Determining the WIMP mass from a single direct detection experiment; a more detailedstudy

Abstract

The energy spectrum of nuclear recoils in weakly interacting massive particle (WIMP)direct detection experiments depends on the underlying WIMP mass. We studyhow the accuracy with which the WIMP mass could be determined by a singledirect detection experiment depends on the detector configuration and the WIMPproperties. We investigate the effects of varying the underlying WIMP mass andcross-section, the detector target nucleus, exposure, energy threshold and maximumenergy, the local circular speed and the background event rate and spectrum. Thenumber of events observed is directly proportional to both the exposure and thecross-section; therefore these quantities have the greatest bearing on the accuracy of theWIMP mass determination. The relative capabilities of different detectors fordetermining the WIMP mass depend not only on the WIMP and target masses, butalso on their energy thresholds. The WIMP and target mass dependence of thecharacteristic energy scale of the recoil spectrum suggests that heavy targets will beable to measure the mass of a heavy WIMP more accurately. We find, however,that the rapid decrease of the nuclear form factor with increasing momentumtransfer 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 bothlead to systematic errors in the WIMP mass determination. For deviations of ± 20 km s−1 in the underlying value of the circular speed the systematic error is of order10%, increasing with increasing WIMP mass. This error can be reduced by also fitting for thecircular speed. With a single detector it will be difficult to disentangle a WIMP signal (andthe WIMP mass) from background if the background spectrum has a similar shape to theWIMP spectrum (i.e. exponential background, or flat background and a heavyWIMP).