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The Leggett-Garg inequality (LGI) as a temporal analogue of Bell'sinequality, derived using the notion of realism, is applied in a hithertounexplored context involving the weak interaction induced two-stateoscillations of decaying neutral kaons and neutrinos. The maximum violation ofLGI obtained from the quantum mechanical results is significantly higher forthe oscillating neutrinos compared to that for the kaons. Interestingly, theeffect of CP non-invariance for the kaon oscillation is to enhance thisviolation while, for neutrinos, it is sensitive to the value of the mixingparameter.

Probing the Leggett-Garg Inequality for Oscillating Neutral Kaons and Neutrinos