Three-flavoured neutrino oscillations and the Leggett–Garg inequality

Abstract

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

Keywords

• Neutrino Oscillation
• Quantum Domain
• Maximum Violation
• Neutrino Flavour
• Kaon