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 The superpotential for the SM fermion Yukawa couplings is 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 ′ 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 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 W ⊃ ( A M$_{Pl}$ ) 5 H$_{d}$L$_{k}$E ′ + ( S 2 M$_{Pl}$ ) E c $_{2}$E ′ + M$_{V}$ E $^{′}$E ′ , (6) X$_{S}$ = 3 / 2 , X$_{E}$ ′ = − 5 , X$_{E}$ ′ = 5 . (5) Y$_{u}$ ∼   $^{ϵ}$$^{8}$ ϵ 5 ϵ 3 ϵ 7 ϵ 4 ϵ 2 ϵ 5 ϵ 2 1    , Y$_{d}$ ∼ Y T e ∼   $^{ϵ}$$^{5}$ ϵ 4 ϵ 4 ϵ 4 ϵ 3 ϵ 3 ϵ 2 ϵ 1 ϵ 1    , Y$_{ν}$ ∼   $^{ϵ}$$^{2}$ ϵ ϵ ϵ 1 1 ϵ 1 1    , (4) W ⊃ ( A M$_{Pl}$ ) X$_{H}$$_{u}$ + X$_{Q}$$_{i}$ + X$_{U}$ c j Q$_{i}$H$_{u}$U c j + ( A M$_{Pl}$ ) X$_{H}$$_{d}$ + X$_{Q}$$_{i}$ + X$_{D}$ c j Q$_{i}$H$_{d}$D c j + A M$_{Pl}$ X$_{H}$$_{d}$ + X$_{L}$$_{i}$ + X$_{E}$ c j L$_{i}$H$_{d}$E c j + A M$_{Pl}$ X$_{H}$$_{u}$ + X$_{L}$$_{i}$ + X$_{N}$ c j L$_{i}$H$_{u}$N c j , (3) X$_{Q}$$_{1}$ = 3 , X$_{Q}$$_{2}$ = 2 , X$_{Q}$$_{3}$ = 0 , X$_{U}$ c 1 = 5 , X$_{U}$ c 2 = 2 , X$_{U}$ c 3 = 0 , X$_{D}$ c 1 = 1 , X$_{D}$ c 2 = 0 , X$_{D}$ c 3 = 0 , X$_{L}$$_{1}$ = 1 , X$_{L}$$_{2}$ = 0 , X$_{L}$$_{3}$ = 0 , X$_{E}$ c 1 = 3 , X$_{E}$ c 2 = 2 , X$_{E}$ c 3 = 0 , X$_{H}$$_{u}$ = 0 , X$_{H}$$_{d}$ = 0 . (2) 6