Status of the two-Higgs-doublet model in light of the CDF $m_W$ measurement

The most recent $W$-boson mass measurement by the CDF collaboration with a substantially reduced uncertainty indicates a significant deviation from the standard model prediction, as large as $7\sigma$ if taken literally. Then the Peskin-Takeuchi parameters of $S$ and $T$ shift to larger values, which has profound consequences in searching for physics beyond the SM. In the framework of two-Higgs-doublet models, we study the effect of the new $W$-boson mass measurement on the parameter space. Combined with other constraints including theoretical requirements, flavor-changing neutral currents in $B$ physics, the cutoff scale above 1 TeV, Higgs precision data, and direct collider search limits from the LEP, Tevatron, and LHC experiments, we find upper bounds on the masses of the heavy Higgs bosons: $M_{H,A,H^{\pm }}\lesssim 1.1$ TeV in type I, II, X, and Y for the normal Higgs scenario; $M_{H^{\pm }}\lesssim 450$ GeV and $M_A\lesssim 420$ GeV in type I and X for the inverted scenario where the heavier $CP$-even Higgs boson is the observed one. Another important finding is that type II and type Y in the inverted scenario are completely excluded. Such unprecedented findings imply that the upcoming LHC run can readily close out a large portion of the still-available parameter space.