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The new measurement of the $W$ boson mass performed by the CDF experiment atthe Tevatron shows a significant deviation not only with the expectation in theStandard Model but also with other precision measurements performed at LEP, theTevatron and the LHC. We nevertheless take this new measurement at face valueand interpret it as an effect of new physics. We particularly try to link itwith other possible anomalies such as the recent muon $g-2$ and consider ascenario that addresses some shortcomings of the Standard Model. We show that amodel with two doublets and a light pseudoscalar Higgs fields, supplemented bya stable isosinglet fermion, can simultaneously explain the possible $M_W$ and$(g-2)_\mu$ anomalies and accounts for the weakly interacting massive particlethat could be responsible of the dark matter in the universe.

The 2HD+a model for a combined explanation of the possible excesses in the CDF $\mathbf{M_W}$ measurement and $\mathbf{(g-2)_\mu}$ with Dark Matter