be at or below those of the left-handed, or active, neutrinos since their masses arise from Dirac Yukawa couplings to the left-handed neutrinos. Models with two sterile neutrinos are sometimes called 3+2 models in the literature, where the three represents the active neutrinos. ]{}. Majorana masses for the active neutrinos are generated through an effective type I seesaw mechanism [@Minkowski:1977sc; @Yanagida; @GellMann:1980vs; @Mohapatra:1979ia] where the seesaw fields include the one heavy right-handed neutrino and the neutralinos. Once the heavy seesaw fields are integrated out, the Majorana contribution to the neutrino mass matrix is $$\label{nu.mass.1}
    {m_\nu}_{ij} = A {v_L}_i^* {v_L}_j^* + B \left({v_L}_i^* \epsilon_j + \epsilon_i {v_L}_j^* \right) + C \epsilon_i \epsilon_j \ .$$ The non-flavored parameters, $A$, $B$ and $C$, are the results of integrating out the heavy fields. They, and more details, are given in Appendix A. The Dirac neutrino mass contributions are simply given by the product of the up-type Higgs VEV and the neutrino Yukawa couplings that do not couple to the third generation right-handed neutrino: $\frac{1}{\sqrt 2}{Y_\nu}_{i, j \neq 3} v_u$.

One of the main tools at our disposal for probing the neutrino sector is the observation of neutrino oscillations. Such oscillations between two neutrinos are 