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There are several possible minimal $B-L$ extensions of the MSSM of the form $SU(3)_C \otimes SU(2)_L \otimes U(1) \otimes U(1)'$, characterized by different choices of the two $U(1)$ factors. If these are remnants of a GUT theory, such as SO(10), then these possibilities are all physically equivalent, but will be characterized by different kinetic mixing between the two $U(1)$ factors. Among these possibilities, as shown in [@Ovrut:2012wg], there is a unique choice that will have vanishing kinetic mixing–not only at the GUT scale, but at any lower scale. This choice of $U(1)$ factors is $U(1)_{3R} \times U(1)_{B-L}$, where $U(1)_{3R}$ is the third component of right-handed isospin. The fact that this basis has no kinetic mixing greatly simplifies the present analysis. Therefore, in this paper, we proceed using the specific minimal extension gauge group $$SU(3)_C \otimes SU(2)_L \otimes U(1)_{3R} \otimes U(1)_{B-L} \ .$$ We will comment later in the paper on how our results apply to the other similar extensions. The gauge structure in this case is such that the hypercharge, $Y$, is related to the $B-L$ and third component of right-handed isospin charges by $$Y = I_{3R} + \frac{B-L}{2},$$ analogous to the relationship between the electric charge, hypercharge and 