Mixed states for mixing neutrinos

TL;DR

This paper explores how flavor neutrinos produced or detected in processes involving multiple neutrinos require a density matrix description rather than pure states, and discusses the implications of neutrino mixing, including heavy neutrinos and scattering effects.

Contribution

It introduces a density matrix framework for flavor neutrinos in multi-neutrino processes and analyzes the effects of neutrino mass differences and mixing with heavy neutrinos.

Findings

Flavor neutrinos need density matrices for accurate description.

Pure flavor states are valid only when neutrino mass differences are neglected.

Mixing with heavy neutrinos can be decoupled or incoherent.

Abstract

Here we discuss the description of flavor neutrinos produced or detected in processes which involve more than one neutrino. We show that in these cases flavor neutrinos cannot be separately described by pure states, but require a density matrix description. We consider explicitly the examples of $\nu_{e}$ and $\bar\nu_{\mu}$ production in $\mu^{+}$ decay and $\nu_{\mu}$ detection through scattering on electrons. We show that the density matrix which describes a flavor neutrino can be approximated with a density matrix of a pure state only when the differences of the neutrino masses are neglected in the interaction process. In this approximation, the pure states are the standard flavor states and one recovers the standard expression for the neutrino oscillation probability. We discuss also the effects of mixing of the three standard light neutrinos with heavy neutrinos which can be either decoupled because their masses are much larger than the maximum neutrino energy in the neutrino production process or because they are produced and detected incoherently. Finally, we discuss the more complicated case of neutrino-electron elastic scattering, in which the initial and final neutrinos do not have determined flavors, but there is a flavor dependence due to the different contributions of charged-current and neutral-current interactions.