Test of local realism via entangled $$\Lambda \bar{\Lambda }$$ system

The non-locality of quantum correlations is a fundamental feature of quantum theory. The Bell inequality serves as a benchmark for distinguishing between predictions made by quantum theory and local hidden variable theory (LHVT). Recent advancements in photon-entanglement experiments have addressed potential loopholes and have observed significant violations of variants of Bell inequality. However, examples of Bell inequalities violation in high energy physics are scarce. In this study, we utilize (10.087 ± 0.044) × 10⁹ J/ψ events collected with the BES-III detector at the BEPCII collider, performing non-local correlation tests using the entangled hyperon pairs. The massive-entangled \(\Lambda \bar{\Lambda }\) systems are formed and decay through strong and weak interactions, respectively. Through measurements of the angular distribution of \(p\bar{p}\) in J/ψ → γη_c and subsequent \({\eta }_{c}\to \Lambda (p{\pi }^{-})\bar{\Lambda }(\bar{p}{\pi }^{+})\) cascade decays, a significant violation of LHVT predictions is observed. The exclusion of LHVT is found to be statistically significant at a level exceeding 5.2σ in the testing of three Bell-like inequalities.