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.