Neutrino Mass: theory, data and interpretation

In these two lectures I describe first the theory of neutrino mass and then discuss the implications of recent data (including 708--day data Super--Kamiokande data) which strongly indicate the need for neutrino conversions to account for the solar and atmospheric neutrino observations. I also mention the LSND data, which provides an intriguing hint. The simplest ways to reconcile all these data in terms of neutrino oscillations invoke a light sterile neutrino in addition to the three active ones. Out of the four neutrinos, two are maximally-mixed and lie at the LSND scale, while the others are at the solar mass scale. These schemes can be distinguished at neutral-current-sensitive solar & atmospheric neutrino experiments. I discuss the simplest theoretical scenarios, where the lightness of the sterile neutrino, the nearly maximal atmospheric neutrino mixing, and the generation of $\Delta {m^2}_\odot$ & $\Delta {m^2}_{atm}$ all follow naturally from the assumed lepton-number symmetry and its breaking. Although the most likely interpretation of the present data is in terms of neutrino-mass-induced oscillations, one still has room for alternative explanations, such as flavour changing neutrino interactions, with no need for neutrino mass or mixing. Such flavour violating transitions arise in theories with strictly massless neutrinos, and may lead to other sizeable flavour non-conservation effects, such as $\mu \to e + \gamma$, $\mu-e$ conversion in nuclei, unaccompanied by neutrino-less double beta decay.