Leptonic Precision Test of Leptophilic Two-Higgs-Doublet Model

The type X (lepton-specific) two-Higgs-doublet model at large $\tan \beta$ becomes leptophilic and thus allows a light pseudoscalar $A$ accommodating the observed muon $g-2$ deviation without conflicting with various hadronic constraints. On the other hand, it is strongly constrained by leptonic precision observables such as lepton universality test in the neutral and charged currents. Treating all the lepton universality data in a consistent way, we show how the current data constrain the parameter space of $m_A$ and $\tan \beta$ for given degenerate masses of heavy Higgs bosons $H$ and $H^{\pm }$. While no overlapping region is found at $1\sigma$, a sizable region is still viable at $2\sigma$ for $H\mathrm{/}{H}^{\pm }$ masses at around 200$\sim$400 GeV.