\pi$ are in good agreement with data. The form factor of $\rho^0 \to \pi^0 \gamma$ exhibits a hidden charge-asymmetry enhancement effect which agree with the prediction of the effective Lagrangian theory.