Neutrino Quantum Kinetic Equations: The Collision Term

TL;DR

This paper derives the detailed collision term for neutrino quantum kinetic equations, incorporating flavor and spin degrees of freedom, relevant for early universe and astrophysical environments.

Contribution

It presents the full matrix structure of the collision term, including neutrino-neutrino, electron-positron, and nucleon interactions, with analysis of limiting cases.

Findings

Full matrix structure of collision term derived

Simplified isotropic limit formulated for early universe studies

Interpretation of off-diagonal helicity terms provided

Abstract

We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.