Chiral-symmetry breaking, the Dashen mass formula, and the decayη→3π

The recently proposed extended partially conserved axial-vector current (EPCAC) hypothesis is used in order to obtain the chiral-SU(3) × SU(3)-symmetry-breaking corrections to (a) the Dashen mass formula, (b) the soft-meson theorem relevant to the $\eta \to 3\pi$ decay, and (c) the $\Delta I=1\mathrm{}$ baryon mass differences. It is found that the EPCAC hypothesis together with current algebra and an ${\epsilon }_3{u}_3$ term in the chiral Hamiltonian provides a working explanation for the $\eta \to 3\pi$ puzzle in the framework of the (3,$3^{*}$) + ($3^{*}$,3) model.