SCALAR DARK MATTER AND DAMA

# Scalar Dark Matter and Dama

Service de Physique Théorique, Université Libre de Bruxelles, B-1050 Brussels, Belgium
Institut für Theoretische Physik E, RWTH Aachen University, D-52056 Aachen, Germany
Sarah.Andreas@rwth-aachen.de

\abstracts

A light scalar WIMP is studied in view of the recent results of the DAMA collaboration. In a scenario where both the WIMP’s annihilation and its elastic scattering on nuclei occur dominantly through Higgs exchange, a one-to-one relation between the WIMP’s relic density and its spin-independent direct detection rate is established. The ratio of the relevant cross sections depends only on the dark matter mass if the range allowed by the DAMA results (m 10 GeV) is considered. We show that if such a light scalar WIMP possesses a direct detection rate compatible with DAMA, it naturally obtains a relic abundance in agreement with WMAP. Indirect detection both with gammas from the Galactic centre and neutrinos from the Sun opens possibilities to test this light dark matter scenario.

## 1 Introduction

The recent observation of an annual modulation in the nuclear recoil rate by the DAMA collaboration [1] can be reconciled with null results of other direct detection searches [2] for a spin-independent (SI) scattering cross section and dark matter (DM) mass in the ranges

 3×10−41cm2≲σSIp≲5×10−39cm2and3GeV≲mDM≲8GeV (1)

when taking into account the channeling effect [3]. These results have already been studied in various specific models [4, 5, 6, 7] and are discussed in the following in view of a light scalar WIMP 1. For this DM candidate we also present the signature in indirect detection through gammas from the Galactic centre (GC) [7] and neutrinos from the Sun [8].

## 2 Light scalar Dark Matter

Assuming only one Higgs boson, such a scenario is of interest since for a light scalar DM candidate, a natural one-to-one relation between the annihilation cross section and the one for SI scattering on a nucleon  arises as both processes occur in a Higgs-channel and connects the DM abundance to the direct detection rate. The sole possible tree level annihilation process (figure 1a) is through a Higgs boson in a s-channel into a pair of fermions, among which only , and are relevant, since all other SM fermions have small Yukawa couplings 2. The SI elastic scattering occurs exclusively through a Higgs in the t-channel (figure 1b) and is induced by the same DM-Higgs coupling.

The scalar DM candidate is introduced in the simplest way as a real scalar singlet , odd under a symmetry, by adding the four following renormalizable terms to the SM lagrangian:

 L∋12∂μS∂μS−12μ2SS2−λS4S4−λLH†HS2 (2)

with the Higgs doublet . The mass of is thus given by where . In this model, the sole coupling which allows to annihilate into SM particles and to interact with nucleons is . For the annihilation and the elastic scattering cross section (normalized to one nucleon), we obtain

 σ(SS→¯ff)vrel = ncλ2Lπm2fm4hm3S(m2S−m2f)3/2 (3) σ(SN→SN) = λ2Lπm4Nm4h (mS+mN)2f2, (4)

where for quarks (leptons) and is the centre of mass relative velocity between both . The factor parametrizes the Higgs to nucleons coupling from the trace anomaly, . Reflecting the uncertainty in we consider the range with as central value [6]. As for the Yukawa couplings 3, , we consider the pole masses , and .

## 3 DAMA and WMAP

In function of the two free parameters and and for a Higgs mass , we check whether or not agreement with both experiments can be obtained. For the parameter space between the two black lines (figure 1), the relic density, computed with micrOMEGAs [11], with respect to the critical density lies within the WMAP density range  [10]. In the red regions and are in agreement with DAMA and allowed by other direct detection experiments [3] (taking into account the channeling effect 4). We find that the regions of and which are consistent with WMAP and direct detection constraints nicely overlap 5. For the central value , the overlap ranges over while for regions overlap for . For smaller than no overlap exists.

Those results are shown for GeV but agreement may be obtained for other Higgs masses provided the ratio is kept fixed, typically at a value  GeV. To keep the result perturbative () we need that .

## 4 Indirect Detection and LHC

For the parameter range of interest, we make predictions regarding possible indirect detection from DM annihilation through gamma rays from the GC and neutrinos from the Sun.

The gamma fluxes from the GC for a NFW profile are shown in figure 2 for three parameter sets consistent with DAMA and WMAP and . Since those gammas have an energy in the range of the EGRET (and the forthcoming FERMI/GLAST) data we give for comparison the flux seen by EGRET [15]. The predicted flux is of the same order of magnitude and may even be larger than the one observed. We have however refrained from putting constraints on model parameters, given the large uncertainties on the DM density at the GC.

