$\omega -\rho$ Mixing and the $\omega \to \pi \pi \gamma$ Decay

Abstract

We reexamine the $\omega \to {\pi }^0{\pi }^0\gamma$ decay, adding the effect of $\omega -\rho$ mixing to the amplitude calculated with the aid of chiral perturbation theory and vector meson dominance. We predict the neutral decay to occur with a width of $\Gamma ($\omega \to \pi^{0} \pi^{0} \gamma $)=(390\pm 96)\mathrm{eV}$ and also analyze the effect of the $\omega -\rho$ mixing on the $\Gamma ($\omega \to \pi^{0} \pi^{0} \gamma $)/\Gamma ($\omega \to \pi^{+} \pi^{-} \gamma $)$ ratio. Several remarks on the effect of $\omega -\rho$ mixing on certain radiative decays of vector mesons are presented.

Comments: 10 pages, LaTeX, 1 ps-figure. Submitted to Phys. Rev. D