KATRIN bound on 3+1 active-sterile neutrino mixing and the reactor antineutrino anomaly

We present the bounds on 3+1 active-sterile neutrino mixing obtained from the first results of the KATRIN experiment. We show that the KATRIN data extend the Mainz and Troitsk bound to smaller values of $\Delta{m}^2_{41}$ for large mixing and improves the exclusion of the large-$\Delta{m}^2_{41}$ solution of the Huber-Muller reactor antineutrino anomaly. We also show that the combined bound of the Mainz, Troitsk, and KATRIN tritium experiments and the Bugey-3, NEOS, PROSPECT, and DANSS reactor spectral ratio measurements exclude most of the region in the ($\sin^2\!2\vartheta_{ee},\Delta{m}^2_{41}$) plane allowed by the Huber-Muller reactor antineutrino anomaly. Considering two new calculations of the reactor neutrino fluxes, we show that one, that predicts a lower $^{235}\text{U}$ neutrino flux, is in agreement with the tritium and reactor spectral ratio measurements, whereas the other leads to a larger tension than the Huber-Muller prediction. We also show that the combined reactor spectral ratio and tritium measurements disfavor the Neutrino-4 indication of large active-sterile mixing. We finally discuss the constraints on the gallium neutrino anomaly.