the CDMS II experiment. We also assume that the supersymmetry breaking scale is still below 1 TeV, and then we can solve the gauge hierarchy problem without fine-tuning. To explain the PAMELA, ATIC, and FERMI experiments, we introduce a DM particle S with mass around a few TeVs. To produce the SM fermion masess and mixings and have the heavy decay DM particle S , we consider the Froggatt-Nielsen (FN) mechanism [24]. We introduce an anomalous U (1)$_{X}$ gauge symmetry whose anomaly is cancelled by the Green- Schwarz mechanism [25]. Especially, the U (1)$_{X}$ gauge symmetry is broken down to the Z$_{2}$ symmetry around the string scale under which S is odd while all the SM particles are even. Thus, S can be a DM particle. Similar to the discussions in Refs. [26–29], the SM fermion masses and mixings can be generated as well. With a pair of heavy vector-like particles that are SM singlets and have U (1)$_{Y}$ charges ± 1 respectively, we obtain that the leading Yukawa coupling terms between S and the SM particles are S $^{2}$H$_{d}$ L$_{i}$E c j where H$_{d}$ is the Higgs field, and L$_{i}$ and E c j are the i -th family of the SM lepton doublet and j -th family of the right-handed charged lepton, respectively. In Model I, we have ( i, j ) = (2 , 2) and (3 , 2), while in Model II, we have ( i, j ) = (1 , 1). After S obtains a vacuum expectation value (VEV) at the TeV scale, S can decay dominantly to the second/third family of the SM leptons via dimension-six operators (three-body decay) in Model I, and to the first family of the SM leptons in Model II. To realize our idea, we present a benchmark point from the constrained minimal supersymmetric Stanard Model (CMSSM). The lightest neutralino ˜ N 0 1 contributes to part of the whole DM relic density, i.e. , Ω$_{˜}$ N 0 $_{1}$h 2 ≈ 0 . 08. The LSP neutralino- nucleon elastic-scattering spin independent cross section is about 5 × 10 − 9 pb. Thus, this benchmark point is consistent with the CDMS II results. In addition, for the S lifetime about τ ∼ 10 25 − 10 $^{27}$s , we can explain the PAMELA, FERMI and CDMS II experiments in Model I with S mass 3 TeV, and explain the PAMELA, ATIC and CDMS II experiments in Model II with S mass 1.8 TeV. 

The paper is organized as follows. In Section II, we explain the SM fermion masses and mixings as well as the leading Yukawa terms S $^{2}$L$_{i}$ H$_{d}$E c j via the FN mechanism. In Section III, we present a benchmark point in the CMSSM parameter space, and we discuss the DM particle S three-body cascade decay. We fit the PAMELA and FERMI data and the PAMELA and ATIC data in Section IV. Section V is our discussion and conclusions. We present more technical details in Appendices A, B, and C. 

## II. TWO SUPERSYMMETRIC STANDARD MODELS 

In this Section, we will present two supersymmetric Standard Models with decaying and stable DM particles. To have a decay DM particle, we introduce a SM singlet field S and a new Z$_{2}$ symmetry. Under this Z$_{2}$ symmetry, S is odd while all the SM particles 

