Implications of the new CDF II <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math> -boson mass on two-Higgs-doublet models

We present the implications of recent measurement $W$ boson at CDF II on two-Higgs-doublet model (2HDM). In analysis, we impose theoretical bounds such as vacuum stability and perturbative unitarity, several experimental constraints. addition, take into account ${\mathrm{sin}}^{2}{\ensuremath{\theta}}_{W}({m}_{Z}{)}_{\overline{\mathrm{MS}}}$ top $W$-boson mass to investigate how $S$ $T$ parameters are determined. explore two possible scenarios depending whether Higgs observed LHC is lighter or heavier $CP$-even neutral bosons for 2HDM type I II. Using results, show parameter space constrained, compare it with one based PDG average ${m}_{W}$. Furthermore, phenomenological consequences electroweak precision observables that can be affected by ${m}_{W}$ within predictions 2HDM, reduction in expected from future measurements Future Circular Lepton Collider.