Vector-Like Fermions and Inert Scalar Solutions to the Muon g-2 Anomaly and collider probes at the HL-LHC and FCC-hh

We examine simple models with an inert scalar and vector-like leptons that can explain the recent $g_{\mu }-2$ measurement reported at FNAL. Prompted by this exciting result, we explore the viability of a simple interpretation and determine the required parameters. We also embed these models within a 3-3-1 gauge extension of the Standard Model (SM), showing that the $g_{\mu }-2$ anomaly can be accommodated in agreement with current data. We also show how our theory can be tested at high-energy colliders such as HL-LHC and FCC-hh.