Excluding Local Hidden Variables in $\Lambda\bar{\Lambda}$ Production: The Incompatibility with Angular-Momentum Conservation and CPT Invariance

TL;DR

This paper compares quantum field theory predictions with local hidden-variable theories for spin entanglement in $\\Lambda\bar{\Lambda}$ pairs, showing fundamental incompatibilities with local realism under certain conditions and proposing experimental tests.

Contribution

It demonstrates that LHVTs respecting locality and angular momentum conservation cannot reproduce QFT predictions for scalar production, and identifies conditions under which LHVTs can mimic QFT in pseudoscalar production.

Findings

LHVTs cannot reproduce QFT distributions for scalar production respecting locality.

CPT-symmetric LHVTs are excluded by positivity constraints in pseudoscalar production.

Relaxing CPT symmetry allows LHVTs to match QFT results under specific response function conditions.

Abstract

We analyze spin entanglement in $\Lambda\bar{\Lambda}$ 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 $\Lambda \to p\pi^-$ and $\bar{\Lambda} \to \bar{p}\pi^+$, we derive the joint angular distributions within QFT. Our key findings are: For scalar production $h \to \Lambda\bar{\Lambda}$, no LHVT respecting locality and angular-momentum conservation can reproduce the QFT distribution. For pseudoscalar production $a \to \Lambda\bar{\Lambda}$, 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 $b_1 c_1 = 3\alpha_{\Lambda}\alpha_{\bar{\Lambda}}$, can match the QFT result. These distinct signatures provide clear, experimentally testable criteria to discriminate between QFT and LHVT in $\Lambda\bar{\Lambda}$ systems across different production mechanisms.