Wimp Mass From Direct, Indirect Dark Matter Detection Experiments and Colliders: A Complementary and Model-Independent Approach.
Laboratoire de Physique Théorique, Bâtiment 210,
Université Paris-Sud XI, 91405 Orsay Cedex, France
We study the possibility of identifying dark matter properties from direct (XENON) and indirect (GLAST) detection experiments. In the same way, we examine the perspectives given by the next generation of colliders (ILC). All this analysis is done following a model-independent approach. We have shown that the three detection techniques can act in a highly complementary way. whereas direct detection experiments will probe efficiently light WIMPs, given a positive detection (at the level for GeV), GLAST will be able to confirm and even increase the precision in the case of a NFW profile, for a WIMP-nucleon cross-section pb. However, for heavier WIMP ( GeV), the ILC will lead the reconstruction of the mass.
1 Direct detection
Dark Matter (DM) direct detection experiments measure the elastic collisions between WIMPs and target nuclei in a detector, as a function of the recoil energy . The detection rate depends on the density GeV cm and velocity distribution of WIMPs near the Earth (a Maxwellian halo will be considered). The differential rate per unit detector mass and per unit of time can be written as:
where is the WIMP-nucleus scattering cross section, the WIMP mass and is the WIMP-nucleon reduced mass. is the nucleus form factor; we assume it has the Woods-Saxon form.
The XENON  experiment aims at the direct detection of DM via its elastic scattering off xenon nuclei. In this study we will consider the case of a kg Xenon-like experiment and years taking data. We consider energy bins between and keV. For this experiment we took a zero background scenario; of course a more detailed analysis could take into account non-zero background simulating the detector and in particular the neutron spectrum. So, in that sense our results will be optimistic.
One option to discriminate between a DM signal and the background is to use the method. Let us call the signal, the background and the total signal measured by the detector. For an energy range divided into bins the is defined as:
We assume a Gaussian error on the measurement, where is the detector mass and the exposure time.
2 Indirect detection
The spectrum of gamma–rays generated in dark matter annihilations and coming from the galactic center can be written as
where the discrete sum is over all dark matter annihilation channels, is the differential gamma–ray yield, is the annihilation cross-section averaged over the WIMPs’ relative velocity distribution and is the branching ratio of annihilation into the i-th final state. It is possible to concentrate ourselves on a process which gives annihilation into pairs, as this choice will not influence significantly the result of the study . The dark matter density is usually parametrized as
We assume a NFW profile with , and kpc, producing a profile with a behavior in the inner region of the galaxy.
The gamma-ray telescope GLAST  will perform an all-sky survey covering an energy range GeV.
We will consider a GLAST-like experience with an effective area and angular resolution on the order of cm and ( sr) respectively, who will be able to point and analyze the inner centre of our galaxy.
We consider also years of effective data acquisition experiment.
For this experiment, the background can be modeled by interpolating  the gamma-ray spectrum measured by HESS  (for GeV) and EGRET  (for GeV) missions.
Recently an approach was proposed by A. Birkedal et al. which allows to perform a model-independent study of WIMP properties at lepton colliders.
Since the known abundance of DM gives specific values for the DM annihilation cross section, one might hope this cross section can be translated into a rate for a measurable process at a collider.
The starting point is to relate total annihilation cross section to the cross section into pairs
Then we can use the detailed balancing equation to relate to , for non-relativistic WIMPs.
But this kind of process containing only WIMPs in the final state is not visible in a collider since they manifest themselves just as missing energy.
However this process can be correlated to the radiative WIMP pair-production using the collinear factorization.
This approach is valid for photons which are either soft or collinear with respect to the colliding beams.
The accuracy of the approximation outside the previous region has been discussed  with the conclusion that the approach works quite well.
So, starting from the total annihilation cross section we can compute
Here , is the angle between the photon and the incoming beam, and are the spin of the WIMP and the dominant value of the angular momentum in the velocity expansion for .
We place ourselves in the framework of the ILC project with a center-of-mass energy of GeV and an integrated luminosity of fb. For this process with only a single photon detected, the main background in the standard model is radiative neutrino production .
Recently, several works have studied the determination of the WIMP mass for the case of direct and indirect  detection experiments.
Furthermore, Drees and Shan  showed that one can increase such a precision with a combined analysis of two experiments of direct detection.
In figure 1 we compare the precision levels for direct and indirect detection experiments, along with the corresponding results of the method we followed for the ILC for and two cases of WIMP masses (left panel) and GeV (right panel).
All the results are plotted for a confidence level.
The green-dashed lines correspond to the results for a GLAST-like experiment assuming a NFW halo profile.
The total annihilation cross-section has been taken to be cms.
The red-plain line represents the result for an ILC-like collider with non-polarized beams.
The blue-dotted line corresponds to a kg XENON-like experiment, assuming a WIMP-nucleus scattering cross-section of pb.
All the parameter space points that lie within the marked regions can not be discriminated by the corresponding experiments.
It is pertinent to study the complementarity between the three experiences listed above firstly because the mass reconstruction yields comparable results, hence a combination of these data can substantially improve the final result. Secondly, because we can probe different regions in the parameter space.
For the case of a GeV WIMP, a GLAST- or an ILC-like experiment alone can provide a limited precision for the WIMP mass (). Combined measurements can dramatically increase the precision , reaching an accuracy of . If we additionally include direct detection measurement, we can reach a precision of the order of .
In table 1 we show the precision expected for several dark DM masses. A light WIMP mass ( GeV) can be reconstructed by both direct and indirect DM experiments with a high level of precision; however for the ILC the model independent procedure fails because of the relativistic nature of the WIMP. On the contrary, the ILC will be particularly efficient to measure a WIMP with a mass of about GeV. Concerning a GeV WIMP, only a loose lower bound could be extracted form direct and indirect experiments. In this case the ILC will not be kinematically able to produce so heavy WIMPs.
I would like to thank the organising committee for inviting me at this pleasant conference. Likewise, I would like to thank the ENTApP Network of the ILIAS project RII3-CT-2004-506222 and the French ANR project PHYS@COL&COS for financial support. The work reported here is based in collaboration with A. Goudelis, Y. Mambrini and C. Muñoz.
- J. Angle et al. [XENON Collaboration], Phys. Rev. Lett. 100 (2008) 021303 [arXiv:0706.0039 [astro-ph]].
- N. Bernal, A. Goudelis, Y. Mambrini and C. Muñoz, arXiv:0804.1976 [hep-ph].
- N. Gehrels and P. Michelson, Astropart. Phys. 11, 277 (1999).
- F. Aharonian et al. [The HESS Collaboration], Astron. Astrophys. 425 (2004) L13 [arXiv:astro-ph/0408145].
- S. D. Hunger et al., Astrophys. J. 481 (1997) 205.
- A. Birkedal, K. Matchev and M. Perelstein, Phys. Rev. D 70, 077701 (2004) [arXiv:hep-ph/0403004].
- A. M. Green, JCAP 0708 (2007) 022 [arXiv:hep-ph/0703217]; A. M. Green, arXiv:0805.1704 [hep-ph].
- S. Dodelson, D. Hooper and P. D. Serpico, Phys. Rev. D 77 (2008) 063512 [arXiv:0711.4621 [astro-ph]].
- M. Drees and C. L. Shan, arXiv:0803.4477 [hep-ph]; C. L. Shan and M. Drees, arXiv:0710.4296 [hep-ph].