Bell inequality, nonlocality and analyticity

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The Bell and the Clauser–Horne–Shimony–Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein–Podolsky–Rosen–Bohm experiments for spin 1 2 particles and photons, in both the deterministic and stochastic cases. Therefore, the theoretical and experimental violation of the inequalities by quantum mechanics excludes all hidden variables theories with that kind of nonlocality. In particular, real analyticity leads to negative definite correlations, in contradiction with quantum mechanics.