| Summary: | Abstract We present the results of an updated fit of short-baseline neutrino oscillation data in the framework of 3+1 active-sterile neutrino mixing. We first consider ν e and ν ¯ e $$ {\overline{\nu}}_e $$ disappearance in the light of the Gallium and reactor anomalies. We discuss the implications of the recent measurement of the reactor ν ¯ e $$ {\overline{\nu}}_e $$ spectrum in the NEOS experiment, which shifts the allowed regions of the parameter space towards smaller values of |U e4|2. The β-decay constraints of the Mainz and Troitsk experiments allow us to limit the oscillation length between about 2 cm and 7 m at 3σ for neutrinos with an energy of 1 MeV. The corresponding oscillations can be discovered in a model-independent way in ongoing reactor and source experiments by measuring ν e and ν ¯ e $$ {\overline{\nu}}_e $$ disappearance as a function of distance. We then consider the global fit of the data on short-baseline ν μ − → ν e − $$ {}_{\nu_{\mu}}^{\left(-\right)}{\to}_{\nu_e}^{\left(-\right)} $$ transitions in the light of the LSND anomaly, taking into account the constraints from ν e − $$ {}_{\nu_e}^{\left(-\right)} $$ and ν μ − $$ {}_{\nu_{\mu}}^{\left(-\right)} $$ disappearance experiments, including the recent data of the MINOS and IceCube experiments. The combination of the NEOS constraints on |U e4|2 and the MINOS and IceCube constraints on |U μ4|2 lead to an unacceptable appearance-disappearance tension which becomes tolerable only in a pragmatic fit which neglects the MiniBooNE low-energy anomaly. The minimization of the global χ 2 in the space of the four mixing parameters Δm 41 2 , |U e4|2, |U μ4|2, and |U τ4|2 leads to three allowed regions with narrow Δm 41 2 widths at Δm 41 2 ≈ 1.7 (best-fit), 1.3 (at 2σ), 2.4 (at 3σ) eV2. The effective amplitude of short-baseline ν μ − → ν e − $$ {}_{\nu_{\mu}}^{\left(-\right)}{\to}_{\nu_e}^{\left(-\right)} $$ oscillations is limited by 0.00048 ≲ sin2 2ϑ eμ ≲ 0.0020 at 3σ. The restrictions of the allowed regions of the mixing parameters with respect to our previous global fits are mainly due to the NEOS constraints. We present a comparison of the allowed regions of the mixing parameters with the sensitivities of ongoing experiments, which show that it is likely that these experiments will determine in a definitive way if the reactor, Gallium and LSND anomalies are due to active-sterile neutrino oscillations or not.
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