Future $\nu_\tau$ Oscillation Experiments and Present Data

Our goal in this paper is to examine the discovery potential of laboratory experiments searching for the oscillation $\nu_\mu(\nu_e) \rightarrow \nu_\tau$, in the light of recent data on solar and atmospheric neutrino experiments, which we analyse together with the most restrictive results from laboratory experiments on neutrino oscillations. In order to explain simultaneously $all$ present results we use a four-neutrino framework, with an additional sterile neutrino. Our predictions are rather pessimistic for the upcoming experiments NOMAD and CHORUS, which, we find, are able to explore only a small area of the oscillation parameter space. On the other hand, the discovery potential of future experiments is much larger. We consider three examples. E803, which is approved to operate in the future Fermilab main injector beam line, MINOS, a proposed long-baseline experiment also using the Fermilab beam, and NAUSICAA, an improved detector which improves by an order of magnitude the performance of CHORUS/NOMAD and can be operated either at CERN or at Fermilab beams. We find that those experiments can cover a very substantial fraction of the oscillation parameter space, having thus a very good chance of discovering $both$ $\nu_\mu \rightarrow \nu_\tau$ and $\nu_e \rightarrow \nu_\tau$ oscillation modes.