ABSTRACT
As the outline of the neutrino mixings pattern is beginning to emerge from recent solar and atmospheric neutrino experiments, understanding the neutrino mass matrix has become one of the central problems in theoretical particle physics. The experimental situation can be roughly summarized as follows: while the mixings responsible for both solar and atmospheric neutrino oscillations are close to getting determined! 1 ], the pattern of masses seem to remain undetermined. The first puzzle that emerges is that two of the three neutrino mixing angles unlike the quark mixings are large. As far as the masses go, since neutrino oscillations are sensitive to only mass differences, three distinct patterns appear to be equally suitable for describing data: (i) normal hierarchy i.e m \ < m 2 ra3; (ii) inverted hierarchy i.e. mi ~ - m 2 > m 3 and (iii) degenerate i.e. mi ~ ra2 ~ ra3. Once some of the contemplated long baseline neutrino experiments[2 ] and high precision searches for neutrinoless double beta decay [3] are carried out{, the true mass pattern will very likely be revealed or at least the choice will narrower. From a theoretical point of view, each pattern could be an indication of a different symmetry of physics beyond the standard model. Therefore, before those experiments are carried out, it is of interest in our opinion to explore the symmetry approach to understanding neutrino masses and isolate their tests. Combination of the future experimental results and the theoretical explorations can then decide the nature of physics beyond the standard model.
