Isospin Breaking and $ω$->$ππ$ Decay

Abstract

We study $ω\toπ^+π^-$ 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 $m_u\neq m_d$ and electromagnetic interaction of mesons. We illustrate that in the formlism both nonresonant contact interaction and $ρ$ resonance exchange contribute to this process, and the contribution from $ρ$ resonance exchange is dominant. We obtain that transition matrix element is $<~ρ|H_{ρω}|ω>=[-(3956\pm 280)-(1697\pm 130)i]$MeV$^2$, and isospin breaking parameter is $m_d-m_u=3.9\pm 0.22$MeV at energy scale $μ\sim m_ω$.