Large nuₘu->nuₜau and nuₑ->nuₜau transitions in short-baseline experiments?

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Considering four-neutrino schemes of type 3+1, we identify four small regions of the neutrino mixing parameter space compatible with all data. Assuming a small mixing between the sterile neutrino and the isolated mass eigenstate we show that large nuₘu->nuₜau and nuₑ->nuₜau transitions are predicted in short-baseline experiments and could be observed in the near future in dedicated experiments. We discuss also implications for solar, atmospheric and long-baseline neutrino experiments and we present a formalism that allows to describe in 3+1 schemes atmospheric neutrino oscillations, long-baseline nuₘu disappearance and nuₘu->nuₜau transitions in matter.