Leggett-Garg test inequality with spin and flavour neutrino oscillations in a constant magnetic field

The Leggett-Garg inequality (LGI), an analogue of Bellś inequality involving correlations of measurements of one observable on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. In this work, we investigate its implications in the context of neutrino flavour (${\nu }_e^L\leftrightarrow {\nu }_{\mu }^L$) and spin (${\nu }_e^L\leftrightarrow {\nu }_e^R$) oscillations in the presence of a constant transverse magnetic field. For systems with strong magnetic fields, we show that, for both cases, there are length regions $\mathrm{\Delta }L$ where the LGI is violated, as quantified by the correlator functions $K_3$ and $K_4$.