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 $1/2+\overline{1/2}$, $1/2+\overline{3/2}$ ($+\mathrm{c}.\mathrm{c}.$) and $3/2+\overline{3/2}$. 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 $J/\psi$ 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 $e^{+}{e}^{-}\to \psi (2S)\to {\mathrm{\Omega }}^{-}{\overline{\mathrm{\Omega }}}^{+}$ 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.

Figure 1

Orientation of the axes in baryon $B_1$ and antibaryon ${\overline{B}}_2$ helicity frames.