Prospects for Dark Matter signal discovery and model selection via timing information in a low-threshold experiment

In the recent years, many low-threshold dark matter (DM) direct detection experiments have reported the observation of unexplained excesses of events at low energies. Exemplary for these, the experiment CRESST has detected unidentified events below an energy of about 200 eV - a result hampering the detector performance in the search for GeV-scale DM. In this work, we test the impact of nuclear recoil timing information on the potential for DM signal discovery and model selection on a low-threshold experiment limited by the presence of an unidentified background resembling this population of low-energy events. Among the different targets explored by the CRESST collaboration, here we focus on Al2O3, as a sapphire detector was shown to reach an energy threshold as low as 19.7 eV [1]. We test the ability of a low-threshold experiment to discover a signal above a given background, or to reject the spin-independent (SI) interaction in favour of a magnetic dipole (MD) coupling in terms of p-values. We perform our p-value calculations: 1) taking timing information into account; and 2) assuming that the latter is not available. By comparing the two approaches, we find that under our assumptions timing information has a marginal impact on the potential for DM signal discovery, while provides more significant results for the selection between the two models considered. For the model parameters explored here, we find that the p-value for rejecting SI-interactions in favour of a MD-coupling is about 0.11 when the experimental exposure is 460 g x year and smaller (about 0.06) if timing information is available. The conclusion on the role of timing information remains qualitatively unchanged for exposures as large as 1 kg x year. At the same time, our results show that a 90% C.L. rejection of SI-interactions in favour of a MD-coupling is within reach of an upgrade of the CRESST experiment [2].