Broken Chiral Symmetry and theηMeson

Abstract

The scheme of broken chiral symmetry given by Gell-Mann, Oakes, and Renner is generalized to include the $\ensuremath{\eta}$ meson with proper consideration of the octet-singlet mixing. It is shown that at least one of the $\ensuremath{\eta}$ and the ${\ensuremath{\eta}}^{\ensuremath{'}}$ must violate the partially conserved axial-vector current (PCAC) condition (or Adler's condition). This is not simply because they are much heavier than the pion. The analysis of the decays $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}2\ensuremath{\gamma}$, which are known for large deviations from the simple $S{U}_{3}$ predictions, indicates that PCAC for the $\ensuremath{\eta}$ is violated rather severely.