On the hadronic contribution to sterile neutrino production

TL;DR

This work develops a first-principles, nonperturbative framework to quantify hadronic uncertainties in keV-scale sterile-neutrino production via active–sterile mixing. By deriving a master formula that expresses the sterile-neutrino production rate in terms of the active-neutrino spectral function and then linking that spectral function to hadronic vector and axial current correlators from finite-temperature QCD, the authors provide a concrete path to incorporate QCD effects near the QCD crossover. In the perturbative limit, the formalism reduces to Boltzmann equations, while in the nonperturbative regime it translates the problem into well-studied hadronic correlators obtainable from lattice QCD, sum rules, or resummed perturbation theory. This framework enables systematic estimation of hadronic uncertainties in the sterile-neutrino relic abundance and the $M_s$–$\theta$ parameter space, with clear directions for numerical evaluation and extensions to leptonic contributions.

Abstract

Sterile neutrinos with masses in the keV range are considered to be a viable candidate for warm dark matter. The rate of their production through active-sterile neutrino transitions peaks, however, at temperatures of the order of the QCD scale, which makes it difficult to estimate their relic abundance quantitatively, even if the mass of the sterile neutrino and its mixing angle were known. We derive here a relation, valid to all orders in the strong coupling constant, which expresses the production rate in terms of the spectral function associated with active neutrinos. The latter can in turn be expressed as a certain convolution of the spectral functions related to various mesonic current-current correlation functions, which are being actively studied in other physics contexts. In the naive weak coupling limit, the appropriate Boltzmann equations can be derived from our general formulae.