Beam-polarization-enabled witness of four-dimensional entanglement in ${\Omega }^{-}{\bar{\Omega }}^{+}$ pairs

Abstract

We study the entanglement structure of ${\Omega }^{-}{\bar{\Omega }}^{+}$ pairs produced in $e^{+}{e}^{-}\to \psi (3686)$, focusing on whether the entanglement requires the full four-dimensional spin space of each spin-$3/2$ baryon. Beam polarization controls the parent-state populations and coherence, thereby modifying helicity interference. Using the negativity criterion $\Neg>1$ and the measured BESIII helicity parameters, we find critical polarizations of about $0.65$ per beam for equal transverse polarization and $0.57$ per beam for equal-and-opposite longitudinal polarization. Full transverse polarization gives a near-maximal peak negativity, $\Neg_{\rm peak}\simeq1.50$, with a production-rate-weighted angular fraction of $0.60$ satisfying the witness. At the optimal production directions, destructive interference removes the unequal-helicity channels, while the near equality of the relevant equal-helicity amplitudes yields nearly equal Schmidt coefficients. Constituent-quark benchmarks further show that the angular extent of the witness is more sensitive to relative phases than the peak negativity. These results link polarization-controlled helicity interference to four-dimensional entanglement in high-spin baryon production.

arXiv comment11 pages, 3 figures