Do we have enough evidence to invalidate the mean-field approximation adopted to model collective neutrino oscillations?

TL;DR

This paper critically examines the validity of the mean-field approximation for modeling collective neutrino oscillations in astrophysical environments, highlighting fundamental differences from many-body treatments and the limitations of current approaches.

Contribution

It demonstrates that common modeling assumptions, such as plane waves and finite neutrino numbers, lead to discrepancies between mean-field and many-body results, questioning the approximation's reliability.

Findings

Plane wave models differ significantly from wavepackets with finite size.

Mean-field includes only coherent scattering, unlike many-body which includes incoherent effects.

Finite neutrino numbers cause divergence in flavor evolution outcomes.

Abstract

Recent body of work points out that the mean-field approximation, widely employed to mimic the neutrino field within a neutrino-dense source, might give different results in terms of flavor evolution with respect to the correspondent many-body treatment. In this paper, we investigate whether such conclusions derived within a constrained framework should hold in an astrophysical context. We show that the plane waves, commonly adopted in the many-body literature to model the neutrino field, provide results that are crucially different with respect to the ones obtained using wavepackets of finite size streaming with a non-zero velocity. The many-body approach intrinsically includes coherent and incoherent scatterings. The mean-field approximation, on the other hand, only takes into account the coherent scattering in the absence of the collision term. Even if incoherent scatterings are included in the mean-field approach, the nature of the collision term is different from that in the many-body approach. Because of this, if only a finite number of neutrinos is considered, as often assumed, the two approaches naturally lead to different flavor outcomes. These differences are further exacerbated by vacuum mixing. We conclude that existing many-body literature, based on closed neutrino systems with a finite number of particles, is neither able to rule out nor assess the validity of the mean-field approach adopted to simulate the evolution of the neutrino field in dense astrophysical sources, which are open systems.