The effect of Majorana phase in degenerate neutrinos

There are physical Majorana phases in the lepton flavor mixing matrix when neutrinos are Majorana fermions. In the case of two degenerate neutrinos, the physical Majorana phase plays a crucial role in the stability of the maximal flavor mixing between the second and the third generations with respect to quantum corrections. The physical Majorana phase of pi guarantees that the maximal mixing is stable with respect to quantum corrections, while the Majorana phase of zero causes the maximal mixing destroyed by quantum corrections when neutrino masses are of O(1 eV). The continuous change of the Majorana phase from pi to 0 makes the maximal mixing destroyed by quantum corrections with O(1 eV) degenerate neutrino masses. On the other hand, when there is a large mass hierarchy among neutrinos, the maximal flavor mixing is not destroyed by quantum corrections independently of the Majorana phase.