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^2_s - (m_d + m_u)^2/4)/(m^2_d - m^2_u)} $ 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.