Relation among theπNandKNCharge-Exchange Differential Cross Sections from theSU(3)Regge-Pole Theory

The $\mathrm{SU}\left(3\right)\mathrm{}$ Regge-pole theory, applied to $\pi N$ and $\mathrm{KN}$ interactions, is reinvestigated. With the simple constraints provided by the $\mathrm{SU}\left(3\right)\mathrm{}$ relations on the scattering amplitudes, the relation among the $\pi N$ and $\mathrm{KN}$ charge-exchange differential cross sections is found to be $\frac{d\sigma }{\mathrm{dt}}(K^{-}p\to {\overline{K}}^{0}n)+\frac{d\sigma }{\mathrm{dt}}(K^{+}n\to K^{0}p){|}_{\mathrm{same} E, t}=\frac{d\sigma }{\mathrm{dt}}({\pi }^{-}p\to {\pi }^{0}n)+\frac{3}{{F_0}^2}\frac{d\sigma }{\mathrm{dt}}({\pi }^{-}p\to {\eta }^{0}n){|}_{\mathrm{same} E, t},$ where $F_0=1\mathrm{}$ for the exact $\mathrm{SU}\left(3\right)\mathrm{}$. However, $F_0$ can be allowed to deviate from 1, and on the basis of the fit to the experimental data, we find that $F_0$ is not far away from 1. From the above relation, a prediction for $K^{+}n\to K^{0}p$ is possible in a straightforward way.