Constraining minimal anomaly free $\mathrm{U}(1)$ extensions of the Standard Model

We consider a class of minimal anomaly free $\mathrm{U}(1)$ extensions of the Standard Model with three generations of right-handed neutrinos and a complex scalar. Using electroweak precision constraints, new 13 TeV LHC data, and considering theoretical limitations such as perturbativity, we show that it is possible to constrain a wide class of models. By classifying these models with a single parameter, $\kappa$, we can put a model independent upper bound on the new $\mathrm{U}(1)$ gauge coupling $g_z$. We find that the new dilepton data puts strong bounds on the parameters, especially in the mass region $M_{Z'}\lesssim 3~ \mathrm{TeV}$.