Bounds on long-baseline ${\overline{\nu }}_e\to {\overline{\nu }}_e$ and ${\stackrel{\mathrm{(-)}}{\nu }}_{\mu }\to {\stackrel{\mathrm{(-)}}{\nu }}_e$ transition probabilities

We discuss long-baseline neutrino oscillations in the framework of the two 4-neutrino schemes which can accommodate all existing neutrino oscillation data. Negative results of short-baseline reactor and accelerator experiments allow us to obtain rather strong bounds on the long-baseline ${\overline{\nu }}_e\to {\overline{\nu }}_e$ and ${\stackrel{\mathrm{(-)}}{\nu }}_{\mu }\to {\stackrel{\mathrm{(-)}}{\nu }}_e$ transition probabilities. We consider in detail matter effects and show that the vacuum bounds are not substantially modified. We also comment on corresponding bounds in 3-neutrino scenarios.