property of superpotential. Because E ′ and E ′ are heavy, we should integrate them out below their mass scale. From the above superpotential, we obtain from equations of motion (EOMs) for E ′ and E ′ Using the above EOMs for E ′ and E $^{′}$, we obtain that the superpotential in Eq. (6) becomes To simplify the discussions, we assume that the coefficient of S $^{2}$H$_{d}$ L$_{2}$E c 2 is about three times larger than that of S $^{2}$H$_{d}$ L$_{3}$E c $_{2}$. Thus, we will concentrate on the term S $^{2}$H$_{d}$ L$_{2}$E c 2 in the following discussions. In the Model II, we want to explain the PAMELA and ATIC experiments. We choose the U (1)$_{X}$ charges for S , E ′ and E ′ as follows Similar to the Model I, the U (1)$_{X}$ gauge symmetry is broken down to a Z$_{2}$ symmetry after A obtains a VEV. 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 Similar to the Model I, integrating out the vector-like particles E ′ and E $^{′}$, we obtain In this paper, we will define M 2 ∗ = M$_{Pl}$M$_{V}$/ϵ n where n is equal to 5 in Model I and 4 in Model II. With M$_{V}$ around 10 13 GeV, we obtain that M$_{∗}$ is around 10 17 GeV. To get M$_{V}$ around 10 13 GeV, we can introduce additional global U (1) ′′ symmetry and a SM singlet field S ′ which breaks the U (1) ′′ symmetry. The U (1) ′′ charges for L$_{i}$ , E c $_{i}$, E $^{′}$, S , and S ′ are 1, − 1, − 1, 1 / 2 and 1, while the U (1) ′′ charges for all the other particles are zero. Therefore, all the previous terms in the superpotential including the SM fermion Yukawa coupling terms are invariant except the term M$_{V}$ E $^{′}$E $^{′}$. The vector-like mass term for E ′ and E ′ can be generated by the following superpotential term after the U (1) ′′ symmetry breaking W ⊃ S $^{′}$E $^{′}$E ′ . (12) W ⊃ − ϵ 4 ( S 2 M$_{Pl}$M$_{V}$ ) H$_{d}$L$_{1}$E c 1 . (11) W ⊃ ( A M$_{Pl}$ ) 4 H$_{d}$L$_{1}$E ′ + ( S 2 M$_{Pl}$ ) E c $_{1}$E ′ + M$_{V}$E $^{′}$E ′ . (10) X$_{S}$ = 1 / 2 , X$_{E}$ ′ = − 4 , X$_{E}$ ′ = 4 . (9) W ⊃ − ϵ 5 ( S 2 M$_{Pl}$M$_{V}$ ) H$_{d}$L$_{k}$E c 2 . (8) E ′ = − H$_{d}$L$_{k}$ M$_{V}$ , E ′ = − S $^{2}$E c 2 M$_{V}$ M$_{Pl}$ . (7) 7