One can not deny the possibility that the three neutrino masses may be approximately degenerate at the low energy scale : m1 ~ m2 ~ m3. Is this possible that we can experience the situations either m1=m2 or m1=m2=m3? at some higher energy scale. Can any one suggest me any framework where these possibilities may appear naturally ?
this is the idea of our paper Phys.Rev.Lett. 86 (2001) 3488-3491 Consistent symmetry reaization in Phys.Lett. B552 (2003) 207-213 Revamped to induce theta13 and predict CPV in Phys.Rev. D88 (2013) 016003 CHEERS
If we examine experimental numbers for solar and atmospheric mass splittings, it seems natural that a pair of neutrinos can be approximately degenerate. The third eigenvalue could be either heavier or lighter than the degenerate pair. If degenerate (solar) pair is heavy then we call it inverted hierarchy and if the degenerate pair is lighter than the third mass eigenvalue we call it normal hierarchy.
I am just giving an example to show that this could indeed be the case. Impose Lμ-Lτ symmetry in the neutrino mass matrix. Then, mass eigenvalues will be quasi degenerate and one of the mixing angles will be maximal.
The neutrino mass values are quite close, based on current experiments. However, if we consider the behavior of the masses for the three families charged, we can suppose some hierarchy existed in the sector of neutrinos.
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