Potential of constraining the Fifth Force Using the Earth as a Spin and Mass Source from space

We explore the potential of conducting an experiment in a low Earth orbit spacecraft and using the Earth a spin and mass source to constrain beyond-the-standard-model (BSM) long-range spin- and velocity-dependent interactions, which are mediated by the exchange of an ultralight $\left(m_{Z^{\prime}}<10^{-10}\text{eV}\right)$ or massless intermediate vector boson. The high speed of the low Earth orbit spacecraft can enhance the sensitivity to velocity-dependent interactions. The periodicity enables efficient extraction of signals from background noise, thereby improving the experiment’s accuracy. Combining these advantages, we demonstrate theoretically that the novel Spacecraft-Earth model can improve existing bounds on these exotic interactions by up to three orders of magnitude, using the China Space Station (CSS) as a representative low-Earth-orbit carrier. Such a model, if successfully implemented, may provide an innovative strategy for detecting ultralight dark matter and yield tighter constraints on certain coupling constants of exotic interactions.

💡 Research Summary

The manuscript proposes a novel experimental scheme to search for long‑range, spin‑ and velocity‑dependent forces—often dubbed “fifth forces”—by exploiting the Earth itself as a massive, polarized spin source and a low‑Earth‑orbit (LEO) spacecraft as a detector platform. Building on the theoretical framework originally developed by Moody and Wilczek and later refined to include six velocity‑dependent spin‑spin potentials (V₆, V₇, V₈, V₁₄, V₁₅, V₁₆) as well as mixed electron‑nucleon terms (V₄+₅, V₁₂+₁₃), the authors express each interaction in terms of axial (g_A) and vector (g_V) coupling constants, the boson mass (through the range λ = ħ/m′c), the relative velocity v, and the unit separation vector r̂.

A key insight is that a LEO platform such as the China Space Station (CSS), orbiting at ~400 km altitude with a velocity of ~7.7 km s⁻¹, experiences a relative speed with respect to Earth’s rotating interior that is more than twenty times larger than any laboratory‑based experiment. This high speed directly amplifies the velocity‑dependent terms, while the 90‑minute orbital period introduces a clean, periodic modulation of the signal as the spacecraft traverses different latitudes and longitudes. The authors argue that this periodicity can be exploited with Fourier‑based analysis to separate a genuine exotic‑force signal from background noise.

To quantify the expected sensitivity, the authors model the Earth’s polarized electron density ρ_e(r′) and unpolarized nucleon density ρ_n(r′) using spherically symmetric profiles derived from geophysical data, incorporate temperature gradients, and adopt the World Magnetic Model (WMM 2020) for the geomagnetic field. The total potential is obtained by integrating the microscopic potentials over the entire Earth (or mantle for electrons) weighted by the local polarization factor μ_B B/(k_B T). The relative velocity v is computed as the vector difference between the spacecraft’s orbital velocity and the local rotational velocity Ω × r′.

Two representative interaction ranges are examined: λ = 10²·⁵ km (comparable to the orbital altitude) and λ = 10⁵ km (about twice Earth’s radius, where the potential saturates). Assuming an energy resolution of 10⁻²⁰ eV—slightly worse than the best laboratory Lorentz‑invariance‑violation (LLI) experiments but plausible for a space‑based magnetometer—the authors simulate the pseudo‑magnetic field B_psd that would be measured by a spin‑sensitive sensor (e.g., NV‑diamond or SERF magnetometer). The simulated B_psd exhibits a clear 90‑minute sinusoidal pattern for all considered potentials.

By comparing the simulated space‑based limits with existing ground‑based constraints (primarily from torsion‑balance and comagnetometer experiments), the authors find that the “Spacecraft‑Earth” configuration could improve bounds on the coupling products g_A g_V, g_A g_A, and g_V g_V by up to three orders of magnitude for interaction ranges λ ≳ 10³ km. The improvement is most pronounced for the velocity‑dependent terms, which are otherwise poorly constrained because laboratory experiments have limited relative velocities (≈ 0.3 km s⁻¹).

The paper also acknowledges several practical challenges: maintaining ultra‑low‑noise conditions in microgravity, mitigating spacecraft vibrations and magnetic disturbances, calibrating the spin sensor orientation relative to the geomagnetic field, and refining Earth‑model asymmetries (e.g., mantle heterogeneities, core magnetization) that were neglected in the spherical approximation. Nevertheless, the authors argue that the combination of high relative speed and intrinsic signal periodicity offers a powerful new avenue for probing ultralight vector bosons (including dark photons or dark Z′) that could constitute dark matter or mediate exotic forces.

In conclusion, the work presents a compelling theoretical case that a modest space mission—potentially using an existing platform like the CSS—could dramatically tighten constraints on long‑range spin‑velocity interactions, opening a fresh experimental window on physics beyond the Standard Model. Future extensions could involve polar or higher‑altitude orbits, multi‑sensor arrays, and more sophisticated Earth‑density models to further enhance sensitivity.