Determining the WIMP mass using direct detection experiments

We study the accuracy with which the WIMP mass could be determined by a superCDMS-like direct detection experiment, given optimistic assumptions about the detector set-up and WIMP properties. We consider WIMPs with an interaction cross-section of \sigma_{\rm p} = 10^{-7} {\rm pb} (just below current exclusion limits) and assume, initially, that the local WIMP velocity distribution and density are known and that the experiment has negligible background. For light WIMPs (mass significantly less than that of the target nuclei) small variations in the WIMP mass lead to significant changes in the energy spectrum. Conversely for heavy WIMPs the energy spectrum depends only weakly on the WIMP mass. Consequently it will be far easier to measure the WIMP mass if it is light than if it is heavy. With exposures of {\cal E}= 3 \times 10^{3}, 3 \times 10^{4} and 3 \times 10^{5} {\rm kg day} (corresponding, roughly, to the three proposed phases of SuperCDMS) it will be possible, given the optimistic assumptions mentioned above, to measure the mass of a light WIMP with an accuracy of roughly 25%, 15% and 2.5 % respectively. These numbers increase with increasing WIMP mass, and for heavy WIMPs, m_{\chi} > {\cal O}(500 {\rm GeV}), even with a large exposure it will only be possible to place a lower limit on the mass. Finally we discuss the validity of the various assumptions made, and the consequences if these assumptions are not valid. In particular if the local WIMP distribution is composed of a number of discrete streams it will not be possible to determine the WIMP mass.