The Supersymmetric $(B-L)$ model with three non-identical right-handed neutrinos

We build a supersymmetric version with $SU(3)_{C}\otimes SU(2)_{L}\otimes U(1)_{Y^{\prime}}\otimes U(1)_{(B-L)}$ gauge symmetry, where $Y^{\prime}$ is a new charge and ($B$) and ($L$) are the usual baryonic and leptonic numbers, respectivelly. The model has three right-handed neutrinos with non identical $(B-L)$ charges. We will use the superfield formalism in order to build our lagrangian and it is possible to accommodate all fermion masses at the tree level. In particular, the type-I seesaw mechanism is implemented for the generation of the active neutrino masses and also explain the mixing angle at the fermion sector. There are good candidates to Dark Matter, it can be the lighest righ-handed neutrinos or lighest right-handed sneutrinos or the lighest usual scalar field and due a Majorana phase at sneutrinos right-handed masses, it can induce Leptogenesis in this model.