A resolution of the flavor problem of two Higgs doublet models with an extra U(1)H symmetry for Higgs flavor

We propose to implement the Natural Flavor Conservation criterion in the two Higgs doublet model (2HDM) to an extra U(1)H gauge symmetry for Higgs flavor, assuming two Higgs doublets carry different U(1)H charges. Then one can easily avoid the tree-level FCNC from neutral Higgs mediations using local gauge symmetries, instead of softly broken ad hoc Z2 symmetry, and the pseudoscalar boson could be eaten by extra ZH boson. Imposing the anomaly cancellation, we find that the U(1)H in the Type-II and Type-IV 2HDMs become leptophobic and leptophilic, respectively. For the Type-I case, U(1)H depends on two parameters, and some simple cases include U(1)H=U(1)B−L, U(1)R, or U(1)Y. We sketch qualitative phenomenology of these models.