Calcium Isotope Data Reveals Non-Linear King Plot, Suggesting Fifth Fundamental Force

The ongoing quest to reconcile the Standard Model of particle physics with cosmological observations, such as the nature of dark matter, continues to drive exploration into new fundamental physics, including the potential existence of a fifth fundamental force. Recent international research focusing on precise atomic measurements has yielded compelling, though preliminary, evidence supporting this possibility.

The investigation, detailed in the journal Physical Review Letters in 2025, centered on measuring atomic transition shifts across a series of calcium isotopes: Ca-40, Ca-42, Ca-44, Ca-46, and Ca-48. These transitions, which involve electrons moving to higher energy orbitals and subsequently emitting energy upon return to the ground state, are intrinsically linked to the nuclear structure defined by the varying neutron count, which ranges from 20 to 28 across the measured set. The Standard Model predicts that when these transition shifts are plotted on a King plot, they should align in a strictly linear correlation.

Researchers meticulously documented these shifts and observed a subtle but distinct non-linear deviation from the expected straight-line relationship. While such a deviation could be attributed to known, unmodeled nuclear effects, physicists interpret this finding as the first tangible indication favoring a weak, additional force acting between electrons and neutrons. This hypothetical interaction would require a mediating particle, theoretically a Yukawa particle or boson, to carry the force.

The 2025 study established the tightest constraints recorded to date on the mass and intensity of this hypothetical carrier particle, estimating its mass to be within the range of approximately 10 to 10 million electronvolts (eV/c²). This work involved a consortium of scientists from Germany, Switzerland, and Australia. Notably, researchers at ETH Zurich achieved energy level shift accuracy of 100 millihertz by simultaneously trapping two isotopes in an ion trap, a precision factor of one hundred greater than previous measurements.

As a direct follow-up, the international team is currently refining their analysis in early 2026 by measuring a third distinct energy transition within the calcium isotopes. This additional data point is intended to construct a three-dimensional representation of the King plot, a critical step to definitively confirm or refute the observed signs pointing toward physics beyond the Standard Model. While other experiments, such as the muon g-2 at Fermilab, have recently confirmed the Standard Model in different contexts, this calcium isotope analysis offers a novel avenue for probing fundamental interactions at the atomic scale.

The successful mapping of these variations onto the first non-linear King plot for calcium represents a significant advancement in constraining the parameters of potential new fundamental interactions governing the cosmos.