On the very nature of neutrinos: the $beta$-decay as a test bench

We discuss the role of neutrino mixing in the context of the neutron β-decay. Calculations are performed for both static and accelerated neutrons. The lepton charge conservation in the neutrino production/detection vertices, which is expected in the tree level approximation of the Standard Model, is taken as our starting point. On this basis, we manage to show that the correct way to describe the emitted (anti-)neutrino is by use of flavor (rather than mass) eigenstates, confirming previous results in the literature.