Extended evolution equations for neutrino propagation in astrophysical and cosmological environments

TL;DR

This paper develops extended evolution equations for neutrino flavor conversion in astrophysical and cosmological environments, incorporating neutrino-antineutrino pairing correlations beyond the mean-field approximation.

Contribution

It introduces a theoretical framework based on the BBGKY hierarchy to include pairing correlations in neutrino evolution equations, extending beyond standard mean-field models.

Findings

Derived extended evolution equations including pairing correlations.

Revealed potential impacts of neutrino-antineutrino correlations on flavor conversion.

Framework applicable to multiple neutrino flavors.

Abstract

We derive the evolution equations for a system of neutrinos interacting among themselves and with a matter background, based upon the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. This theoretical framework gives an (unclosed) set of first-order coupled integro-differential equations governing the evolution of the reduced density matrices. By employing the hierarchy, we first rederive the mean-field evolution equations for the neutrino one-body density matrix associated with a system of neutrinos and antineutrinos interacting with matter and with an anisotropic neutrino background. Then, we derive extended evolution equations to determine neutrino flavor conversion beyond the commonly used mean-field approximation. To this aim we include neutrino-antineutrino pairing correlations to the two-body density matrix. The inclusion of these new contributions leads to an extended evolution equation for the normal neutrino density and to an equation for the abnormal one involving the pairing mean-field. We discuss the possible impact of neutrino-antineutrino correlations on neutrino flavor conversion in the astrophysical and cosmological environments, and possibly upon the supernova dynamics. Our results can be easily generalized to an arbitrary number of neutrino families.