Role of Sterile Neutrino Warm Dark Matter in Rhenium and Tritium Beta
  Decays
  Sterile neutrinos with mass in the range of one to a few keV are important as
extensions of the Standard Model of particle physics and are serious dark
matter (DM) candidates. This DM mass scale (warm DM) is in agreement with both
cosmological and galactic observations. We study the role of a keV sterile
neutrino through its mixing with a light active neutrino in Rhenium 187 and
Tritium beta decays. We pinpoint the energy spectrum of the beta particle, 0 <
T_e < (Q_{beta} - m_s), as the region where a sterile neutrino could be
detected and where its mass m_s could be measured. This energy region is at
least 1 keV away rom the region suitable to measure the mass of the light
active neutrino, located near the endpoint Q_{beta} . The emission of a keV
sterile neutrino in a beta decay could show up as a small kink in the spectrum
of the emitted beta particle. With this in view, we perform a careful
calculation of the Rhenium and Tritium beta spectra and estimate the size of
this perturbation by means of the dimensionless ratio R of the sterile neutrino
to the active neutrino contributions. We comment on the possibility of
searching for sterile neutrino signatures in two experiments which are
currently running at present, MARE and KATRIN, focused on the Rhenium 187 and
Tritium beta decays respectively.
