On flavor conservation in weak interaction decays involving mixed neutrinos

Abstract

In the context of quantum field theory (QFT), we compute the amplitudes of weak interaction processes such as $ W^{+} \rightarrow e^{+} + ν_{e}$ and $ W^{+} \rightarrow e^{+} + ν_μ$ by using different representations of flavor states for mixed neutrinos. Analyzing the short time limit of the above amplitudes, we find that the neutrino states defined in QFT as eigenstates of the flavor charges lead to results consistent with lepton charge conservation. On the contrary, the Pontecorvo flavor states produce a violation of lepton charge in the vertex, which is in contrast with what expected at tree level in the Standard Model.