Detecting Ultralight Dark Matter with Matter Effect

TL;DR

This work develops a comprehensive quantum-mechanical framework to detect ultralight scalar dark matter via matter effects arising from a quadratic scalar–SM coupling. By unifying scattering and background-induced forces within a single formalism, it identifies perturbative and non-perturbative regimes, reveals decoherence and descreening phenomena, and maps how experimental geometries and phase-space distributions influence sensitivity. The authors provide detailed predictions for ISL and EP tests, MICROSCOPE reinterpretation beyond spherical symmetry, and UV completions that realize the quadratic coupling, offering concrete guidance for next-generation acceleration experiments. The results establish a broad, phase-space–aware strategy to probe repulsive quadratic scalar–photon interactions across parameter space, with implications for both terrestrial and space-based setups. The analysis also clarifies how different UV models yield distinct signs of the effective mass in matter and how these signals can be distinguished experimentally.

Abstract

Ultralight particles, with a mass below the electronvolt scale, exhibit wave-like behavior and have arisen as a compelling dark matter candidate. A particularly intriguing subclass is scalar dark matter, which induces variations in fundamental physical constants. However, detecting such particles becomes highly challenging in the mass range above $10^{-6}\,\text{eV}$, as traditional experiments face severe limitations in response time. In contrast, the matter effect becomes significant in a vast and unexplored parameter space. These effects include (i) a force arising from scattering between ordinary matter and the dark matter wind and (ii) a fifth force between ordinary matter induced by the dark matter background. Using the repulsive quadratic scalar-photon interaction as a case study, we develop a unified framework based on quantum mechanical scattering theory to systematically investigate these phenomena across both perturbative and non-perturbative regimes. Our approach not only reproduces prior results obtained through other methodologies but also covers novel regimes with nontrivial features, such as decoherence effects, screening effects, and their combinations. In particular, we highlight one finding related to both scattering and background-induced forces: the descreening effect observed in the non-perturbative region with large incident momentum, which alleviates the decoherence suppression. Furthermore, we discuss current and proposed experiments, including inverse-square-law tests, equivalence principle tests, and deep-space acceleration measurements. Notably, we go beyond the spherical approximation and revisit the MICROSCOPE constraint on the background-induced force in the large-momentum regime, where the decoherence and screening effects interplay. The ultraviolet models realizing the quadratic scalar-photon interaction are also discussed.

Figures (22)

