Cusp Phenomena in the Region of Two Neighboring Thresholds

Previous discussions of the cusp phenomena at the threshold for a new reaction are extended to the case of two neighboring thresholds. The $S$ matrix is constructed from an $n\times n$ $\kappa$ matrix in such a way as to ensure that the physical $S$ matrix is unitary when only $r$ of the $n$ channels are open. As a special application, the amplitude for the reaction ${\pi }^{-}+p\to {\Lambda }^0+K^0$ is studied in the region of the ${\Sigma }^{-}$ and ${\Sigma }^0$ thresholds.