Minimal Z' models

We present the most general solutions for the charges of a Z ′ with a minimal content of fermions. From our analysis, we show the existence of three different scenarios which, as far as we know, are new in the litera- ture. However, these solutions reduce to very well-known cases for particular choices of the free param- eters. We also define several benchmark models in order to show the flexibility of our parameterizations. In order to make a connection with the phenomenology, we show that it is possible to adjust some of these benchmark models to several observables, including C 9 and C 10 which are involved in the LHCb anomalies. We use the upper limits on the Z ′ cross-sections of extra gauge vector bosons Z ′ decaying into dileptons from the ATLAS data at 13 TeV with an accumulated luminosity of 36.1~fb −1 to set the 95\% CL allowed regions in the parameter space for a Z ′ mass of 5~TeV