Model Independent Determination of the Dark Matter Mass from Direct Detection Experiments

Determining the dark matter (DM) mass is of paramount importance for understanding dark matter. We present a novel parametrization of the DM speed distribution which will allow the DM mass to be accurately measured using data from weakly interacting massive particle (WIMP) direct detection experiments. Specifically, we parametrize the natural logarithm of the speed distribution as a polynomial in the speed $v$. We demonstrate, using mock data from upcoming experiments, that by fitting the WIMP mass and interaction cross section, along with the polynomial coefficients, we can accurately reconstruct both the WIMP mass and speed distribution. This new method is the first demonstration that an accurate, unbiased reconstruction of the WIMP mass is possible without prior assumptions about the distribution function. We anticipate that this technique will be invaluable in the analysis of future experimental data.

Figure 1

The speed distribution for the three benchmark models defined in the text: SHM (solid blue line), $\mathrm{SHM}+\mathrm{DD}$ (dot-dashed green line), and stream (dashed red line).

Figure 2

68% and 95% confidence contours for the WIMP mass $m_{\chi }$ and cross section ${\sigma }_p$ obtained using the speed parametrization described in the text. Results are shown for three different underlying speed distributions: SHM (solid blue), $\mathrm{SHM}+\mathrm{DD}$ (dot-dashed green), and stream (dashed red). The true parameter values are shown as a black cross.

Figure 3

Reconstructed speed distributions for the SHM (top panel), $\mathrm{SHM}+\mathrm{DD}$ (middle panel), and stream (bottom panel) benchmarks. The true distribution is shown as a solid curve, while the best fit reconstructed value is shown as a dashed curve. Also shown are the marginalized 68% credible intervals (shaded pink).