We show an interesting correlation between the recent high precision measurement of the $W$-boson mass by the CDF Collaboration and the muon ($g-2$) anomaly in the context of the two Higgs doublet model. One-loop diagrams involving the exchange of neutral scalar bosons can explain the muon ($g-2$), which, however, requires significant mass splittings among members of the second Higgs doublet. These splittings also generate a positive shift in the mass of the $W$ boson, consistent with the recent CDF measurement. The charged and neutral scalars of the model cannot be heavier than about 600 GeV for a simultaneous explanation of the two anomalies. The entire parameter space of the model can be tested at the LHC by a combination of same sign dimuon signals in $pp\to ({\mu }^{+}{\mu }^{+}jj+{\cancel{E}}_T)$ and $pp\to ({\mu }^{+}{\mu }^{-}{\tau }^{+}{\tau }^{-}+X)$ signals.

• Received 1 May 2022
• Accepted 23 August 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.121803

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Published by the American Physical Society