Bound on 3+1 Active-Sterile Neutrino Mixing from the First Four-Week Science Run of KATRIN

We report on the light sterile neutrino search from the first four-week science run of the KATRIN experiment in 2019. Beta-decay electrons from a high-purity gaseous molecular tritium source are analyzed by a high-resolution MAC-E filter down to 40 eV below the endpoint at 18.57 keV. We consider the framework with three active neutrinos and one sterile neutrino. The analysis is sensitive to the mass, m$_{4}$ f the fourth mass state for m$_{4}$$^{2}$ ≲1000 eV$^{2}$ and to active-to-sterile neutrino mixing down to |U$_{e4}$|$^{2}$≳2×10$^{-2}$. No significant spectral distortion is observed and exclusion bounds on the sterile mass and mixing are reported. These new limits supersede the Mainz results for m$_{4}$$^{2}$ ≲1000 eV$^{2}$ and improve the Troitsk bound for m$_{4}$$^{2}$< 30 eV$^{2}$. he reactor and gallium anomalies are constrained for 100<Δ m$_{41}$$^{2}$< 1000 eV$^{2}$.