Isospin Breaking and $\omega$->$\pi \pi$ Decay

We study $\omega \to {\pi }^{+}{\pi }^{-}$ decay up to including all orders of the chiral expansion and one-loop level of mesons in formlism of chiral constituent quark model. This G-parity forbidden decay is caused by $m_u\mathrm{\ne }{m}_d$ and electromagnetic interaction of mesons. We illustrate that in the formlism both nonresonant contact interaction and $\rho$ resonance exchange contribute to this process, and the contribution from $\rho$ resonance exchange is dominant. We obtain that transition matrix element is $<\rho \mathrm{\mid }{H}_{\rho \omega }\mathrm{\mid }\omega >=[-(3956\pm 280)-(1697\pm 130)i]$MeV${}^2$, and isospin breaking parameter is $m_d-m_u=3.9\pm 0.22$MeV at energy scale $\mu\sim m_\omega$.