Unification and mass spectrum in the minimal $B-L$ model

Gauging $B-L$ symmetry provides a simple realization of the seesaw mechanism in a naturally anomaly free extension to the MSSM gauge group, $SU(3)_c\times SU(2)_L\times U(1)_Y \times U(1)_{B-L}$. However, as we discuss in here, it turns out that the simplest $B-L$ extension of the MSSM may change some of the conceptions about the path for gauge unification as well as to affect the predicted spectrum of the supersymmetric particles at low energy. For instance, the coupling $g_{B-L}$ ended up to be smallest of all of them and the lightest gaugino is the one related to $B-L$. RGE also help to understand the spontaneous breaking of the $U(1)_{B-L}$ and the vacuum expectation value of the sneutrino at low energies, which occurs in this type of models.