Implications of the new CDF-II $W$-boson mass on two-Higgs-doublet models

We present the implications of the recent measurement of $W$ boson at CDF II on the two-Higgs-doublet model (2HDM). In the analysis, we impose theoretical bounds such as vacuum stability and perturbative unitarity, and several experimental constraints. In addition, we take into account the measurement of $\sin^2\theta_W(m_Z)_{\rm \bar{MS}}$ on top of the CDF $W$-boson mass to investigate how the $S$ and $T$ parameters are determined. We explore two possible scenarios depending on whether the Higgs boson observed at the LHC is the lighter or heavier of $CP$-even neutral Higgs bosons for 2HDM type I and II. Using the results, we show how the parameter space is constrained, and compare it with the one based on the PDG average of $m_W$. Furthermore, we explore phenomenological consequences of electroweak precision observables that can be affected by $m_W$ within the predictions of the 2HDM, and the reduction in parameter space expected from future measurements at the Future Circular Lepton Collider.Comment: 26 pages, 10 figures. Analysis separated according to CP-even neutral scalar masses. Added estimations using expected FCC-ee precision. Updated to match published versio