The invisible variant axion model is very attractive as it is free from the domain wall problem. This model requires two Higgs doublets at the electroweak scale where one Higgs doublet carries a nonzero Peccei-Quinn (PQ) charge and the other is neutral under the PQ U(1) symmetry. We consider the most interesting and less constrained scenario of the variant axion model, where only the right-handed top quark is charged under the PQ symmetry and couples with the PQ-charged Higgs doublet. As a

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... t, the top quark can decay to the observed standard-model-like Higgs boson h and the charm or up quark, t → h c/u, which is testable soon at the LHC Run-II. Moreover, we propose a method to probe the chiral nature of the Higgs flavor-changing interaction using the angular distribution of t → ch decays if a sufficient number of such events are observed. We also show that our model has the capacity to explain the h → τ µ decay reported by the CMS collaboration, if the right-handed tau lepton also carries a PQ charge and couples to the PQ-charged Higgs boson.