Detecting meV-Scale Dark Matter via Coherent Scattering with an Asymmetric Torsion Balance

Dark matter with mass in the crossover range between wave dark matter and particle dark matter, around $(10^{-3},, 10^3),$eV, remains relatively unexplored by terrestrial experiments. In this mass regime, dark matter scatters coherently with macroscopic objects. The effect of the coherent scattering greatly enhances the accelerations of the targets that the dark matter collisions cause by a factor of $\sim 10^{23}$. We propose a novel torsion balance experiment with test bodies of different geometric sizes to detect such dark matter-induced acceleration. This method provides the strongest constraints on the scattering cross-section between the dark matter and a nucleon in the mass range $(10^{-3}, 1),$eV.

💡 Research Summary

The paper addresses a largely unexplored region of dark‑matter (DM) parameter space: masses between roughly 10⁻³ eV and 10³ eV, where the particle’s de Broglie wavelength is macroscopic. In this regime the DM behaves like a wave and can scatter coherently off an entire macroscopic object. The authors point out that when the inverse momentum transfer (1/q) exceeds the size of the target, the total scattering cross‑section is enhanced by the square of the number of nucleons, σ_tot ≈ N_A² σ_χN (with N_A ≈ 10²³). Consequently the acceleration imparted to a target, a ≈ (ρ_χ m_χ σ_tot v_χ q)/m_tot, is amplified by a factor of order N_A, i.e. ∼10²³, compared with ordinary particle‑DM scattering.

To exploit this effect they propose a torsion‑balance experiment that deliberately uses test masses of identical total mass but very different geometric size. The design consists of four tungsten test bodies suspended from a pendulum: two solid cubes (edge ≈ 0.8 cm) and two hollow cubic shells (outer edge ≈ 4.2 cm, wall thickness ≈ 50 µm). Both types weigh about 10 g, so the nucleon number per body is the same, yet their volumes differ by more than an order of magnitude. For DM masses such that the de Broglie wavelength λ = 1/(m_χ v_χ) lies between the cube size and the shell size (L_cube < λ < L_shell), the cube experiences the full coherent enhancement (σ ≈ N_A² σ_χN) while the shell’s interior is effectively “shadowed” and its cross‑section drops sharply. The resulting difference in acceleration, Δa = |a_cube − a_shell|, produces a measurable torque on the pendulum.

The authors derive the form factor F(q,L) for a cube and for a shell, showing that the coherent enhancement fades when q L ≫ 1. Figure 1 displays the total cross‑sections for the two geometries as a function of the DM momentum along the rotation axis; the difference peaks when λ is between the two sizes. They then calculate the average acceleration by integrating over the Maxwell‑Boltzmann velocity distribution of the Galactic DM halo, keeping only the momentum component along the torsion‑balance axis (q_z). The detectable acceleration difference is compared with the projected experimental uncertainty.

The experimental setup builds on existing high‑precision torsion balances used for equivalence‑principle tests. The pendulum is placed in vacuum, rotated continuously on a turntable, and its angular position is read out by an autocollimator. By synchronising the rotation frequency with the expected DM‑wind direction, the DM‑induced torque appears as a sinusoidal signal at a known frequency, allowing optimal signal‑to‑noise extraction. Systematic uncertainties considered include magnetic coupling, local gravitational multipoles (the dominant term q_31 ≈ 10 g·cm³), temperature gradients, tilt of the rotation axis, and rotation‑rate fluctuations. Using conservative amplification factors for these effects, the authors estimate a total acceleration uncertainty of δa ≈ 1.4 × 10⁻¹² cm s⁻² (1σ), corresponding to a 95 % confidence bound of |δa| < 2.7 × 10⁻¹² cm s⁻².

With this sensitivity, the authors map out the reachable region in the (m_χ, σ_χN) plane. For DM masses between 10⁻³ eV and 1 eV, the experiment can probe nucleon‑DM cross‑sections down to σ_χN ≈ 10⁻⁵¹ cm², roughly two to three orders of magnitude stronger than existing astrophysical limits from supernova cooling and big‑bang nucleosynthesis. The sensitivity curve is flat where the cross‑section difference between cube and shell is constant, and it rises (i.e., becomes weaker) where the difference diminishes. The strongest reach occurs precisely when λ lies between the two test‑mass dimensions, because the cube retains full coherence while the shell’s coherence is lost.

The paper also discusses the limits of the approach. If the DM‑nucleon interaction is too strong, the DM wave is reflected at the surface and the coherent enhancement saturates at the geometric cross‑section, eliminating the N_A² boost. Therefore the method is only applicable to weakly interacting DM, which is precisely the regime of interest for sub‑eV candidates.

In summary, the authors present a conceptually simple yet powerful technique: using a non‑symmetric torsion balance to convert the enormous coherent‑scattering enhancement of ultra‑light dark matter into a measurable torque. The proposal leverages mature torsion‑balance technology, requires only modest modifications (different‑size test bodies), and promises unprecedented sensitivity to DM masses in the meV–eV range. If realized, it would open a new experimental window on the wave‑particle crossover region of dark‑matter physics, complementing existing searches that focus either on heavier particle‑like DM or on ultra‑light wave‑like fields.