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Besides using the laser beam, it is very tempting to directly testify theBell inequality at high energy experiments where the spin correlation isexactly what the original Bell inequality investigates. In this work, we followthe proposal raised in literature and use the successive decays$J/\psi\to\gamma\eta_c\to \Lambda\bar\Lambda\to p\pi^-\bar p\pi^+$ to testifythe Bell inequality. Our goal is twofold, namely, we first make a Monte-Carlosimulation of the processes based on the quantum field theory (QFT). Since theunderlying theory is QFT, it implies that we pre-admit the validity of quantumpicture. Even though the QFT is true, we need to find how big the databaseshould be, so that we can clearly show deviations of the correlation from theBell inequality determined by the local hidden variable theory. There have beensome critiques on the proposed method, so in the second part, we suggest someimprovements which may help to remedy the ambiguities indicated by thecritiques. It may be realized at an updated facility of high energy physics,such as BES III.

Testing the Bell Inequality at Experiments of High Energy Physics