Interpreting the W-mass and muon (gμ − 2) anomalies within a 2-Higgs doublet model

In this study, we investigate the anomalous magnetic moment of the muon $(g_{\mu }-2)$ as reported by Fermilab (FNAL), along with the recent measurement of the W-boson mass by the CDF-II collaboration. Both findings show significant deviations from the predictions of the Standard Model (SM), hinting at the possibility of new physics. Our focus is on the Type III two-Higgs-doublet model (2HDM), wherein both Higgs doublets couple with all fermions, leading to the induction of flavour-changing neutral currents (FCNCs) at the tree level. Within this framework, we investigate a lepton-flavour-violating (LFV) scenario, aiming to explain both observed anomalies, while satisfying the up-to-date theoretical and experimental constraints.