Two particle states, lepton mixing and oscillations

Abstract

Discussions of lepton mixing and oscillations consider generally only flavor oscillations of neutrinos and neglect the accompanying charged leptons. In cases of experimental interest like pion or nuclear beta decay an oscillation pattern is expected indeed only for neutrinos if only one of the two produced particles is observed. We argue that flavor oscillations of neutrinos without detecting the accompanying lepton is a peculiarity of the two-particle states $|l\nu>$ produced in pion or nuclear beta decay. Generally, an oscillation pattern is only found if both particles are detected. We discuss in a pedagogical way how this distinction of the neutrinos arises, although on the level of the Lagrangian lepton mixing does not single them out against charged leptons. As examples, we discuss the difference between the state $|l\nu>$ produced by the decay of real $W$ boson and a $W$ originating from pion decay.