Spin density matrix for and its polarization alignment in * *Supported by the National Natural Science Foundation of China (12247121)

Abstract

We investigate the spin density matrix of in the Cartesian coordinate system of baryon-antibaryon pairs produced in 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 in the BESIII experiment. By decomposing the polarization state of particles along different coordinate axes, we examine the polarization dependence of the cross-section. Our results demonstrate that 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 the best of our knowledge, this is the first study to calculate the polarization dependence of the cross-section distributions for the annihilation process . Our theoretical predictions are in good agreement with the experimental measurements.