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Abstract

Neutrino oscillations involving eV-scale neutrino mass states are investigated in the context of global neutrino oscillation data including short and long-baseline accelerator, reactor, and radioactive source experiments, as well as atmospheric and solar neutrinos. We consider sterile neutrino mass schemes involving one or two mass-squared differences at the eV$^2$ scale denoted by 3+1, 3+2, and 1+3+1. We discuss the hints for eV-scale neutrinos from $\nu_e$ disappearance (reactor and Gallium anomalies) and $\nu_\mu\to\nu_e$ appearance (LSND and MiniBooNE) searches, and we present constraints on sterile neutrino mixing from $\nu_\mu$ and neutral-current disappearance data. An explanation of all hints in terms of oscillations suffers from severe tension between appearance and disappearance data. The best compatibility is obtained in the 1+3+1 scheme with a p-value of 0.2% and exceedingly worse compatibilities in the 3+1 and 3+2 schemes.