ΔI=1Mass Differences andη→3πDecay

The octet baryon $\Delta I=1\mathrm{}$ mass shifts, kaon electromagnetic mass shift, and $\eta \to 3\pi$ decay amplitude are all correlated in the framework of the linear $\mathrm{SU} \mathrm{}\left(3\right)\mathrm{}$ $\sigma$ model. It is shown how this model provides a natural realization of the "tadpole" idea of Coleman and Glashow. An attempt is made to resolve the long-standing mystery associated with the $\eta \to 3\pi$ process, and the rare mode ${\eta }^{\prime }\to 3\pi$ is also calculated. Finally, it is shown that the chiral-symmetry-breaking and isospin-nonconserving coefficients in the Lagrangian have the same order of magnitude.