A Three Higgs Doublet Model for the Fermion Mass Hierarchy Problem

In this paper we propose a possible explanation to the Fermion mass hierarchy problem by fitting the type-II seesaw mechanism into the Higgs doublet sector, such that their vacuum expectation values are hierarchal. We extend the Standard Model with two extra Higgs doublets as well as a spontaneously broken $U_X(1)$ gauge symmetry. All the fermion Yukawa couplings except that of top quark are of order ${\cal O} (10^{-2})$ in our model. Constraints on the parameter space from Electroweak precision measurements are studied. Besides, the neutral component of the new fields, which are introduced to cancel the anomalies of the $U(1)_X$ gauge symmetry can be dark matter candidate. We investigate its signature in the dark matter direct detection.