Digging for Dark Matter: Spectral Analysis and Discovery Potential of Paleo-Detectors

Paleo-Detectors are ancient minerals which can record and retain tracks induced by nuclear recoils over billion year timescales. They may represent the most sensitive method for the direct detection of Dark Matter (DM) to date. Here, we improve upon the cut-and-count approach previously employed for paleo-detectors by performing a full spectral analysis of the DM- and background-induced track length distributions. This spectral analysis allows us to project improved exclusion limits and detection thresholds for DM. Further, we investigate the impact of background shape uncertainties using realistic background models. We find that in the most optimistic case of a %-level understanding of the background shape, we can achieve sensitivity to DM-nucleon scattering cross sections up to a factor of 100 smaller than current XENON1T bounds for DM masses above $100\,$GeV. For DM lighter than $ 10\,$GeV, paleo-detectors can probe DM-nucleon cross sections many orders of magnitude below current experimental limits. Allowing for larger uncertainties in the shape of the backgrounds, we find that the impact on the sensitivity is considerable. However, assuming 10% bin-to-bin shape uncertainties, the sensitivity of paleo-detectors still improves over XENON1T limits by a factor of $\sim 8$ for DM heavier than $ 100\,$GeV. For lighter DM candidates, even with 50% bin-to-bin background shape uncertainties, paleo-detectors could achieve sensitivities an order of magnitude better than proposed conventional low-threshold experiments. Finally we show that, in the case of a DM discovery, regions in which the mass can be constrained extend to significantly higher DM masses than for proposed conventional experiments. For DM-nucleon cross sections just below current XENON1T limits, paleo-detectors could constrain the DM mass even if the new particle is as heavy as $ 1 \mathrm{\,TeV}$.