Three Flavoured neutrino oscillations and the Leggett Garg Inequality

Abstract: Three flavoured neutrino oscillations are investigated in the light of the Leggett-Garg inequality. The outline of an experimental proposal is suggested whereby the findings of this investigation may be verified. The results obtained are: (a) The maximum violation of the Leggett Garg Inequality (LGI) is $2.17036$ for neutrino path length $L_{1}=140.15 $ Km and $\Delta L=1255.7 $ Km.(b) Presence of the mixing angle $\theta_{13}$ enhances the maximum violation of LGI by $4.6\%$.(c) The currently known mass hierarchy parameter $\alpha = 0.0305$ increases the the maximum violation of LGI by $3.7\%$. (d)Presence of CP violating phase parameter enhances the maximum violation of LGI by $0.24\%$, thus providing an \textit{alternative indicator of CP violation} in 3-flavoured neutrino oscillations.