Neutrino oscillations in matter: from microscopic to macroscopic description

TL;DR

This paper rigorously derives the macroscopic neutrino evolution equation from microscopic principles, clarifying the conditions under which standard flavor oscillation models are valid in nonuniform and rarefied media.

Contribution

It provides the first explicit averaging procedure from microscopic to macroscopic neutrino evolution equations, clarifying the applicability of standard models.

Findings

Established the proper averaging method for microscopic potentials.

Defined the domain where standard neutrino oscillation equations are valid.

Analyzed neutrino propagation in rarefied media like interstellar space.

Abstract

Neutrino flavour transmutations in nonuniform matter are described by a Schr\"{o}dinger-like evolution equation with coordinate-dependent potential. In all the derivations of this equation it is assumed that the potential, which is due to coherent forward scattering of neutrinos on matter constituents, is a continuous function of coordinate that changes slowly over the distances of the order of the neutrino de Broglie wavelength. This tacitly assumes that some averaging of the microscopic potential (which takes into account the discrete nature of the scatterers) has been performed.The averaging, however, must be applied to the microscopic evolution equation as a whole and not just to the potential. Such an averaging has never been explicitly carried out. We fill this gap by considering the transition from the microscopic to macroscopic neutrino evolution equation through a proper averaging procedure. We discuss some subtleties related to this procedure and establish the applicability domain of the standard macroscopic evolution equation. This, in particular, allows us to answer the question of when neutrino propagation in rarefied media (such as e.g.\ low-density gases or interstellar or intergalactic media) can be considered within the standard theory of neutrino flavour evolution in matter.