Constraining a general U(1)$^prime$ inverse seesaw model from vacuum stability, dark matter and collider

We consider a class of gauged $U(1)$ extensions of the Standard Model (SM), where the light neutrino masses are generated by an inverse seesaw mechanism. In addition to the three right handed neutrinos, we add three singlet fermions and demand an extra $Z_2$ symmetry under which, the third generations of both of the neutral fermions are odd, which in turn gives us a stable dark matter candidate. We express the $U(1)$ charges of all the fermions in terms of the U(1) charges of the standard model Higgs and the new complex scalar. We study the bounds on the parameters of the model from vacuum stability, perturbative unitarity, dark matter relic density and direct detection constraints. We also obtain the collider constraints on the $Z$ mass and the $U(1)$ gauge coupling. Finally we compare all the bounds on the $Z$ mass versus the $U(1)$ gauge coupling plane.