New physics interpretations of the muon g-2 and W boson mass anomalies

The anomalous magnetic moment of the muon represents one of the most interesting and long-standing hint for new physics. Recently, the E989 experiment at Fermilab has confirmed previous results by the E821 experiment at BNL. Comparing the experimental average with the Standard Model prediction, leads to an interesting 4.2σ discrepancy. Moreover, the recent high-precision measurement of the W mass by the CDF collaboration is in sharp tension with the Standard Model prediction as obtained by the electroweak fit. If confirmed, this finding can only be explained in terms of new physics effects. The main goal of this thesis work is to develop compelling theoretical frameworks where both experimental results can be naturally explained, and derive predictions for other low- and high-energy observables, which will help to probe such models.