Dark Matter Attenuation Effects: Sensitivity Ceilings for Spin-Dependent and Spin-Independent Interactions

Abstract: Direct detection experiments aimed at uncovering the elusive nature of dark matter (DM) have made significant progress in probing ever lower cross-sections for DM-nucleon interactions. At the same time, an upper limit in the cross-section sensitivity region is present due to DM scattering in the Earth and atmosphere and as a result never reaching the detector. We investigate the impact of this effect for both spin-dependent and spin-independent interactions. In contrast to previous studies that assume a straight line path for DM scattering we employ a semi-analytic diffusion model that takes into account the impact of potentially large angle deviations prevalent for light DM masses. We find that for sufficiently low energy thresholds, this difference in modelling impacts the DM interaction cross-section sensitivity. This study evaluates the impact in the context of the QUEST-DMC experiment, which utilises surface-based detectors with superfluid Helium-3 bolometers to search for sub-GeV DM exploiting low energy threshold. At masses below 1 GeV$/c^2$ the deviation between the two frameworks becomes pronounced. The ceiling sensitivity limit for QUEST-DMC on spin-dependent DM-neutron cross-sections is $\sim 3 \times 10^{-24}$ cm$^2$ using the diffusive framework and approximately doubles with the straight-line path DM scattering. Similarly, for spin-independent DM-nucleon cross-sections, the ceiling limit is $\sim 7.5 \times 10^{-27}$ cm$^2$ under the diffusive framework and also increases about a factor of two with the straight-line path approximation, within the mass range of 0.025-5 GeV$/c^2$.