Refined analysis of ${\Omega }^{-}{\overline{\Omega }}^{+}$ polarization in electron-positron annihilation process

We investigate the production of spin-$3/2$ hyperon pairs, ${\Omega }^{-}{\overline{\Omega }}^{+}$, in electron-positron annihilation within the helicity formalism. A refined selection of helicity basis matrices is proposed to relate polarization expansion coefficients and spin density matrix elements and to illuminate their inherent physical interpretations and symmetrical properties. With a novel parametrization scheme of helicity amplitudes, we perform an analysis of polarization correlation coefficients for double-tag ${\Omega }^{-}{\overline{\Omega }}^{+}$ pairs. We present three sets of expressions to describe the decay of ${\Omega }^{-}$ hyperons, and further address the existing tension in the measurements of its decay parameters, particularly ${\varphi }_{\Omega }$. The method and the framework developed in this paper can also be applied to studies of the production and decay mechanisms of other spin-$3/2$ particles.