As a prototype, we consider supersymmetic (SUSY) models with extra charged singlets while direct interac- tion between DM and nuclei can be forbidden in the leading order. The magnetic dipole moment is generi- cally induced by one-loop diagram. Such models have been discussed in a certain class of leptophilic scenarios for explaining recent cosmic ray anomalies, where DM particle has suppressed coupling with colored particles. We also emphasize that our analysis fully includes nu- clear anomalous magnetic moment interactions. With- out the photon exchange as in the neutralino case, the F$_{2}$ form factor effects of such nucleus are usually neg- ligible since the range of the DM–nucleus interaction is much smaller than the size of nucleus. However, the in- teraction through photon exchange can make the contri- bution comparable. The nucleus magnetic moment effect has not been considered properly in the previous works. Here, we present the DM detection rates including such effects and compare them with the recent CDMS II data. This paper is organized as follows. In Sec. II, we cal- culate the effective magnetic moment operator from a simple class of supersymmetric models. In generic mod- els beyond the SM, one-loop induced magnetic moment should usually have a similar structure calculated in this section. In Sec. III, we calculate the decoupling tem- perature of N by solving the Boltzmann equation. We also use the ( g − 2)$_{e}$ bound to constrain the hypothetical Yukawa coupling λ . In Sec. IV, we calculate the direct detection cross-section and show the Q $^{2}$-dependence due to the magnetic moment, which can be observed by the recoil energy distribution. The behavior due to the mag- netic moment is distinguishable from the predictions of other DM models. Next, the CDMS II experimental re- port is discussed in the context of DM models with a large magnetic moment. In this section, we also comment on the collider phenomenology of this class of models. Sec. V is a brief conclusion, summarizing the allowed mag- netic moment f of Dirac or almost-Dirac DM models. A neutral Dirac fermion N can acquire a magnetic mo- ment as shown in Fig. 1 if it couples to charged par- ticles, fermion ψ and boson φ , by a Yukawa coupling, λ ¯ ψ$_{R}$N$_{L}$φ +h.c. In the MSSM, the lightest supersymmet- ric particle (LSP) is not a Dirac fermion and thus the LSP DM cannot acquire a magnetic moment. However, in the extensions of MSSM with extra singlet chiral su- perfield, which have been proposed for many reasons : to address µ -problem or to raise the mass of the lightest Higgs boson, the LSP χ of the MSSM sector and the ad- ditional singlet N may form a single Dirac fermion state [11, 12]. For a specific calculation, we consider the following superpotential which has been discussed in [11], For a Dirac-type neutral fermion, its electromagnetic interaction is dominated by the magnetic moment, as pointed out for the case of neutrinos [8]. Let us define the magnetic moment of N as However, in the extension of MSSM, the interaction type λ ¯ ψ$_{R}$N$_{L}$φ +h.c. is present through NH$_{u}$H$_{d}$ which however has to be avoided by the following reasons. Firstly, after the Higgs fields H$_{u}$ and H$_{d}$ develop VEVs, they give a VEV to N , which is harmful because of the mass mixing with the electron e . Second, it splits masses of N and N , and the anomalous magnetic moment inter- action is a transition type between two mass eigenstates, and hence the direct detection rate as a function of re- coil energy must be considered more carefully if the mass difference is of order 1–10 keV. FIG. 1: One-loop diagrams for the magnetic moment of N . ef 2 m$_{N}$ Niσ $^{µν}$NF$_{µν}$ . (2) f = | λ | $^{2}$m2 N 16 π 2 ∫ 1 0 dx { q$_{φ}$ ( x 2 − x $^{3}$) m 2 $_{N}$x 2 + ( m 2 ψ − m 2 $_{N}$) x + m 2 $_{φ}$(1 − x ) − q$_{ψ}$ ( x 2 − x $^{3}$) m 2 $_{N}$x 2 + ( m 2 φ − m 2 $_{N}$) x + m 2 $_{ψ}$(1 − x ) } (3) For Eq. (1), f is estimated from Fig. 1 [13], W = λNe $^{c}$E + m$_{N}$N ¯ N + m$_{E}$EE c + ρN $^{3}$. (1) II. MAGNETIC MOMENT OF N In this model, there is no tree level interaction between N and nucleus because it couples only to leptons and its scalar partners. For the magnetic moment, the existence of the coupling of the type λNe $^{c}$E is the essential one, which can arise in many other models extending the SM. For DM magnetic moment, it is required that N must be a DM component, presumably by an exact Z$_{2}$ symme- try. Actually Eq.(1) is the simplest model in which the magnetic moment can play an essential role in the DM detection. More complicated cases can be obtained by its proper extensions. 2 γ N N λ λ ∗ φ φ ψ (a) γ N N λ λ ∗ ψ ψ φ (b)