Spin Density Matrix for ${\Omega }^{-}$ and its Polarization Alignment in $\psi (3686)\to {\Omega }^{-}{\bar{\Omega }}^{+}$

Abstract

We investigate the spin density matrix of ${\Omega }^{-}$ in the Cartesian coordinate system of baryon-antibaryon pairs produced in $e^{+}{e}^{-}$ annihilation. Using the helicity formalism of Jacob and Wick, we derive the expression for the spin-3/2 density matrices. Our analysis is based on the angular distribution of the process $e^{+}{e}^{-}\to \psi (3686)\to {\Omega }^{-}{\bar{\Omega }}^{+}$ in the BESIII experiment. By decomposing the polarization state of ${\Omega }^{-}$ particles along different coordinate axes, we examine the polarization dependence of the cross-section. Our results demonstrate that ${\Omega }^{-}$ particles exhibit varying degrees of tensor polarization along the x-, y-, and z-axes, as well as weak vector polarization and rank-3 tensor polarization along the y-axis. To our knowledge, this is the first study to calculate the polarization dependence of the cross-section distributions for the annihilation process $e^{+}{e}^{-}\to {\Omega }^{-}{\bar{\Omega }}^{+}$. Our theoretical predictions are in good agreement with the experimental measurements.

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Cited by in corpus (2)

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