h → μτ and muon g − 2 in the alignment limit of two-Higgs-doublet model

We examine the h→μτ and muon g−2 in the exact alignment limit of two-Higgs-doublet model. In this case, the couplings of the SM-like Higgs to the SM particles are the same as the Higgs couplings in the SM at the tree level, and the tree-level lepton-flavor-violating coupling hμτ is absent. We assume the lepton-flavor-violating μτ excess observed by CMS to be respectively from the other neutral Higgses, H and A, which almost degenerates with the SM-like Higgs at the 125 GeV. After imposing the relevant theoretical constraints and experimental constraints from the precision electroweak data, B-meson decays, τ decays and Higgs searches, we find that the muon g−2 anomaly and μτ excess favor the small lepton Yukawa coupling and top Yukawa coupling of the non-SM-like Higgs around 125 GeV, and the lepton-flavor-violating coupling is sensitive to another heavy neutral Higgs mass. In addition, if the μτ excess is from H around 125 GeV, the experimental data of the heavy Higgs decaying into μτ favor mA>230 GeV for a relatively large Ht¯t coupling.