Correlations between Cusps in Differential Cross Sections and in Polarizations

Experiments have shown that partial waves with $l>\mathrm{}1\mathrm{}$ appear in ${\pi }^{-}+p\to \Lambda +K^0$ at the $\Sigma K$ thresholds. This necessitates a reconsideration of the criteria sufficient to determine the $\Sigma \Lambda$ parity $P\left(\Sigma \Lambda \right)$ by the method of cusps. In this paper we start from the usual assumption that contributions which show a cusp in either the differential cross section or the polarization may be ignored beyond some optimal power in $cos\theta$. On this sole basis, previously stated criteria are rendered inadequate due to the occurrence of Minami and other ambiguities. It is shown that under suitable circumstances there exist unambiguous correlations between certain properties of cross-section cusps and of polarization cusps. These correlations could possibly be of use to determine $P\left(\Sigma \Lambda \right)$ and give information as to which states contribute significantly to the $\Lambda K$ production at ∼900 Mev. The finite separation between ${\Sigma }^0{K}^0$ and ${\Sigma }^{-}{K}^{+}$ thresholds is taken into account. The results are summarized in a table of cusp properties.