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 $\mu \sim m_{\omega }$.

Revtex file, 16 pages, four eps figure

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Cited by in corpus (8)

• Molecular States and 1^-+ Exotic Mesons
• A study of $\rho -\omega$ mixing in resonance chiral theory
• Asymmetry of Strange Sea in Nucleons
• Momentum-dependence of $\rho -\omega$ mixing in the pion vector form factor and its effect on $(g-2{)}_{\mu }$
• A note on the mass splitting of K*(892)
• Resummation Studies on Vector Meson Decays and Chiral Symmetry Spontaneously Breaking in Chiral Constituent Quark Model
• Strange sea asymmetry in nucleons
• Status of the $D_s^{+}\to \varphi {\ell }^{+}{\nu }_{\ell }$ decay with a chiral-odd $\varphi$-meson light-cone distribution amplitude