Boson-Pole Model inK-Meson andη-Meson Decays

Abstract

The direct term of the decay mode $K\to \pi +\pi +\gamma$ and the decay amplitudes $K\to \pi +\pi +\pi$ and $\eta \to \pi +\pi +\pi$ are obtained on the basis of the boson-pole model to all orders in the strong interaction, provided the interaction (except for the weak vertex) is S${\mathrm{U}}_3$-invariant. The weak vertex is assumed to transform as K°. Then all $K\to \pi +\pi +\gamma$ modes, except ${K_2}^0\to {\pi }^{+}{\pi }^{-}\gamma$, and all $K\to \pi +\pi +\pi$ and $\eta \to \pi +\pi +\pi$ modes, except ($\eta |{\pi }^{+}{\pi }^{-}{\pi }^0$), are shown to vanish. It is concluded that the boson-pole model together with unitary symmetry is untenable for $K\to 3\pi$ decay modes.