Constraining the $g'_1$ coupling in the minimal $B-L$ Model

We have combined the perturbative unitarity and the renormalisation group equations arguments in order to find a dynamical way to constrain the $g'_1$ coupling of the minimal $B-L$ extension of the Standard Model. We have analysed the role of the $g'_1$ coupling evolution in the perturbative stability of the two-to-two body scattering amplitudes of the vector boson and scalar sectors of the model and we have shown that the perturbative unitarity imposes an upper bound on the $B-L$ gauge coupling. We have made a comparison between this criterion and the triviality arguments, showing that our procedure substantially refines the triviality bounds.