Abstract
The putative recent indication of an unidentified 3.55 keV X-ray line in certain astrophysical sources is taken as a motivation for an improved theoretical computation of the cosmological abundance of 7.1 keV sterile neutrinos. If the line is interpreted as resulting from the decay of Warm Dark Matter, the mass and mixing angle of the sterile neutrino are known. Our computation then permits for a determination of the lepton asymmetry that is needed for producing the correct abundance via the Shi-Fuller mechanism, as well as for an estimate of the non-equilibrium spectrum of the sterile neutrinos. The latter plays a role in structure formation simulations. Results are presented for different flavour structures of the neutrino Yukawa couplings and for different types of pre-existing lepton asymmetries, accounting properly for the charge neutrality of the plasma and incorporating approximately hadronic contributions.
Highlights
Our computation permits for a determination of the lepton asymmetry that is needed for producing the correct abundance via the Shi-Fuller mechanism, as well as for an estimate of the non-equilibrium spectrum of the sterile neutrinos
Our first goal is to derive a closed set of rate equations for the sterile neutrino distribution function and for lepton number densities,1 valid both near and far from equilibrium
An implicit assumption we make is that since the sterile neutrinos are being produced from a statistical plasma, they are decoherent, and their density matrix is assumed to retain the diagonal form in eq (2.3); this assumption would surely be violated by terms of higher order in h
Summary
Our first goal is to derive a closed set of rate equations for the sterile neutrino distribution function and for lepton number densities, valid both near and far from equilibrium. The influence of electric charge neutrality of the plasma on the relation between lepton number densities and lepton chemical potentials was not properly accounted for in ref. The system is completed, where we relate lepton chemical potentials to lepton densities, taking into account electric charge neutrality of the Standard Model plasma
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