On the flavor/mass dichotomy for mixed neutrinos: a phenomenologically motivated analysis based on lepton charge conservation in neutron decay

Abstract

Flavor/mass dichotomy} for mixed fields is one of the most controversial issues in Quantum Field Theory. In this work we approach the problem by considering mixing of neutrinos and computing the transition amplitude for the paradigmatic neutron $\beta$-decay $n\,\rightarrow\, p \,+\,e^ \,+\,\bar\nu$. Calculations are developed by utilizing the following different representations of neutrino states: \emph{i}) Pontecorvo states, \emph{ii}) mass states and \emph{iii}) exact QFT flavor states, which are defined as eigenstates of the flavor charge. As a guiding principle, we invoke the conservation of lepton charge in the interaction vertex, which is fundamentally inbuilt into the Standard Model at tree level. In the short-time limit, we show that the only fully consistent scenario is that based on QFT states, whereas the other two frameworks contradict the underlying theory. This result provides a crucial step towards understanding the r\^ole of neutrino mixing in weak decays and contributes to elucidate the flavor/mass controversy in QFT.