Neutrino decoherence in a fermion and scalar background

TL;DR

This paper investigates how neutrinos lose coherence when traveling through a background of scalars and fermions, calculating damping effects from non-forward scattering, relevant for dark matter interactions.

Contribution

It provides a detailed calculation of decoherence effects from non-forward neutrino scattering in scalar-fermion backgrounds, linking damping terms to the master equation framework.

Findings

Damping terms are explicitly calculated for various background distributions.

Decoherence effects are identified with the imaginary part of the neutrino self-energy.

Results are applicable to dark matter-neutrino interaction models.

Abstract

We consider the decoherence effects in the propagation of neutrinos in a background composed of a scalar particle and a fermion due to the non-forward neutrino scattering processes. Using a simple model for the coupling of the form $\bar f_R\nu_L\phi$ we calculate the contribution to the imaginary part of the neutrino self-energy arising from the non-forward neutrino scattering processes in such backgrounds, from which the damping terms are determined. In the case we are considering, in which the initial neutrino state is depleted but does not actually disappear (the initial neutrino transitions into a neutrino of a different flavor but does not decay into a $f\phi$ pair, for example), we associate the damping terms with decoherence effects. For this purpose we give a precise prescription to identify the decoherence terms, as used in the context of the master or Linblad equation, in terms of the damping terms we have obtained from the calculation of the imaginary part of the neutrino self-energy from the non-forward neutrino scattering processes. The results can be directly useful in the context of Dark Matter-neutrino interaction models in which the scalar and/or fermion constitute the dark-matter, and can also serve to guide the generalizations to other models and/or situations in which the decoherence effects in the propagation of neutrinos originate from the non-forward scattering processes may be important. As a guide to estimating such decoherence effects, the contributions to the absorptive part of the self-energy and the corresponding damping terms are computed explicitly in the context of the model we consider, for several limiting cases of the momentum distribution functions of the background particles.