Abstract
The resonant production of keV sterile-neutrino dark matter mainly takes place during the QCD epoch of the early universe. It has been argued that it could be strongly affected by the opacities (or damping rates) of active neutrinos, which receive non-perturbative QCD-contributions. We find that for lepton asymmetries {n}_{L_{alpha }}/s below 10−6 the opacities significantly affect the sterile-neutrino yield, but that for larger asymmetries, which are necessary for producing a significant fraction of the dark matter, the yield is insensitive to changes of the opacities. Thus non-perturbative QCD contributions to the opacities at temperatures around 160 MeV will not affect this dark matter scenario. We obtain larger sterile-neutrino yields than previous studies, and thus weaker lower limits on the active-sterile mixing angle from Big Bang Nucleosynthesis.
Highlights
The production process typically starts at temperatures of a few GeV and ends at a few MeV prior to the onset of Big Bang Nucleosynthesis (BBN), introducing uncertainties from the QCD epoch T ∼ 160 MeV, when QCD interactions are strong and non-perturbative
Lepton asymmetries much higher than the baryon asymmetry significantly influence the active-neutrino spectral function and resonantly boost sterile-neutrino production
Standard Model input enters our calculation in several places: through susceptibilities, which relate charges to chemical potentials, and through spectral functions of various currents, which determine the opacities of active neutrinos
Summary
We consider the Standard Model augmented by one family of sterile Majorana neutrinos N with Majorana mass M and non-zero Yukawa couplings hα to all active neutrino flavors, L. where φ = iσ2φ∗ is the conjugate Higgs doublet and α = (νLα, eLα) the left-handed lepton doublet. The sterile-neutrino field in the interaction picture reads. The spinors u and v satisfy the Majorana condition u = vc, where c denotes charge conjugation. V denotes the volume of our system. With these operators we define the sterile-neutrino phase space density operators as fkλ ≡ a†kλakλ. Baryon number B is conserved, and its tiny value can be well approximated by zero for our purposes. Electric charge Q is conserved and exactly zero
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