Refined analysis of Ω - Ω<overline> + polarization in electron-positron annihilation process

We investigate the production of spin -3=2 hyperon pairs, S2- over bar S2+, 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 S2- over bar S2+ pairs. We present three sets of expressions to describe the decay of S2- hyperons, and further address the existing tension in the measurements of its decay parameters, particularly phi S2. 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.