Where are we with light sterile neutrinos?

We review the status of searches for sterile neutrinos in the similar to 1 eV range, with an emphasis on the latest results from short baseline oscillation experiments and how they fit within sterile neutrino oscillation models. We present global fit results to a three-active-flavor plus one-sterile-flavor model (3+1), where we find an improvement of Lambda chi(2) = 35 for 3 additional parameters compared to a model with no sterile neutrino. This is a 5 sigma improvement, indicating that an effect that is like that of a sterile neutrino is highly preferred by the data. However we note that separate fits to the appearance and disappearance oscillation data sets within a 3+1 model do not show the expected overlapping allowed regions in parameter space. This tension'' leads us to explore two options: 3+2, where a second additional mass state is introduced, and a 3+1+decay model, where the nu(4) state can decay to invisible particles. The 3+1+decay model, which is also motivated by improving compatibility with cosmological observations, yields the larger improvement, with a Delta chi(2) = 8 for 1 additional parameter beyond the 3+1 model, which is a 2.6 sigma improvement. Moreover the tension between appearance and disappearance experiments is reduced compared to 3+1, although disagreement remains. In these studies, we use a frequentist approach and also a Bayesian method of finding credible regions. With respect to this tension, we review possible problems with the global fitting method. We note multiple issues, including problems with reproducing the experimental results, especially in the case of experiments that do not provide adequate data releases. We discuss an unexpected 5 MeV excess, observed in the reactor flux energy spectrum, that may be affecting the oscillation interpretation of the short baseline reactor data. We emphasize the care that must be taken in mapping to the true neutrino energy in the case of oscillation experiments that are subject to multiple interaction modes and nuclear effects. We point to problems with the Parameter-Goodness-of-Fit test'' that is used to quantify the tension. Lastly, we point out that analyses presenting limits often receive less scrutiny that signals. While we provide a snapshot of the status of sterile neutrino searches today and global fits to their interpretation, we emphasize that this is a fast-moving field. We briefly review experiments that are expected to report new data in the immediate future. Lastly, we consider the 5-year horizon, where we propose that decay-at-rest neutrino sources are the best method of finally resolving the confusing situation. (C) 2020 Elsevier B.V. All rights reserved.