Polarization analysis of ${\chi }_{cJ}$ decay into octet baryonic pairs

This work presents a comprehensive analysis of polarization transfer in the decays ${\chi }_{cJ}$ ($J=0,1,2$) to octet baryon-antibaryon pairs within a polarized electron-positron collision environment. Using the spin density matrix formalism, we trace the polarization from the initial beams through the production chain $e^{+}{e}^{-}\to \psi (2S)\to \gamma {\chi }_{cJ}$ to the final-state baryon-antibaryon system. The helicity amplitude analysis for ${\chi }_{c1}\to B\bar{B}$ confirms the universal angular distribution parameter $\alpha =-1\mathrm{/}3$, as dictated by the charge-conjugation helicity selection rule. For ${\chi }_{c2}$ decays, $\alpha$ and the transverse polarization depend on two independent amplitudes, and our quark-model calculations agree with existing data. We demonstrate that the longitudinal beam polarization $P_z$ modifies the spin observables for ${\chi }_{c1}$ and ${\chi }_{c2}$, offering new experimental handles at future polarized facilities like the Super $\tau$-Charm Facility(STCF) to test decay mechanisms and explore baryonic spin entanglement as a quantum information resource.