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.

8 pages, 5 figures, latex