Correlating $W$-Boson Mass Shift with Muon ${g-2}$ in the 2HDM

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 $pp \rightarrow (\mu^+ \mu^+ jj + {E\!\!\!\!/}_{T})$ and $pp \rightarrow (\mu^+\mu^-\tau^+\tau^-+X)$ signals.