Light quark mass ratio from Dalitz plot of $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay

Abstract

High statistics Dalitz-plot distribution of $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay obtained recently by KLOE collaboration \cite{kloe} is fitted to the results of corresponding theoretical calculations in Chiral Perturbation Theory (ChPT) with unitarity corrections taken into account. The quark mass ratio $Q=\sqrt{(m_s^2-(m_d+m_u{)}^2/4)/(m_d^2-m_u^2)}$ can be otained from this analysis. We get $Q=22.8\pm 0.4$ which differs from the value $Q_{DT}=24.2$ that follows from Dashen's theorem and agrees with recently calculated electromagnetic kaon mass difference.

2 pages, no figures