Prueba de las desigualdades de Leggett-Garg en oscilaciones de sabor y espín de neutrinos en un campo magnético constante

Abstract

The Leggett-Garg (LG) inequalities, derived under the notion of macroscopic realism (MR), are a temporal analogue of the Bell inequalities and arise from our intuitions about the behavior of classical systems. Here, these inequalities are applied in the context of neutrinos in magnetic fields, which represents a suitable setup for studying aspects of quantum mechanics in the case of relativistic elementary particles. In this work, the assumptions of MR were reviewed and, as consequences of these assumptions, the LG inequalities were derived. Two simple examples were discussed: the coin as a classical object and the qubit. The Dirac equation was solved for neutrinos in the presence of a constant magnetic field, which allowed obtaining the transition probabilities for both flavor and spin oscillations. With these probabilities, the temporal correlations needed to evaluate the LG inequalities were calculated. The results show that these inequalities are violated in both types of oscillations when the electromagnetic properties of the neutrino are considered, with the flavor oscillation showing, for certain regions of the distance between measurements, a less pronounced violation in the magnetic field scenario compared to the vacuum case. For spin oscillation, it was determined that the violation is higher in the case where the neutrino mass-squared difference is considered null.