Is the new CDF $M_W$ measurement consistent with the two higgs doublet model?

Motivated by the new CDF measurement of the $W$ boson mass reported recently which clearly illustrates a large deviation compared to the Standard Model (SM) prediction. In the present paper, we study the Two-Higgs Doublet Model (2HDM) contributions to $M_W$ and its phenomenological implications in the case where the heavy CP-even $H$ is identified as the observed Higgs boson with a mass of $125$ GeV. Taking into account theoretical and all the available experimental constraints as well as the new CDF measurement, we demonstrate that the 2HDM parameter space can provide a large correction which predicts the W mass close to the new CDF $M_W$ measurement. It is found that $M_{H\pm}=M_A$ is excluded and the splitting of the charged Higgs boson with all other states is positive. We also discuss the consequence on the effective mixing angle $\sin^2\theta_{\text{eff}}$ as well as the phenomenological implications on the charged Higgs and CP-odd decays.Comment: 11 pages, 6 figure