Improved determination of the WIMP mass from direct detection data

Direct detection experiments searching for weakly interacting massive particle (WIMP) dark matter typically use a simplified model of the Galactic halo to derive parameter constraints. However, there is strong evidence that this Standard Halo Model is not a good approximation to our Galaxy. We discuss previous attempts to extract the WIMP mass, cross-section and speed distribution from direct detection data and show that these lead to significant biases in the reconstructed parameter values. We develop and test an alternative model-independent method based on parametrising the momentum distribution of the WIMPs. This allows us to limit the analysis only to those regions of momentum space to which the experiments are sensitive. The method can be applied to a single experiment to extract information about the distribution function, as well as information on the degenerate WIMP mass and interaction cross-section combined in a single parameter. This degeneracy can be broken by including data from additional experiments, meaning that the WIMP mass and speed distribution can be recovered. We test the momentum parametrisation method using mock datasets from proposed ton-scale direct detection experiments, showing that it exhibits improved coverage properties over previous methods, as well as significantly reduced bias. We are also able to accurately reconstruct the shape of the WIMP speed distribution but distinguishing between different underlying distributions remains difficult.