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

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