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

Abstract

The $\mathrm{SU}(3)$ Regge-pole theory, applied to $\ensuremath{\pi}N$ and $\mathrm{KN}$ interactions, is reinvestigated. With the simple constraints provided by the $\mathrm{SU}(3)$ relations on the scattering amplitudes, the relation among the $\ensuremath{\pi}N$ and $\mathrm{KN}$ charge-exchange differential cross sections is found to be $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}({K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{0}n)+\frac{d\ensuremath{\sigma}}{\mathrm{dt}}({K}^{+}n\ensuremath{\rightarrow}{K}^{0}p){|}_{\mathrm{same} E, t}=\frac{d\ensuremath{\sigma}}{\mathrm{dt}}({\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n)+\frac{3}{{{F}_{0}}^{2}}\frac{d\ensuremath{\sigma}}{\mathrm{dt}}({\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\eta}}^{0}n){|}_{\mathrm{same} E, t},$ where ${F}_{0}=1$ for the exact $\mathrm{SU}(3)$. 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 ${K}^{+}n\ensuremath{\rightarrow}{K}^{0}p$ is possible in a straightforward way.