Kaon nonleptonic decays and chiral-symmetry breaking

A consistent formulation of current algebra and pion partial conservation of axial-vector current is given for the kaon nonleptonic weak decays $K\to 2\pi$ and $K\to 3\pi$. This includes evaluation of kaon $\sigma$ terms and $\Delta I=\frac{1}{2}$ and $\Delta I=\frac{3}{2}$ contributions to the weak current-current Hamiltonian. A large meson $\sigma$ term, ${\sigma }_{\mathrm{KK}}\sim 2{m_{\pi }}^2$, apparently is necessary to explain the $K_{2\pi }$ and $K_{3\pi }$ measured decay parameters. The hyperon nonleptonic decays are then reexamined and also shown to be compatible with a large value for ${\sigma }_{\mathrm{KK}}$. Implications for the (3,¯3) chiral-symmetry-breaking model and for octet dominance of the weak Hamiltonian are then discussed.