Excluding Local Hidden Variables in $Λ\barΛ$ Production: The Incompatibility with Angular-Momentum Conservation and CPT Invariance

TL;DR

This work investigates spin entanglement in $\Lambda\bar{\Lambda}$ pairs produced by scalar and pseudoscalar decays, contrasting quantum-field-theory (QFT) predictions with local hidden-variable theories (LHVTs) under locality, angular-momentum conservation, and CPT invariance. By deriving the fully differential joint angular distributions for the cascades $\Lambda(\to p\pi^-)\bar{\Lambda}(\to \bar{p}\pi^+)$ in the parent decays $h\to\Lambda\bar{\Lambda}$ and $a\to\Lambda\bar{\Lambda}$, the authors identify two sharp results: the scalar channel cannot be reproduced by any LHVT obeying locality and angular-momentum conservation, and the pseudoscalar channel cannot be reproduced by a CPT-symmetric LHVT, although a CPT-violating LHVT can be constructed to match the QFT result. The analysis bridges symmetry, kinematics, and hidden-variable descriptions, providing explicit models and nonnegativity considerations that translate into experimentally testable criteria. The findings offer a clear route for discriminating between QFT and LHVT in baryon systems and motivate measurements of the joint angular distributions across production mechanisms at BESIII, Belle II, and the LHC. The work thus sharpens the foundations of quantum nonlocality in the baryon sector and guides future tests of CPT and locality in high-energy processes.

Abstract

We analyze spin entanglement in $Λ\barΛ$ pairs produced in the decays of scalar ($h$) and pseudoscalar ($a$) particles, contrasting predictions from quantum field theory (QFT) with those of local hidden-variable theories (LHVTs). Using the self-analyzing weak decays $Λ\to pπ^-$ and $\barΛ \to \bar{p}π^+$, we derive the joint angular distributions within QFT. Our key findings are: For scalar production $h \to Λ\barΛ$, no LHVT respecting locality and angular-momentum conservation can reproduce the QFT distribution. For pseudoscalar production $a \to Λ\barΛ$, a CPT-symmetric LHVT is excluded by positivity constraints given the measured analyzing powers; however, if CPT symmetry is relaxed, an explicit LHVT construction, with uniform hidden-variable measure and response functions satisfying $b_1 c_1 = 3α_Λα_{\barΛ}$, can match the QFT result. These distinct signatures provide clear, experimentally testable criteria to discriminate between QFT and LHVT in $Λ\barΛ$ systems across different production mechanisms.