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

TL;DR

This paper investigates the flavor/mass dichotomy in mixed neutrino fields by analyzing neutron beta decay using different neutrino state representations, emphasizing lepton charge conservation to determine the most consistent framework.

Contribution

It demonstrates that only the QFT flavor states, defined as eigenstates of the flavor charge, are consistent with lepton charge conservation in neutron decay.

Findings

QFT flavor states are consistent with lepton charge conservation.

Pontecorvo and mass states contradict the Standard Model at short times.

Provides insight into neutrino mixing's role in weak decays.

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.