Model-Independent Data Analyses
in Direct Dark Matter Detection Experiments

Last updated: December 24, 2008
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There is strong evidence that more than 80% of all matter in the Universe is dark (i.e., interacts at most very weakly with electromagnetic radiation and ordinary matter). The dominant component of this cosmological Dark Matter must be due to some yet to be discovered, non-baryonic particles. Weakly Interacting Massive Particles (WIMPs) with masses roughly between 10 GeV and a few TeV are one of the leading candidates for Dark Matter.

Currently, the most promising method to detect many different WIMP candidates is the direct detection of the recoil energy deposited in a low-background laboratory detector by elastic scattering of ambient WIMPs on the target nuclei. The event rate of elastic WIMP-nucleus scattering depends on various parameters coming from astrophysics, particle physics, and nuclear physics: the local density and the velocity distribution of the halo WIMPs, as well as the WIMP-nucleon couplings and the WIMP mass.

So far most theoretical analyses of direct Dark Matter detection have predicted the detection rate for given (classes of) WIMPs, based on some specific models of the Galactic halo. This can be used for e.g., reconstructing the velocity distribution of halo WIMPs or determining their mass, only by fitting the predicted recoil spectrum to future experimental data.

Reconstructing the one-dimensional velocity distribution of halo WIMPs

The aim of our work is to develop methods which allow to extract information on the nature of halo WIMPs by using data from direct Dark Matter detection experiments directly. As the first step we used a time-averaged recoil spectrum, assumed that no directional information exists, and not only derived expressions that allow to reconstruct the time-averaged, normalized one-dimensional velocity distribution function of WIMPs and its moments by means of a given expression (e.g., a fit to data) for the recoil spectrum, but also developed methods that allow to apply our expressions directly to data, without the need to fit the recoil spectrum to a functional form [1, 2]. All these expressions are independent of the as yet unknown local WIMP density as well as of the WIMP-nucleus cross section; the only information about the nature of halo WIMPs which one needs is its mass.

Taking into account an annual modulation of the event rate

Due to the orbital motion of the Earth around the Sun, an annual modulation of the event rate has been discussed. Hence, as the next step we considered a time-dependent, cosine-like recoil spectrum with a one-year period and extended our method for reconstructing the (moments of the) WIMP velocity distribution to be able to use experimental data with an annual modulated event rate [2]. Moreover, we also developed a method for reconstructing the amplitude of the annual modulation of the velocity distribution as well as an alternative way for confirming the annual modulation of the event rate [2]. The only information needed is the measured recoil energies and the corresponding measuring times.

Determining the WIMP mass

As mentioned above, for reconstruction of the (moments of the) velocity distribution of halo WIMPs from experimental data, the mass of the incident WIMPs is the unique needed input parameter. Hence, by combining two (or more) experimental data sets with different target materials which should lead to the same reconstructed velocity distribution, we developed a method for (self-)determining the WIMP mass [2 - 4]. This method is independent of the model of the Galactic halo as well as of the WIMP-nucleon couplings. Since one can use the whole data sets without binning, in a background-free environment, a WIMP of ~ 50 GeV could in principle be determined with a statistical error of ~ 35% with only ~ 50 events from each experiment.

Determining the ratios of two WIMP-nucleon cross sections

So far for estimating the (exclusion limits of the) WIMP-nucleon cross sections from direct Dark Matter detection experiments, one has to assume whether the spin-independent (SI) or the spin-dependent (SD) WIMP-nucleus interaction dominates and express the results of such data analyses as functions of the as yet unknown WIMP mass. By using the method for estimating the moments of the velocity distribution of halo WIMPs and combining different data sets with different targets, we developed further methods which allow to estimate the ratio of the SI to SD WIMP-nucleon cross sections as well as the ratio of the SD WIMP coupling on neutrons to that on protons from experimental data directly [5]. These methods don't require prior knowledge of the local WIMP density, of the velocity distribution of incident WIMPs, as well as of the WIMP mass; for a WIMP mass of 100 GeV the statistical error is only ~ 10% with only O(20) events from each experiment in the low energy range with relatively high threshold energy, e.g. 5 - 15 keV.

Estimating the spin-independent WIMP-nucleon coupling

In order to determine one of the three WIMP-nucleon couplings - the other two can be determined by the methods described above - we extended the expression for determining the WIMP mass and developed a method for constraining the SI WIMP-nucleon coupling [6]. Due to the degeneracy between the local WIMP density and the WIMP-nucleus cross section, one needs here the local WIMP density as an input parameter. However, comparing to the uncertainty on the local density of a factor of ~ 2, in a background-free environment, for a WIMP mass of 100 GeV one could in principle estimate the SI WIMP coupling on nucleons with a much smaller statistical error of ~ 15% with ~ 50 events from each experiment.

Chung-Lin Shan


  1. M. Drees and C.-L. Shan, "Reconstructing the Velocity Distribution of Weakly Interacting Massive Particles from Direct Dark Matter Detection Data", J. Cosmol. Astropart. Phys. 0706, 011 (2007) (abstract, pdf, html); arXiv:astro-ph/0703651 (abstract, pdf).
  2. C.-L. Shan, Ph.D. thesis, "Theoretical Interpretation of Experimental Data from Direct Dark Matter Detection", online-dissertations at the Rheinischen Friedrich-Wilhelms-Universität Bonn (abstract, pdf); arXiv:0707.0488 [astro-ph] (abstract, pdf).
  3. M. Drees and C.-L. Shan, "Model-Independent Determination of the WIMP Mass from Direct Dark Matter Detection Data", J. Cosmol. Astropart. Phys. 0806, 012 (2008) (abstract, pdf, html); arXiv:0803.4477 [hep-ph] (abstract, pdf).
  4. C.-L. Shan, "Estimating the Spin-Independent WIMP-Nucleon Coupling from Direct Dark Matter Detection Data", arXiv:1103.0481 [hep-ph] (abstract, pdf).
  5. C.-L. Shan, "Determining Ratios of WIMP-Nucleon Cross Sections from Direct Dark Matter Detection Data", J. Cosmol. Astropart. Phys. 1107, 005 (2011) (abstract, pdf); arXiv:1103.0482 [hep-ph] (abstract, pdf).

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