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

Abstract

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 $m_u\ne m_d$ 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 $<\rho |H_{\rho \omega }|\omega >=[-(3956\pm 280)-(1697\pm 130)i]$MeV${}^2$, and isospin breaking parameter is $m_d-m_u=3.9\pm 0.22$MeV at energy scale $\mu \sim m_{\omega }$.

Comments: Revtex file, 16 pages, four eps figure