Model-Independent Determination of the WIMP Mass from Direct Dark Matter Detection Data

Journal of Cosmology and Astroparticle Physics (Impact Factor: 5.88). 05/2008; DOI: 10.1088/1475-7516/2008/06/012
Source: arXiv

ABSTRACT Weakly Interacting Massive Particles (WIMPs) are one of the leading candidates for Dark Matter. We develop a model-independent method for determining the mass $m_\chi$ of the WIMP by using data (i.e., measured recoil energies) of direct detection experiments. Our method is independent of the as yet unknown WIMP density near the Earth, of the form of the WIMP velocity distribution, as well as of the WIMP-nucleus cross section. However, it requires positive signals from at least two detectors with different target nuclei. In a background-free environment, $m_\chi \sim 50$ GeV could in principle be determined with an error of $\sim 35%$ with only $2 \times 50$ events; in practice upper and lower limits on the recoil energy of signal events, imposed to reduce backgrounds, can increase the error. The method also loses precision if $m_\chi$ significantly exceeds the mass of the heaviest target nucleus used.

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    ABSTRACT: We propose an improved method to study recent and near-future dark matter direct detection experiments with small numbers of observed events. Our method determines in a quantitative and halo-independent way whether the experiments point towards a consistent dark matter signal and identifies the best-fit dark matter parameters. To achieve true halo independence, we apply a recently developed method based on finding the velocity distribution that best describes a given set of data. For a quantitative global analysis we construct a likelihood function suitable for small numbers of events, which allows us to determine the best-fit particle physics properties of dark matter considering all experiments simultaneously. Based on this likelihood function we propose a new test statistic that quantifies how well the proposed model fits the data and how large the tension between different direct detection experiments is. We perform Monte Carlo simulations in order to determine the probability distribution function of this test statistic and to calculate the $p$-value for both the dark matter hypothesis and the background-only hypothesis.
    Journal of Cosmology and Astroparticle Physics 09/2014; 2014(12). DOI:10.1088/1475-7516/2014/12/052 · 5.88 Impact Factor
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    ABSTRACT: Results from direct detection experiments are typically interpreted by employing an assumption about the dark matter velocity distribution, with results presented in the $m_\chi-\sigma_n$ plane. Recently methods which are independent of the DM halo velocity distribution have been developed which present results in the $v_{min}-\tilde{g}$ plane, but these in turn require an assumption on the dark matter mass. Here we present an extension of these halo-independent methods for dark matter direct detection which does not require a fiducial choice of the dark matter mass. With a change of variables from $v_{min}$ to nuclear recoil momentum ($p_R$), the full halo-independent content of an experimental result for any dark matter mass can be condensed into a single plot as a function of a new halo integral variable, which we call $\tilde{h}(p_R)$. The entire family of conventional halo-independent $\tilde{g}(v_{min})$ plots for all DM masses are directly found from the single $\tilde{h}(p_R)$ plot through a simple rescaling of axes. By considering results in $\tilde{h}(p_R)$ space, one can determine if two experiments are inconsistent for all masses and all physically possible halos, or for what range of dark matter masses the results are inconsistent for all halos, without the necessity of multiple $\tilde{g}(v_{min})$ plots for different DM masses. We conduct a sample analysis comparing the CDMS II Si events to the null results from LUX, XENON10, and SuperCDMS using our method and discuss how the mass-independent limits can be strengthened by imposing the physically reasonable requirement of a finite halo escape velocity.
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    ABSTRACT: In this paper, we investigate the modification of our expressions developed for the model-independent data analysis procedure of the reconstruction of the (time-averaged) one-dimensional velocity distribution of Galactic Weakly Interacting Massive Particles (WIMPs) with a non-negligible experimental threshold energy. Our numerical simulations show that, for a minimal reconstructable velocity of as high as O(200) km/s, our model-independent modification of the estimator for the normalization constant could provide precise reconstructed velocity distribution points to match the true WIMP velocity distribution with a <~ 10% bias.

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