Spin Correlation Phenomena in the ReactionN¯a+Nb→Y¯c+Yd

Abstract

Reactions of the type ${\overline{N}}_{a}+{N}_{b}\ensuremath{\rightarrow}{\overline{Y}}_{c}+{Y}_{d}$, where ${N}_{a}$ and ${N}_{b}$ are nucleons, and ${Y}_{c}$ and ${Y}_{d}$ are hyperons, occur with significant probabilities in the interactions of energetic antinucleons. Particular examples which have been studied recently are the reactions $\overline{p}+p\ensuremath{\rightarrow}\overline{\ensuremath{\Lambda}}+\ensuremath{\Lambda}, \overline{\ensuremath{\Lambda}}+{\ensuremath{\Sigma}}^{0}, {\overline{\ensuremath{\Sigma}}}^{0}+\ensuremath{\Lambda}, {\overline{\ensuremath{\Sigma}}}^{\ensuremath{-}}+{\ensuremath{\Sigma}}^{+}$. Pais has discussed some consequences for the reaction cross sections and the polarizations of the final particles of the presumed invariance of the relevant strong interactions under the parity and charge-conjugation operations. In the present paper, these considerations are extended to encompass two-particle spin correlations in the ${\overline{Y}}_{c}$, ${Y}_{d}$ system. Measurements of the correlation parameters would provide tests for charge conjugation, parity, and $\mathrm{CP}$ invariance in the strong interactions of strange particles, and could, in addition, be used to check the relation between antihyperon and hyperon decay asymmetry parameters predicted on $\mathrm{CPT}$ and $T$ invariance for the weak interactions, that ${\ensuremath{\alpha}}_{\overline{Y}}=\ensuremath{-}{\ensuremath{\alpha}}_{Y}$. Moreover, measurements of the spin correlation parameters would provide valuable information about the spin dependence of the reactions, hence, some tests for the models have been proposed for the reaction mechanism. Calculations by Bessis, Itzykson, and Jacob, and by Sopkovich using specific models suggest that the correlation parameters may be measurably large. We consider finally in an Appendix the relation between the Wolfenstein-Ashkin spin transition matrix which is used in the body of the paper, and the relativistic parametrization of the transition amplitude in the helicity representation. The general partial-wave expansions of the coefficient functions in the transition matrix are derived.