# Scalar Dark Matter and Dama

\addressService 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

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

(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}

## 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 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:

(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

(3) | |||||

(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}

## 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}^{5}

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}

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

- 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.
- Annihilation through the SM boson is excluded because the DM would contribute to the invisible width [9].
- We neglect the effects of the running of the Yukawa couplings which are expected to be quite moderate.
- There is no region allowed by all experiments if no channeling effect is assumed.
- 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.
- 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].
- 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].

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