Seesaw model in SO(10) with an upper limit on right-handed neutrino masses

Abstract

In the framework of SO(10) gauge unification and the seesaw mechanism, we show that the upper bound on the mass of the heaviest right-handed neutrino $M_{R_3} < 3 \times 10^{11}$ GeV, given by the Pati-Salam intermediate scale of $B-L$ spontaneous symmetry breaking, constrains the observables related to the left-handed light neutrino mass matrix. We assume such an upper limit on the masses of right-handed neutrinos and, as a first approximation, a Cabibbo form for the matrix $V^L$ that diagonalizes the Dirac neutrino matrix $m_D$. Using the inverse seesaw formula, we show that our hypotheses imply a triangular relation in the complex plane of the light neutrino masses with the Majorana phases. We obtain normal hierarchy with an absolute scale for the light neutrino spectrum. Two regions are allowed for the lightest neutrino mass $m_1$ and for the Majorana phases, implying predictions for the neutrino mass measured in Tritium decay and for the double beta decay effective mass $|<m_{ee}>|$.