Muon-specific two-Higgs-doublet model for $(g-2)_\mu$ anomaly, $W$-boson mass-shift, and Zee model

We have investigated one type of 2HDM, the muon-specific two-Higgs-doublet model, as a solution to the muon ($g-2$) and CDF $W$-boson mass anomaly. The additional Higgs boson couplings to muons are enhanced by $\tan \beta$, while the couplings to other fermions are suppressed by $\cot \beta$. One-loop corrections to the $W-\mu-\nu_\mu$ coupling induce a positive shift to the $W$-boson mass, compatible with the CDF measurement. Fixing the charged Higgs mass of $m_{H^\pm}=600$ GeV, our results show that small values of $\tan \beta$ ($\approx 200$) require a large mass splitting of $m_A-m_H \approx 480$ GeV. The small mass splitting case $m_A-m_H \approx 10$ GeV is also possible, provided large $\tan \beta$ ($\approx 5000$). The oblique parameter lies in $T=[0.126,0.198]$ which corresponds to the mass-splitting between the charged and pseudoscalar Higgs in the range typically $10-100$ GeV. This leads to the constrained all Higgs boson masses that cannot be heavier than about 600 GeV. At the end, we also have studied the model in the context of the Zee model, radiative neutrino mass generation at one-loop level, by adding a singly-charged scalar to the model. The model results in the incompatible neutrino mass matrix with solar and KamLAND data.