ETH Zurich researchers detect a possible fifth force of nature

Calcium atoms have produced an unusually clear break from a pattern physicists expected to follow a straight line. The deviation is real, but its cause remains unresolved, sharpening a search for forces that may exist beyond known physics.

The Standard Model of particle physics describes elementary particles and three of the four known fundamental forces with remarkable precision. Yet important gaps remain. It cannot provide a viable dark matter candidate, explain the universe's matter-antimatter imbalance or account for neutrino masses inferred from oscillation measurements.

“The Standard Model is currently the best explanation of the universe, but we know it cannot explain everything,” said Diana Prado Lopes Aude Craik, a physics professor at ETH Zurich. She pointed to dark matter as “one of the biggest mysteries in physics today”.

Some proposed extensions of known physics introduce a fifth fundamental force. One possibility involves an unknown interaction between electrons and neutrons, carried by a hypothetical particle known as a scalar boson.

Instead of creating particles in a high-energy accelerator, physicists can look for such a force by measuring atoms with extraordinary precision.

“As atomic physicists, we can measure the atom with extremely high precision,” Aude Craik said. “Therefore, the idea is to search for this new force between the neutron and the electron using precision atomic spectroscopy.”

The international effort involved ETH Zurich, Germany's Physikalisch-Technische Bundesanstalt, the Max Planck Institute for Nuclear Physics in Heidelberg and research groups carrying out precision theoretical calculations.

The experiment focused on calcium isotopes. These are forms of calcium with the same 20 protons but different numbers of neutrons. Because their electron structures remain essentially the same, comparing isotopes lets physicists search for tiny effects connected to neutron number.

“If this force really exists in the atom, then its strength is proportional to the number of neutrons in the atomic nucleus,” said ETH doctoral student Luca Huber. “That’s why we are experimenting with isotopes to detect this hypothetical force”.

The researchers studied all five stable, even calcium isotopes, with mass numbers 40, 42, 44, 46 and 48. Their nuclei contain between 20 and 28 neutrons.

Electrons occupy specific energy levels within an atom. When they move between those levels, they absorb or emit light at precise frequencies. Differences between isotopes produce tiny changes called isotope shifts.

“To determine these energy shifts, we measure the frequency of the light emitted when our isotopes transition between two energy levels,” Aude Craik said.

At ETH Zurich, the researchers trapped two singly charged calcium isotopes together using electromagnetic fields. Lasers then probed an optical transition in both ions.

Measuring two isotopes at the same time allowed the team to suppress noise shared by both measurements. Using correlation spectroscopy, the group reduced isotope-shift uncertainties to less than 70 millihertz for the calcium-ion transition examined in the paper.

A separate team at PTB studied highly charged calcium ions, Ca14+, using a transition at a wavelength of 570 nanometers. Those ions were produced in an electron-beam ion trap, transferred into a cryogenic Paul trap and cooled with the help of a beryllium ion.

The Ca14+ isotope shifts were measured with uncertainties below about 150 millihertz.

Meanwhile, the PENTATRAP mass spectrometer in Heidelberg measured nuclear mass ratios between the isotopes to better than 4 parts in 100 billion.

Combining these measurements gave the researchers an exceptionally sensitive test known as a King plot.

In its simplest form, a King plot compares isotope shifts from two atomic transitions. Standard calculations predict that the points should form a straight line when the dominant mass and nuclear-size effects are considered.

They did not.

The calcium measurements produced a nonlinear King plot with a statistical significance of roughly 1,000 sigma. Previous calcium King plots had appeared linear within their measurement uncertainties.

That does not mean physicists detected a fifth force.

“The key thing about these King plots: if all the points lie on a straight line, the measured values can be explained by known nuclear physics effects,” Aude Craik said.

A bend in the line can arise from physics beyond the Standard Model, but subtler effects within established physics can create the same general signal.

