Non-Boltzmann behaviour in models of interacting neutrinos

TL;DR

This paper demonstrates that in certain solvable models of interacting neutrinos, two-particle correlations are significant and dominate the dynamics, challenging the adequacy of single-particle Boltzmann approximations even with multiple flavors.

Contribution

It provides an exact analysis showing the dominance of two-particle correlations in interacting neutrino models, highlighting limitations of the Boltzmann approximation.

Findings

Two-particle correlations are not small and dominate the evolution.

The failure of the Boltzmann approximation persists even with multiple flavors.

Correlations are significant despite rapid apparent equilibration.

Abstract

We reconsider the question of the relative importance of single particle effects and correlations in the solvable interacting neutrino models introduced by Friedland and Lunardini and by Bell, Rawlinson and Sawyer. We show, by an exact calculation, that the two particle correlations are not "small", and that they dominate the time evolution in these models, in spite of indications to the contrary from the rate of equilibration. This result holds even after the model in generalized from the original 2 flavor case to $N$ flavors. The failure of the Boltzmann single particle approximation in this model is tentatively attributed to the simplicity of the model, in particular to the assumption that all neutrinos in the initial state are in flavor eigenstates.