third component of left-handed isospin in the SM.

The matter content and its $SU(3)_C \otimes SU(2)_L \otimes U(1)_{3R} \otimes U(1)_{B-L}$ charges is given by three copies of $$Q \sim (\textbf{3}, \textbf{2},0,1/3), \  \,  u^c \sim (\bar{\textbf{3}},\textbf{1},-1/2,-1/3), \  \,  {d}^c \sim (\bar{\textbf{3}},\textbf{1},1/2,-1/3),$$ $${L} \sim (\textbf{1},\textbf{2},0,-1), \  \,  {e}^c \sim (\textbf{1},\textbf{1},1/2,1), \  \,   {\nu}^c \sim (\textbf{1},\textbf{1},-1/2,1), \\$$ while the MSSM Higgs sector is $${H}_u \sim (\textbf{1},\textbf{2},1/2,0) , \ \  {H}_d \sim (\textbf{1},\textbf{2},-1/2,0).$$ The superpotential is similar to that of the MSSM but contains an additional Yukawa coupling to the right-handed neutrino superfield $$\label{W}
    W =
    Y_u {Q} {H}_u {u}^c - Y_d {Q} {H}_d {d}^c
    - Y_e {L} {H}_d {e}^c + Y_\nu {L} {H}_u {\nu}^c
    + \mu  H_u  H_d,$$ where the Yukawa couplings are three-by-three matrices in family space and are in general complex. The soft SUSY breaking Lagrangian is $$\begin{aligned}
    \begin{split}
    -\mathcal{L} _{\rm soft}= &
        \, m_{\tilde \nu^c}^2 |\tilde \nu^c|^2 + m_{\tilde L}^2 |\tilde L|^2 + m_{H_u}^2 |H_u|^2  + m_{H_d}^2 |H_d|^2
\\
        & +
        \left(
            M_R \tilde W_R^2 + M_2 \tilde W^2 + M_{BL} \tilde B'^2 + M_3 \tilde g^2 + a_\nu \tilde L H_u \tilde \nu^c
            + b H_u H_d+ \text{h.c.}
        \right)+ \cdots,
    \end{split}\end{aligned}$$ where the ellipses refer to terms which 