ΔI=1Mass Differences andη→3πDecay

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Abstract

The octet baryon $\ensuremath{\Delta}I=1$ mass shifts, kaon electromagnetic mass shift, and $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay amplitude are all correlated in the framework of the linear $\mathrm{SU} (3)$ $\ensuremath{\sigma}$ 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 $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ process, and the rare mode ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}3\ensuremath{\pi}$ 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.

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