to be more apparent. While models of neutrino masses can certainly be considered without low-energy supersymmetry, our interest in effective Lagrangians deriving from string theories which preserve $N=1$ supersymmetry leads us to couch our discussion in a supersymmetric framework. Then the effective mass operator involving only the light (left-handed) neutrinos has mass dimension five. Once the Higgs fields acquire vacuum expectation values (vevs) the effective neutrino masses are given by $$%
(\mathbf{m}_{\nu})_{ij} = (\lambda_{\nu})_{ij} \frac{v_2^2}{M} ,
%
\label{mnu}$$ where $v_2$ is the vev of the Higgs doublet $H_2$ with hypercharge $Y=+1/2$. The $3 \times 3$ matrix of couplings $\lambda_{\nu}$ is necessarily symmetric in its generation indices $i$ and $j$.

Such an operator can be induced through the exchange of heavy singlet (right-handed) neutrinos $N_R$ – as in the standard or “Type I” see-saw approach [@GRS; @Yanagida; @Valle1] – or through the exchange of heavy triplet states $T$ [@Lazarides:1980nt; @Mohapatra:1980yp; @Schechter:1981cv; @Ma:1998dx; @Hambye:2000ui; @Rossi:2002zb], or both. In either case, the mass scale $M$ is given by the scale at which lepton number is broken (presumably the mass scale of the heavy state being exchanged). In the presence of both contributions to the light neutrino masses we have the general mass matrix 