Current-quark mass ratios fromη→3π

Abstract

Recent data for the $\eta$ meson, together with the $\rho$-dominance assumption for the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ amplitude, are used to estimate the mass-matrix element accounting for the $\eta -\pi$ mixing, ${m_{\eta \pi }}^2=-(4.2\mathrm{}\pm 1.0)\times {10}^{-3\mathrm{}}$ ${\mathrm{GeV}}^2$. From this value one easily obtains $r_{-}\equiv \frac{(m_d-m_u)}{2m_s}=0.013\mathrm{}\pm 0.003$, where $m_q$ are current-quark masses and $r_{-}$ measures the SU(2)- compared to SU(3)-symmetry breaking.