Testing Bell's inequality using charmonium decays

Abstract

This paper discusses the feasibility of testing Bell's inequality with the charmonium decays $\eta _{\mathrm {c}} \rightarrow \Lambda \overline {\Lambda }$ , $\chi _{{\mathrm {c}}0} \rightarrow \Lambda \overline {\Lambda }$ and ${\mathrm {J}}/\psi \rightarrow \Lambda \overline {\Lambda }$ . We develop a new formulation of Bell's inequality represented with particles’ orientations, which can be measured straightforwardly in experiment, and seek to ascertain if it is violated in these decay processes. It is shown that the η_c channel and the $\chi _{c0}$ channel maximally violate Bell's inequality, while the ${\mathrm {J}}/\psi $ channel gives no inconsistency with it. Simulations dealing with experimental aspects are also implemented. The expected statistical fluctuations and achievable significance are estimated as a function of sample size.