Neutrino mass generation via the inverse seesaw mechanism in a $U(1)_{B-L}$ gauge extension

We present anomaly-free solutions suitable for an inverse seesaw realization within a $U(1)_{B-L}$ extension. Implementing such a mechanism, in a phenomenologically viable way, requires the inclusion of at least four exotic fermions, assumed to be Standard Model singlets. In order to build anomaly-free models, the $B-L$ charges of these exotic fermions must satisfy two constraint equations, known as the anomaly equations. Here, we focus on solutions involving four to eight new right-handed fermions, favoring cases where all the $B-L$ charges of these fermions are rational numbers. We showed that, when considering only the right-handed fermions necessary to realize the mechanism, the solutions must have irrational charge values. By adding one more exotic singlet fermion, which does not directly enter the mechanism mass matrix, it becomes possible to find solutions with rational charges, while the addition of a second one enables a reduction of the scalar sector. On top of the two anomaly equations, a set of inequalities and additional constraint equations were added to correctly account for neutrino masses and to minimize the scalar content. So here we present sets of charges that obey the anomaly equations as well as these additional constraints. Finally, we explore the phenomenological implications of such solutions by analyzing their capacity to provide a framework for dark matter candidates, choosing one particular solution as an example.