We study the implications of the existence of two equalities between the elements or cofactors of the neutrino mass matrix. There are 65 structures of this type for each case. Phenomenological implications for unknown parameters like the effective Majorana mass of the electron neutrino and $CP$-violating phases are examined for the viable cases. To illustrate how such forms of the neutrino mass matrices may be realized, we also present a simple $A_4$ model for one of the classes in each case.

• Received 7 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.073011