Spin density matrix of baryon-antibaryon pairs in electron-positron annihilation with $P$ and $CP$ violation including electron mass

In the center-of-mass frame, the spin density matrix for octet baryon-antibaryon pairs produced in polarized electron-positron annihilation is unambiguously determined within the one-photon-exchange approximation. The formalism simultaneously incorporates parity ($P$) and combined parity-charge conjugation ($CP$) violation arising from the coupling of the intermediate virtual photon to the baryon pair. The finite electron mass is explicitly accounted for as a correction to these $P$ and $CP$ violating effects. Built on the spin projection operator, the derived full and compact spin density matrix provides a natural starting point for evaluating other quantities of physical interest – particularly angular distributions of sequential decays and the quantum entanglement of hyperon pairs.