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We analyze the mass spectrum of the charged and neutral Higgs bosons in theframework of two Higgs doublet model (2HDM) in the light of the precisionmeasurement of the $W$ boson mass by the CDF collaboration. We have consideredthe most general 2HDM potential with explicit CP violation in the Higgs basiswhich contains the three CP-mixed neutral mass eigenstates $H_1$, $H_2$, and$H_3$ with $M_{H_1}\leq M_{H_2}\leq M_{H_3}$. The high-precision CDFmeasurement of the $W$ boson mass is characterized by the large positive valueof the $T$ parameter. By identifying the lightest neutral Higgs boson $H_1$ asthe SM-like one discovered at the LHC, we find that it is necessary to have themass splitting between the charged Higgs boson $H^\pm$ and the second heaviestneutral one $H_2$ to accommodate the sizable positive deviation of the $T$parameter from its SM value of $0$. By combining the mass splitting between$H^\pm$ and $H_2$ with the theoretical constraints from the perturbativeunitarity and for the Higgs potential to be bounded from below, we implementcomprehensive analysis of the mass spectrum of the heavy Higgs bosons takingaccount of the effects of deviation from the alignment limit and also the masssplitting between $H_3$ and $H_2$. We further analyze the behavior of theheavy-Higgs mass spectrum according to the variation of the $T$ parameter.Finally, concentrating on the heavy mass region $M\equiv(M_{H_2}+M_{H^\pm})/2\gsim 500$ GeV in which we find a mass hierarchy of $M\ggM_{H_1}\sim |\Delta| \gsim \delta$ with $\Delta \equiv M_{H_2}-M_{H^\pm}$ and$\delta \equiv M_{H_3}-M_{H_2}$, we discuss some benchmarking scenarios for thesearches of heavy Higgs bosons at future colliders such as the high luminosityoption of the LHC and a 100 TeV hadron collider.

On the mass spectrum of heavy Higgs bosons in two-Higgs-doublet model in the light of the CDF $W$-mass anomaly