# Constraining WIMP magnetic moment from CDMS II experiment 

Won Sang Cho ( a $^{)}$, Ji-Haeng Huh( a $^{)}$, Ian-Woo Kim( b $^{)}$, Jihn E. Kim( a $^{)}$, and Bumseok Kyae( a ) 

( a $^{)}$Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea and 

( b $^{)}$Department of Physics, University of Wisconsin, Madison, WI 53706, USA 

We consider a degenerate or a nearly degenerate dark matter sector where a sizable magnetic moment of an almost Dirac type neutral dark matter candidate N is anticipated. Then, due to soft photon exchange, the cross-section in direct detection of N can be enhanced at low Q 2 region. We discuss the implication of this type of models in view of the recent CDMS II report. 

Recent cosmological and astrophysical observations strongly suggests that a significant portion of energy density of the universe exists in a form of dark matter (DM). DM has been speculated after the observation of the galaxy matter velocity distribution. The angular fre- quency distribution of the cosmic microwave background radiation, recent surveys of the expansion rate of remote galaxies and the simulation of the structure formation support around 25% of energy density in a form of non- relativistic matter while only one sixths of such matter has been identified as visible one. 

Among many plausible theories of DM [1] or equiva- lent modification of gravity [2], weakly interacting mas- sive particles (WIMP) are of particular interest [3]. The scenario with WIMP assumes that DM particles were produced in the early Universe by thermal processes and the DM relic density has been frozen out by decoupling since that epoch. The DM energy density from the cur- rent observation is well matched with such a thermal pro- duction scenario with an electroweak scale DM mass and appropriate electroweak scale interactions. It is also very interesting if DM has some interesting connection with the origin of the electroweak symmetry breaking as in the minimal supersymmetric standard model (MSSM) [4]. Above all, this WIMP scenario motivates searches for DM particles by detecting and/or producing them directly in the laboratory. 

Direct detection of DM has been carried out for several decades and the experimental sensitivity has been drasti- cally improved in recent years [5, 6]. The abundant DM particles that flows through Earth may sporadically col- lide with ordinary matter nuclei, resulting in the recoil of a nucleus. The current WIMP search through the en- ergy deposit in the cryogenic detector device has reached the DM cross-section with ordinary matter nuclei at the order of ∼ 10 − 44 cm $^{2}$, and the upgraded CDMS II ex- periment [6] has reached to this level. 

In most DM models, fermionic DM is a Majorana par- ticle, such as neutralino of the MSSM [7]. However, we 

PACS numbers: 13.40.Ks, 95.35.+d, 14.80.Nb Keywords: Dark matter, Magnetic moment, WIMP, CDMS II experiment 

## I. INTRODUCTION 

cannot rule out a Dirac fermionic DM N at present, and hence it is very important to consider physical effects of such Dirac fermionic nature of DM. In this regard, we consider an appreciable magnetic moments of DM. In fact, the magnetic moments of neutral fermions were considered for a long time since the time of weak neutral currents [8] up to the present age of DM [9]. 

One notable feature in the scattering through mag- netic moment of neutral fermion is that it has a larger cross section for a lower momentum photon exchange. The trend observed by two CDMS II candidates [6] in- deed show this behavior: the energy deposit at 12.3 keV and 15.5 keV (just above the threshold of 10 keV) while much larger energy deposit is allowed in that experiment. At this time with two possible low Q 2 candidates of the CDMS II experiment [6], therefore, it is appropriate to scrutinize the Dirac DM aspect more closely. In partic- ular, we will pay attention to the magnetic moment f of N . 1 In principle, this study includes the effects of the electric dipole moment also, but we will not specify them explicitly which would have needed an additional assumption about CP violation. 

There have been several works on the DM dipole mo- ments [9, 10]. In these works, various observational con- straints ( e.g. the cosmic microwave background radi- ation, the cosmic γ –ray detection,the DM relic abun- dance) have been considered. Although the authors of Ref. [9, 10] commented other possibilities, they mainly considered DM models in which the thermal DM relic density is determined only by annihilation due to mag- netic dipole interactions. However, as pointed out by [9, 10], models that give rise to the DM magnetic mo- ment interaction with the photon exchange usually have other annihilation channels. Here, we consider the cases in which the relic density does not constrain the DM mag- netic dipole moment. Nonetheless, DM direct detection can constrain the DM magnetic dipole moment. 

