Duality, Exchange Degeneracy, and Regge-Cut Models inK−n→π−Λandπ+n→K+Λ

We investigate Regge-cut models in the hope of understanding the specific mechanism responsible for the difference between the differential cross sections and behavior of the polarizations for $K^{-}n\to {\pi }^{-}\Lambda$ and ${\pi }^{+}n\to K^{+}\Lambda$. We find that, although it is difficult to make any definite conclusions, Regge-Regge cuts probably do not produce large enough effects to be responsible for the observed differences between the differential cross sections. We find that a model with exchange degeneracy (EXD) of $K^{**}$ and $K^{*}$ poles plus an exchange-degenerate pair of daughter trajectories ($K^{**\prime }$ and $K^{*\prime }$) plus Pomeranchukon-Regge cuts gives an excellent fit to all the data for both $K^{-}n\to {\pi }^{-}\Lambda$ and ${\pi }^{+}n\to K^{+}\Lambda$. In this model duality is exact for the bare poles. The poles produce an amplitude that is purely real when the corresponding duality diagram is nonplanar. The Pomeranchukon-Regge cuts "break" the EXD of the bare poles. The polarization can be understood simply in terms of the interference between the Regge poles and the Pomeranchukon-Regge cuts. We display the calculated values of the differential cross-section slope parameter $b$ and the $A$ and $R$ parameters for $K^{-}n\to {\pi }^{-}\Lambda$ and ${\pi }^{+}n\to K^{+}\Lambda$.