The Standard Model of particle physics is one of the most precisely tested frameworks in science, but it is not complete. It does not explain dark matter, dark energy, or why matter dominates over antimatter in the universe. One leading possibility is the existence of new particles, axions, Z’ bosons, dark photons, that mediate forces beyond the Standard Model. The challenge is that these particles, if they exist, interact so weakly with ordinary matter that they have evaded detection.
Now, a team of physicists at Amherst College and Keene State College has set the most stringent constraints to date on certain classes of these exotic interactions, improving previous limits by up to a factor of 17.
A comagnetometer on a turntable
The experiment, led by the group of Larry R. Hunter at Amherst College, uses a ¹⁹⁹Hg–¹³³Cs comagnetometer, a device that simultaneously measures the precession of two different atomic species in the same magnetic field. By comparing how mercury (whose precession is sensitive to nuclear spin) and cesium (whose precession is sensitive to electron spin) behave, the team could isolate any spin-dependent force that couples differently to the two atoms.
The apparatus consists of three stacked vapor cells: one containing ¹⁹⁹Hg vapor flanked by two containing ¹³³Cs. A 1 μT magnetic field gives a precession frequency of about 7 Hz for the mercury and roughly 3.5 kHz for the cesium, the 500-fold difference means the cesium cycles 120 times per mercury cycle, providing a continuous high-resolution readout of any differential spin signal.
The key innovation is mounting the entire comagnetometer on a precision rotation platform with reproducibility of 0.004 degrees. The Earth itself serves as the spin source: the team used the net polarization of electrons in the Earth’s mantle and crust, estimated at 5 × 10³⁸ or more aligned electrons along the rotation axis, as a massive, naturally occurring source of polarized spins. By rotating the apparatus between north-south and east-west orientations, any exotic spin-spin interaction would modulate the precession frequency in a predictable pattern.
The numbers
Running the experiment in both orientations with blind analysis (random offsets applied until unblinding) and accounting for 13 local and 5 global systematic corrections, the team obtained null results, the signal was consistent with zero at all orientations. These null results translate into upper bounds on the coupling constants of exotic spin-dependent forces.
In the north-south orientation, the team achieved a frequency bound of 72 nHz for the differential precession signal. The corresponding energy bound on any total spin-dependent coupling is 7.49 × 10⁻²³ eV.
The most constraining result sets an upper limit on the electron-neutron axial coupling constant |g_A^e g_A^n| ≤ 3.0 × 10⁻⁴⁸, roughly 17 million times weaker than the gravitational interaction between an electron and a neutron. For the electron-proton axial coupling, the bound is |g_A^e g_A^p| ≤ 3.0 × 10⁻⁴⁷.
For masses below about 10⁻¹² eV (corresponding to interaction ranges beyond 1 km), these are the best experimental limits ever set.
What this means for dark matter and new physics
The exotic particles constrained by this experiment cover a broad range of dark matter candidates:
- Axions and axion-like particles (ALPs): predicted by solutions to the strong CP problem and leading dark matter candidates, constrained through their axial-axial coupling to electrons and nucleons.
- Z’ bosons and dark photons: hypothetical force carriers of new U(1) gauge symmetries, constrained through their axial-vector couplings.
- Torsion gravity models: extensions of general relativity that introduce spin-dependent gravitational couplings.
The experiment does not rule out these particles entirely, it narrows the allowed parameter space. For each candidate, the range of possible coupling constants has been reduced by roughly an order of magnitude compared to previous best measurements.
Methodology matters
Several experimental advances contributed to the 17-fold improvement over the earlier state of the art (including the same group’s 2013 Science paper). The team used a free-precession geometry that suppresses vector AC light shifts from the pump lasers, four-layer mu-metal magnetic shielding providing attenuation of roughly 3 million, a precision rotation platform for orientation control, and thorough systematic characterization with 18 separate corrections.
The blind analysis protocol, standard in particle physics at large facilities but less common in tabletop precision experiments, adds confidence that unconscious experimental bias did not influence the result.
Funding was provided by NSF Grant PHY-2110523. The paper was submitted to arXiv on June 30, 2026.
Source
Clayburn, N.B., Glassford, A., Uelmen, T., Kyung, A.R., Boneva, Y., Salim, S., Weiss, A.S., Waldherr, F., Carlin, C., Peck, S.K., and Hunter, L.R. “New Bounds on Exotic Long-Range Spin-Spin Interactions.” arXiv:2607.00200 physics.atom-ph] (2026). [https://arxiv.org/abs/2607.00200