Dark matter which has been captured in the Sun [12] annihilates and produces neutrinos that can be observed at the Earth after converting into muons close to the detector volume. The expected flux of neutrino induced muons from the Sun for is presented in figure 2 together with the WMAP and DAMA regions from figure 1 as well as the CDMS and XENON limits. With our horizontally from higher [14] to lower DM masses conservatively extrapolated Super-Kamiokande sensitivity 6 (blue line) it can be seen that Super-Kamiokande is potentially able to test the light scalar DM and a part of the DAMA allowed region ([8].

Additionally, in this framework, the Higgs boson is predicted to be basically invisible at LHC for . The large coupling to the Higgs leads to its large decay rate into a pair of scalar WIMPs, e.g. for , for , and for ,  [7].

## 5 Conclusions

Light scalar DM has a one-to-one relation between SI direct detection rate and relic abundance since both processes occur in a Higgs channel. We show that this model can at the same time give the correct WMAP abundance and account for the DAMA results without contradicting other direct searches. The presented signatures in indirect detection show potential to further test this model. Gamma rays from the GC might be in reach of the upcoming FERMI/GLAST satellite and Super-Kamiokande might set constraints through neutrinos from the Sun. A striking consequence for LHC Higgs searches is the severe reduction of the visible branching ratio.7

## Acknowledgments

The work presented here was done in collaboration with Michel H. G. Tytgat and Thomas Hambye. We thank Jean-Marie Frère for stimulating discussions. Preprint ULB-TH/09-09.

## References

### Footnotes

1. The WIMP relic density is determined by thermal freeze-out assuming a mundane, radiation dominated expansion of the universe. We use general assumptions on abundance and velocity of the DM distribution in our neighbourhood.
2. Annihilation through the SM boson is excluded because the DM would contribute to the invisible width [9].
3. We neglect the effects of the running of the Yukawa couplings which are expected to be quite moderate.
4. There is no region allowed by all experiments if no channeling effect is assumed.
5. A DM mass in the relevant range demands some fine tuning, which is in our opinion not unbearable nor surprising, given the minimal number of parameters of the model. To obtain the quite large SI cross section needed to fit the DAMA data a large, albeit still perturbative coupling is required.
6. The low energetic neutrinos from light DM might be observed with Super-Kamiokande if its sensitivity is extended down to 2 GeV by including stopped, partially contained or fully contained muons [13].
7. The results discussed here apply for any scalar DM model (like the inert doublet or Higgs portal models) for which annihilation and SI scattering would be dominated by the diagrams of figure 1a,b. For a fermionic DM candidate we find that other channels must be present in order to match the WMAP and DAMA observations [7].

### References

1. R. Bernabei et al. [DAMA collaboration], Eur. Phys. J. C 56, 333 (2008); Riv. Nuovo Cim. 26N1 (2003) 1; Int. J. Mod. Phys. D13 (2004) 2127.
2. Z. Ahmed et al. [CDMS Collaboration], Phys. Rev. Lett. 102 (2009) 011301; J. Angle et al. [XENON Collaboration], Phys. Rev. Lett. 100 (2008) 021303.
3. F. Petriello and K. M. Zurek, JHEP 0809, 047 (2008), see also talk by K. M. Zurek at this conference.
4. R. Foot, Phys. Rev. D78 (2008) 043529;
5. J. L. Feng, J. Kumar and L. E. Strigari, Phys. Lett. B670 (2008) 37.
6. A. Bottino, F. Donato, N. Fornengo and S. Scopel, Phys. Rev. D78 (2008) 083520.
7. S. Andreas, T. Hambye and M. H. G. Tytgat, JCAP 0810 (2008) 034.
8. S. Andreas, M. H. G. Tytgat and Q. Swillens JCAP 0904 (2009) 004.
9. C. Amsler et al. [Particle Data Group], Phys. Lett. B667 (2008) 1
10. D. N. Spergel et al., Astrophys. J. Suppl. 170 (2007) 377. U. Seljak, A. Slosar and P. McDonald, JCAP 0610 (2006) 014.
11. G. Belanger, F. Boudjema, A. Pukhov and A. Semenov, Comput. Phys. Commun. 176 (2007) 367.
12. G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept. 267 (1996) 195.
13. J. L. Feng, J. Kumar, J. Learned and L. E. Strigari, arXiv:hep-ph/0808.4151
14. S. Desai et al. [Super-Kamiokande collaboration], Phys. Rev. D70 (2004) 083523
15. S. D. Hunger et al., Astrophys. J. 481 (1997) 205.
137291