Atmospheric neutrinos, long-baseline neutrino beams and the precise measurement of the neutrino oscillation parameters

Measurements of atmospheric neutrinos by Super-Kamiokande an other detectors have given evidence for the existence of neutrino oscillations with large mixing and $\Delta m^2$ in the range 10^{-3}-10^{-2} eV^2. In this work we discuss critically some of the possible experimental strategies to confirm this result and determine more accurately the neutrino oscillation parameters. A possible method is the development of long-baseline accelerator neutrino beams. The accelerator beams can have higher intensity and higher average energy than the atmospheric flux, and if (\nu_\mu \leftrightarrow \nu_\tau) oscillations are indeed the cause of the atmospheric neutrino anomaly, they can produce a measurable rate of $\tau$ leptons for most (but not all) of the values of the oscillation parameters that are a solution to the atmospheric data. On the other hand measurements of atmospheric neutrinos with large statistics and/or better experimental resolutions, can also provide convincing evidence for oscillations, thanks to unambiguous detectable effects on the energy, zenith angle and L/E_\nu distributions of the events. The study of these effects can provide a precise determination of the oscillations parameters. The range of L/E_\nu available for atmospheric neutrinos is much larger than in long-baseline accelerator experiments, and the sensitivity extends to lower values of \Delta m^2