Coherence from Randomness: Sub-keV Dark Matter Scattering off Random, Heterogeneous Materials

TL;DR

This work addresses the challenge of detecting sub-keV dark matter by exploiting coherence within random, heterogeneous materials. By modeling the target with a density field $n(\mathbf r)=n_0+\delta n(\mathbf r)$ and its two-point correlator, the authors show that density fluctuations can enable local, phase-coherent DM scattering within patches of size $\xi$, boosting the total cross section to scale as $\sigma_{\rm tot}\sim N_c N_{\rm tot}$ and the induced acceleration by an additional factor $N_c$. Applying the framework to MICROSCOPE's Ti–6Al–4V test masses, they derive a bound of $\sigma_{\chi N}\lesssim4\times10^{-38}\ \mathrm{cm^2}$ at $m_χ\approx0.02\ \mathrm{keV}$, and they argue that future torsion-balance experiments with optimized porous materials could improve sensitivity to $\sim5\times10^{-43}\ \mathrm{cm^2}$. Overall, the paper introduces a novel coherence mechanism in random media for light DM, yielding new parameter-space coverage and motivating precision experiments with density-contrast materials for acceleration-based DM searches.

Abstract

The sub-keV mass range has long posed a challenge for the direct detection of dark matter via elastic scattering. In this Letter, we propose a new mechanism in which dark matter, assumed to be quadratically coupled to SM particles, scatters from random heterogeneous materials with intrinsic density fluctuations, yielding an enhanced coherent response. This effect can substantially increase the total scattering rate and induce measurable accelerations of the target. Using this idea, we derive new constraints from the MICROSCOPE mission that extend into previously unexplored parameter space for sub-keV dark matter, probing cross sections down to $\sim 4\times10^{-38}\,\mathrm{cm^2}$.

Figures (3)

• Figure 1: Scattered waves from particles within the same cluster (orange) are in phase and therefore add coherently. In contrast, waves originating from different clusters (red and blue) carry random relative phases due to the fluctuating sign of the density contrast $\delta n$, so their average contribution vanishes, and the signals from different clusters add only incoherently.
• Figure 2: Form factors for different correlation lengths $\xi$ for spherical (solid) and cubic (dashed) targets with equal volume $V = 1\,\mathrm{cm}^3$ at a fixed momentum transfer $q = 0.1\,\mathrm{eV}$. The variance is set to $\overline{\delta n^2} = n_0^2$. For the cubic target, the momentum $\mathbf{q}$ is taken along one of its principal edges.
• Figure 3: Constraints on the DM–nucleon scattering cross section from the MICROSCOPE mission (red) and a projected torsion-balance experiment (dashed cyan), compared with bounds from cosmic-ray–boosted DM and stellar-cooling.