Spin polarization and quantum entanglement of baryon-antibaryon pairs produced in electron-positron annihilation

Abstract

In this work, we systematically investigate the evolution of spin polarization and quantum entanglement in cascade decays of baryon-antibaryon pairs, which are produced in electron-positron annihilation. We derive a fully analytical spin density matrix explicitly expressed in terms of spin polarization observables, extend this formalism to multi-step cascade decay scenarios, and establish compact recursive relations to facilitate density matrix calculations for such processes. It is found that when maximal parity violation occurs during a decay, the resulting final-state particles are fully polarized and exist in a non-entangled state. Furthermore, we demonstrate that quantum entanglement amplification is a generic characteristic of charge-conjugate decays under $CP$ conservation when the initially produced baryon-antibaryon pair is polarized.

Figures (2)

• Figure 1: Definition of the coordinate system for the $e^+e^- \to B \bar{B}$ reaction in the center-of-mass frame. The $z$-axis is chosen along the momentum of the outgoing baryon $B$, and the $y$-axis is perpendicular to the scattering plane defined by $\vec{p}_1 \times \vec{k}_1$. The scattering angle $\theta$ is the polar angle between the incident electron momentum $\vec{k}_1$ and $\vec{p}_1$.
• Figure 2: Maximum entanglement amplification factor $Z_{\max}$ as a function of $\cos\theta$ for the final proton in the $J/\psi \to \Lambda\bar{\Lambda}$, $\Sigma^+ \bar{\Sigma}^-$, and $\Xi^- \bar{\Xi}^+$ processes with subsequent weak decays. $\Lambda\bar{\Lambda}$ (purple dash-dotted) with $\Lambda\to p\pi^-$, $\Sigma^+\bar{\Sigma}^-$ (green dashed) with $\Sigma^+\to p\pi^0$, $\Xi^-\bar{\Xi}^+$ (orange solid) with $\Xi^-\to\Lambda\pi^-$, and the multi-step cascade decays of the $\Xi^-\bar{\Xi}^+$ (black solid) with $\Xi^-\to \Lambda \pi^- \to p \pi^-\pi^-$. The corresponding charge-conjugate decays are implied.