{U^c}
                    -D (\lambda_d v_1) {D^c}
                    -E (\lambda_e v_1) {E^c} + {\rm h.c.} \label{SRNDLagUDE} \\
{\cal L}_{N}     &=&-N (\lambda_\nu v_2) {N^c}
            -{\textstyle {1\over 2}} {N^c} M_{RR} {N^c} + {\rm h.c.}
\label{SRNDLagN}\end{aligned}$$ where the upper case letters now denote the fermionic components of the superfields in ${\cal W}$, for example $u$ contains $(U,\tilde u)\equiv (U_L,\tilde u_L)$ and $u^c$ contains $(U^c, \tilde u^c)\equiv(U^*_R,\tilde u^*_R)$. The Yukawa matrices in Eq.  can be diagonalized by bi-unitary transformations $S$ and $T$ defined by : $$T^{u*} \lambda_u S^{uT} = \lambda'_u \qquad
T^{d*} \lambda_d S^{dT} = \lambda'_d \qquad
T^{e*} \lambda_e S^{eT} = \lambda'_e$$ Thus the physical (primed) states $U'_{R,L}$ are related to the gauge eigenstates $U_{R,L}$ by $U'_R = S^u U_R$ and $U'_L = T^u U_L$, [*etc*]{}.. In this model, the left-handed neutrino masses are generated via see-saw mechanism [@seesaw] by the terms in Eq.  which can be re-arranged into a two-by-two block matrix in the following way : $${\cal L}_N = - {\textstyle {1\over 2}}
                ( N \, N^c )
                \left( \matrix{ 0      & m_{LR} \cr
                               m^T_{LR} &   M_{RR} }\right)
                \left( \matrix{ N \cr N^c} \right) + {\rm h.c.}$$ where $m_{LR} = \lambda_\nu v_2$. Thus, after the heavy $N^c$ fields are integrated out, the light left-handed neutrinos 