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We build a supersymmetric version with $SU(3)_{C}\otimes SU(2)_{L}\otimesU(1)_{Y^{\prime}}\otimes U(1)_{(B-L)}$ gauge symmetry, where $Y^{\prime}$ is anew 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 ourlagrangian and it is possible to accommodate all fermion masses at the treelevel. In particular, the type-I seesaw mechanism is implemented for thegeneration of the active neutrino masses and also explain the mixing angle atthe fermion sector. There are good candidates to Dark Matter, it can be thelighest righ-handed neutrinos or lighest right-handed sneutrinos or the lighestusual scalar field and due a Majorana phase at sneutrinos right-handed masses,it can induce Leptogenesis in this model.

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