Constraining 3-3-1 Models at the LHC and Future Hadron Colliders

In this work, we derive lower mass bounds on the Z' gauge boson based on the dilepton data from LHC with 13 TeV of center-of-mass energy, and forecast the sensitivity of the High-Luminosity-LHC with $L=3000 fb^{-1}$, the High-Energy LHC with $\sqrt{s}=27$ TeV, and also at the Future Circular Collider with $\sqrt{s}=100$ TeV. We take into account the presence of exotic and invisible decays of the Z' gauge boson to find a more conservative and robust limit, different from previous studies. We investigate the impact of these new decays channels for several benchmark models in the scope of two different 3-3-1 models. We found that in the most constraining cases, LHC with $139fb^{-1}$ can impose $m_{Z^{\prime}}>4$ TeV. Moreover, we forecast HL-LHC, HE-LHC, and FCC bounds that yield $m_{Z^{\prime}}>5.8$ TeV, $m_{Z^{\prime}}>9.9$ TeV, and $m_{Z^{\prime}}> 27$ TeV, respectively. Lastly, put our findings into perspective with dark matter searches to show the region of parameter space where a dark matter candidate with the right relic density is possible.