Neutrino Spectral Split in the Exact Many Body Formalism

TL;DR

This paper presents an exact many-body solution for neutrino interactions in supernovae, demonstrating a spectral split phenomenon consistent with mean field predictions but derived without approximation.

Contribution

It provides a novel exact many-body framework for neutrino spectral evolution, moving beyond the mean field approximation in supernova modeling.

Findings

Spectral split occurs at the same energy as mean field predictions.

Eigenstates do not undergo level crossings during evolution.

Initial states decompose into special many-body eigenstates.

Abstract

We consider the many-body system of neutrinos interacting with each other through neutral current weak force. Emerging many-body effects in such a system could play important roles in some astrophysical sites such as the core collapse supernovae. In the literature this many-body system is usually treated within the mean field approximation which is an effective one-body description based on omitting entangled neutrino states. In this paper, we consider the original many-body system in an effective two flavor mixing scenario under the single angle approximation and present a solution without using the mean field approximation. Our solution is formulated around a special class of many-body eigenstates which do not undergo any level crossings as the neutrino self interaction rate decreases while the neutrinos radiate from the supernova. In particular, an initial state which consists of electron neutrinos and antineutrinos of an orthogonal flavor can be entirely decomposed in terms of those eigenstates. Assuming that the conditions are perfectly adiabatic so that the evolution of these eigenstates follow their variation with the interaction rate, we show that this initial state develops a spectral split at exactly the same energy predicted by the mean field formulation.