• Figure 1: Classification of scattering between ultralight dark matter and ordinary matter in the $k_0\text{-}m_\text{M}$ plane, where $k_0$ is the mean incident momentum of dark matter, $m_\text{M}$ is the effective mass of dark matter due to its coupling to ordinary matter, and $R$ is the size of the ordinary matter. Regions A and B are perturbative, and the remaining regions are non-perturbative. The screening effect becomes stronger as $m_\text{M}$ increases, while the decoherence effect becomes stronger as $k_0$ increases. In the strongly-coupled region, the descreening effect emerges at large $k_0$. Region A: $R^{-1}>m_\text{M},k_0$. The scattering occurs in the perturbative regime, where the scattered ordinary matter is treated as a point-like object. Region B: $k_0 > R^{-1}$ and $(k_0 R^{-1})^{1/2}>m_\text{M}$. The scattering remains in the perturbative regime; however, it is necessary to take the finite size into account. Region C: $m_\text{M} > R^{-1} > k_0$. This corresponds to low-momentum hard-sphere scattering. Region D: $m_\text{M} > k_0 > R^{-1}$. This corresponds to high-momentum hard-sphere scattering. Region E: $k_0 > m_\text{M}, \, R^{-1}$. This corresponds to high-momentum solid-sphere scattering, where the effective potential is treated as a finite well. In Region E$\setminus$B, the wave function enters the non-perturbative regime.
• Figure 2: Schematic representation of scalar wave scattering off a sphere of radius $R$ composed of ordinary matter. $\psi_\text{inc}$ represents the incident plane wave propagating with the momentum $\mathbf{k}$, while $\psi_\text{sc}$ represents the scattered wave. The observer at position $\mathbf{r}$ with an angle $\theta$ (referred to as the reflection angle) detects the wave with momentum $\mathbf{k}'$, and the corresponding momentum transfer is represented by $\mathbf{q} = \mathbf{k}' - \mathbf{k}$. For the scattering force, the gray sphere represents the test mass $\mathcal{T}$ experiencing an additional acceleration due to dark matter collisions. For the background-induced force, the gray sphere represents the source mass $\mathcal{S}$. It generates a spatially inhomogeneous scalar potential, which in turn induces the acceleration of the test mass $\mathcal{T}$ in its vicinity (not shown in the figure).
• Figure 3: Coordinate frame for phase space integration. The mean momentum $\mathbf{k}_0$ of the dark matter is aligned with the z-axis, and the position vector $\mathbf{r}$ lies in the $x\text{-}z$ plane at an angle $\theta_\mathbf{r}$ relative to $\mathbf{k}_0$. The forward direction corresponds to $\theta_\mathbf{r} = 0$, while the backward direction corresponds to $\theta_\mathbf{r} = \pi$. A monochromatic mode in the phase space distribution is represented by $\mathbf{k}$, which has a polar angle $\theta_\mathbf{k}$ and an azimuthal angle $\phi_\mathbf{k}$. $\theta$, defined as the angle between the monochromatic momentum $\mathbf{k}$ and the position vector $\mathbf{r}$, is shown in Fig. \ref{['fig:qm_sca']} and is referred to as the deflection angle in quantum mechanical scattering processes.
• Figure 4: The ratio of the scattering force over the background-induced force in the perturbative region for different $k_0$. The scattering force is measured using a sphere of radius $R$, while the background-induced force is measured using two identical spheres of the same radius and material, separated by a distance $r$. We plot the ratio $|\mathbf{F}_\text{sc}|/|\mathbf{F}_\text{bg}|$ for separations $r=2R$ (brown), $r=3R$ (red), and $r=5R$ (orange). When $k_0 r >1$, the scattering force dominates. When $k_0 r <1$, the background-induced force dominates. For the background-induced force, we assume the most optimistic sensitivity by considering the forward direction ($\theta_\mathbf{r} = 0$). In other directions ($0 < \theta_\mathbf{r} \leq \pi$), $\abs{\mathbf{F}_\text{bg}}$ decreases by one to two orders of magnitude when $k_0 r > 1$.
• Figure 5: The dark matter-induced acceleration as a function of the Platinum spherical radius. Solid lines represent the exact accelerations calculated using the partial wave analysis, while dashed lines represent the accelerations obtained via the Born approximation. The $a$-$R$ curves for different values of $\Lambda_\gamma$ are shown in purple, magenta, and orange, respectively. In the small-$R$ region, where $m_\text{M}, k < R^{-1}$ (Region A), the solid lines closely match the dashed lines. Left: $m_0 = 10^{-5}\,\text{eV}$. The maximum accelerations occur at $R \sim m_\text{M}^{-1}$. As $R$ increases further, the acceleration approaches saturation, following the $\sigma_\text{T} = 4 \pi R^2$ line. Right: $m_0 = 10^{-2}\,\text{eV}$. The purple and magenta lines exhibit maximum accelerations at $R \sim m_\text{M}^{-1}$. As $R$ increases, these lines initially follow the $\sigma_\text{T} = 4 \pi R^2$ line before transitioning to the $\sigma_\text{T} = \pi R^2$ line when $R > k^{-1}$. The orange solid line aligns closely with the orange dashed line, as it lies in the weakly coupled region. As $R$ increases, it reaches its maximum at $R \sim k^{-1}$ and subsequently decreases, following a power-law behavior of $a \propto R^{-1}$.