Polarization observables in $e^{+}{e}^{-}$ annihilation to a baryon-antibaryon pair

Using the helicity formalism of Jacob and Wick we derive spin density matrices of baryon antibaryon pairs produced in $e^{+}{e}^{-}$ annihilation. We consider the production of pairs with spins $1\mathrm{/}2+\overline{1\mathrm{/}2}$, $1\mathrm{/}2+\overline{3\mathrm{/}2}$ (+c.c.) and $3\mathrm{/}2+\overline{3\mathrm{/}2}$. We provide modular expressions to include chains of weak hadronic two-body decays of the produced hyperons. The expressions are suitable for the analysis of high statistics data from $J\mathrm{/}\psi$ and $\psi (2S)$ decays at $e^{+}{e}^{-}$ colliders, by fits to the fully differential angular distributions of the measured particles. We illustrate the method by examples, such as the inclusive measurement of the $e^{+}{e}^{-}\to \psi (2S)\to {\mathrm{\Omega }}^{-}{\bar{\mathrm{\Omega }}}^{+}$ process where one decay chain ${\mathrm{\Omega }}^{-}\to \mathrm{\Lambda }{K}^{-}$ followed by $\mathrm{\Lambda }\to p{\pi }^{-}$ is considered. Finally we show that the inclusive angular distributions can be used to test spin assignment of the produced baryons.