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under SU (3)$_{C}$ × SU (2)$_{L}$ × U (1)$_{Y}$ are ( 1 , 1 , − 1 ) and ( 1 , 1 , 1 ), respectively. In addition, the U (1)$_{X}$ charges for all the particles in our models are denoted by appropriate subscripts, for example, for a generic particle φ , its U (1)$_{X}$ charge is X$_{φ}$ . In our models, we choose the U (1)$_{X}$ charges for the SM fermions and Higgs fields as follows 

<img src='content_image/352786.jpg'>

The superpotential for the SM fermion Yukawa couplings is 

<img src='content_image/352785.jpg'>

where i, j = 1 , 2 , 3, and all the coefficients are assume to be order one in the above superpotential. Thus, we obtain the SM fermion Yukawa coupling matrixes Y$_{u}$ , Y$_{d}$ , Y$_{e}$ and Y$_{ν}$ respectively for up-type quarks, down-type quarks, charged leptons and active neutrinos 

where T is transpose. We can show that the observed SM fermion masses and mixings can be generated [27, 29], and tan β = 〈 H 0 u 〉 / 〈 H$_{d}$ 〉 0 is 25. 

In the Model I, we would like to explain the PAMELA and FERMI experiments. We choose the following U (1)$_{X}$ charges for S , E ′ and E ′ 

<img src='content_image/352784.jpg'>

<img src='content_image/352783.jpg'>

Note that A has U (1)$_{X}$ charge − 1, the U (1)$_{X}$ charges for the SM particles are integers, while the U (1)$_{X}$ charge for S is half integer, thus, the U (1)$_{X}$ gauge symmetry is broken down to a Z$_{2}$ symmetry after A obtains a VEV. In particular, under this Z$_{2}$ symmetry, only S is odd while all the other SM particles are even. Then the leading Yukawa coupling terms between S and the SM particles in the superpotential are 

<img src='content_image/352782.jpg'>

where k = 2 , 3, and M$_{V}$ is the vector-like particle mass around the 10 13 GeV. In particu- lar, the superpotential mass terms E c $_{i}$E ′ and A $^{n}$Ec$_{i}$E ′ are forbidden due to the holomorpic 

