determined by the amount of mixing between the two neutrinos and their mass difference. In a purely Dirac neutrino case, the active-sterile mixing is maximal but the mass difference is zero and, therefore, no active-sterile oscillations result. Here, in the pure Majorana case, the mass difference is significant but the mixing is negligible. A situation in which both Dirac and Majorana mass contributions are comparable would lead to large active-sterile oscillations which have not been observed and are therefore ruled out, *e.g.* [@deGouvea:2009fp; @Antonello:2012pq].

The question then remains, should this analysis assume that neutrinos receive their masses dominantly from Dirac or Majorana mass terms? Here, already, the connection to $R$-parity becomes important. Prompt LSP decays, which were argued to be of interest in the last section, will allow significant Majorana masses. Since these cannot coexist with significant Dirac masses, neutrinos must receive their masses dominantly from Majorana mass terms. This makes further study of the Majorana mass matrix, Eq. (\[nu.mass.1\]), fruitful.

As a first step, it is important to notice that the determinant of the neutrino mass matrix in Eq. (\[nu.mass.1\]) is zero. This is a consequence of the flavor structure and is independent of the $A, B$ and $C$ 