Determining the WIMP mass from a single direct detection experiment, a more detailed study

The energy spectrum of nuclear recoils in Weakly Interacting Massive Particle (WIMP) direct detection experiments depends on the underlying WIMP mass. We study how the accuracy with which the WIMP mass could be determined by a single direct detection experiment depends on the detector configuration and the WIMP properties. We investigate the effects of varying the underlying WIMP mass and crosssection, the detector target nucleus, exposure, energy threshold and maximum energy, the local circular speed and the background event rate and spectrum. The number of events observed is directly proportional to both the exposure and the cross-section, therefore these quantities have the greatest bearing on the accuracy of the WIMP mass determination. The relative capabilities of different detectors to determine the WIMP mass depend not only on the WIMP and target masses, but also on their energy thresholds. The WIMP and target mass dependence of the characteristic energy scale of the recoil spectrum suggests that heavy targets will be able to measure the mass of a heavy WIMP more accurately. We find, however, that the rapid decrease of the nuclear form factor with increasing momentum transfer which occurs for heavy nuclei means that this is in fact not the case. Uncertainty in the local circular speed and non-negligible background would both lead to systematic errors in the WIMP mass determination. For deviations of ±20 km s in the underlying value of the circular speed the systematic error is of order 10%, increasing with increasing WIMP mass. This error can be reduced by also fitting for the circular speed. With a single detector it will be difficult to disentangle a WIMP signal (and the WIMP mass) from background if the background spectrum has a similar shape to the WIMP spectrum (i.e. exponential background, or flat background and a heavy WIMP).