The team examined two important possibilities. One was a second-order mass shift, a higher-order effect connected to nuclear recoil. Calculations showed that this contribution alone could not reproduce the observed pattern.

The researchers then considered nuclear polarization. This occurs when interactions with electrons deform or excite the nucleus in ways that can slightly alter atomic energy levels.

Calculating that effect accurately is difficult. The team estimated a 50 percent uncertainty for relevant parts of the nuclear-polarization calculation. Within that uncertainty, nuclear polarization could account for the remaining nonlinearity.

“We can’t say that we’ve discovered new physics here,” Aude Craik emphasised. “However, we know how strong the new force can be at most because we would have seen it otherwise in our measurements, even with the uncertainties”.

The researchers went further by combining three different calcium transitions in a generalized King-plot analysis. They first subtracted their calculated second-order mass-shift contribution, then used the additional transition to remove another source of nonlinearity.

The resulting generalized King plot was consistent with a straight line, with a nonlinearity significance below one sigma.

That allowed the team to place 95 percent confidence limits on the possible interaction strength of a hypothetical scalar boson coupling electrons to neutrons.

For most of the parameter space examined, the paper reports the strongest King-plot-derived constraints yet on such a particle.

Those limits remain restricted by uncertainties in calculations of second-order mass shifts in singly charged calcium and by the precision of one additional calcium transition, currently measured at roughly 20 hertz.

The team is now measuring another energy transition with still greater precision.

“We are currently measuring a third energy transition in the calcium isotopes,” Huber said, “and doing so with even greater precision than before.”

More accurate calcium measurements could help physicists distinguish subtle nuclear effects from signals that cannot be explained by the Standard Model.

Expanding the analysis to additional precisely measured transitions would also test whether nuclear polarization consistently produces the remaining nonlinear pattern. Better theoretical calculations could reduce one of the largest current uncertainties.

“We hope that this will help us overcome the theoretical challenges and make further progress in the search for this new force,” Aude Craik said.

If future measurements and calculations account for the anomaly using known physics, they would improve physicists' understanding of nuclear effects in precision spectroscopy. If a residual pattern remains after those contributions are controlled, calcium could become an even more sensitive laboratory for testing forces beyond the Standard Model.

These resources explore how precision atomic spectroscopy can test new forces, while showing why nuclear structure and other Standard Model effects must be separated from genuine signs of new physics.

Isotope Shift Spectroscopy in Mercury Vapors: A Promising Alternative to Ytterbium for New Physics Search
Ultra-precise measurements of mercury isotopes revealed significant King-plot nonlinearity and established mercury as another promising system for testing nuclear effects and hypothetical boson-mediated forces. (Physical Review Letters, 2026)

Toward a global search for new physics with isotope shifts
This work develops a broader framework for combining isotope-shift measurements across different atomic systems, potentially improving searches for new electron-neutron interactions and reducing degeneracies that complicate individual experiments. (Physical Review A, 2025)

Precision isotope-shift spectroscopy for new physics searches and nuclear insights
This expert review explains how isotope shifts and King plots can probe new particles while also revealing nuclear structure, and examines the theoretical effects that can imitate signals of physics beyond the Standard Model. (Nature Reviews Physics, 2025)

Probing New Bosons and Nuclear Structure with Ytterbium Isotope Shifts
Precision measurements of ytterbium isotopes combined atomic spectroscopy with exceptionally accurate mass ratios to investigate King-plot nonlinearities, nuclear structure and possible fifth-force particles coupling electrons and neutrons. (Physical Review Letters, 2025)

Systematic-free limit on new light scalar bosons via isotope shift spectroscopy in Ca+
Measurements of trapped calcium ions produced a King plot consistent with linearity at the parts-per-billion level and tightened limits on hypothetical light scalar bosons, providing important groundwork for later calcium fifth-force searches. (Physical Review A, 2024)

Research findings are available online in the journal Physical Review Letters.

The original story "ETH Zurich researchers detect a possible fifth force of nature" is published in The Brighter Side of News.

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