Leggett–Garg Test Inequality with Spin and Flavour Neutrino Oscillations in a Constant Magnetic Field

The Leggett–Garg inequality (LGI), an analogue of Bell’s 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 (\(\nu _{e}^{\rm L}\leftrightarrow \nu _{\mu }^{\rm L}\)) and spin (\(\nu _{e}^{\rm L}\leftrightarrow \nu _{e}^{\rm R}\)) 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 \(\Delta L\) where the LGI is violated, as quantified by the correlator functions \(K_3\) and \(K_4\). Abstract Published by the Jagiellonian University 2026 authors