  The dispersive analysis of the decay $\eta\to3\pi$ is reviewed and thoroughly
updated with the aim of determining the quark mass ratio
~$Q^2=(m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$. With the number of subtractions we are
using, the effects generated by the final state interaction are dominated by
low energy $\pi\pi$ scattering. Since the corresponding phase shifts are now
accurately known, causality and unitarity determine the decay amplitude within
small uncertainties -- except for the values of the subtraction constants. Our
determination of these constants relies on the Dalitz plot distribution of the
charged channel, which is now measured with good accuracy. The theoretical
constraints that follow from the fact that the particles involved in the
transition represent Nambu-Goldstone bosons of a hidden approximate symmetry
play an equally important role. The ensuing predictions for the Dalitz plot
distribution of the neutral channel and for the branching ratio
$\Gamma_{\eta\to3\pi^0}/ \Gamma_{\eta\to\pi^+\pi^-\pi^0}$ are in very good
agreement with experiment. Relying on a known low-energy theorem that relates
the meson masses to the masses of the three lightest quarks, our analysis leads
to $Q=22.1(7)$, where the error covers all of the uncertainties encountered in
the course of the calculation: experimental uncertainties in decay rates and
Dalitz plot distributions, noise in the input used for the phase shifts, as
well as theoretical uncertainties in the constraints imposed by chiral symmetry
and in the evaluation of isospin breaking effects. Our result indicates that
the current algebra formulae for the meson masses only receive small
corrections from higher orders of the chiral expansion, but not all of the
recent lattice results are consistent with this conclusion.
