Type-X two Higgs doublet model in light of the muon $\mathbf{g-2}$: confronting Higgs and collider data

The recent Fermilab measurement of the muon anomalous magnetic moment yields $4.2 \sigma$ deviations from the SM prediction when combined with the BNL E821 experiment results. In the Type-X two Higgs doublet model, we study the consequence of imposing the observed muon $g-2$, along with the constraints from theoretical stabilities, electroweak oblique parameters, Higgs precision data, and direct searches. For a comprehensive study, we scan the whole parameter space in two scenarios, the normal scenario where $h_{\rm SM} = h$ and the inverted scenario where $h_{\rm SM}=H$, where $h$ ($H$) is the light (heavy) CP-even Higgs boson. We found that large $\tan\beta$ (above 100) and light pseudoscalar mass $M_A$ are required to explain the muon $g-2$ anomaly. This breaks the theoretical stability unless the scalar masses satisfy $M_A^2 \simeq M_{H^\pm}^2 \simeq m_{12}^2 \tan\beta \approx M_{H/h}^2$. The direct search bounds at the LEP and LHC exclude the light $A$ window with $M_A \lesssim 62.5~$GeV. We also show that the observed electron anomalous magnetic moment is consistent with the model prediction, but the lepton flavor universality data in the $\tau$ and $Z$ decays are not. For a separate exploration of the model, we propose the golden mode $pp \to A h/AH \to 4 \tau$ at the HL-LHC.