In a groundbreaking advancement for quantum physics, researchers at the Max Planck Institute for Quantum Optics (MPQ) in Garching, collaborating with Prof. Dr. Randolf Pohl of Johannes Gutenberg University Mainz (JGU), have achieved an unprecedented level of precision in measuring hydrogen’s atomic energy levels. This experiment, fine-tuned to the 13th decimal place, represents the most exacting test of the Standard Model of particle physics conducted to date using hydrogen atoms. Their meticulous work not only affirms fundamental physical theories but also sheds light on the enduring mysteries surrounding the proton radius puzzle, a significant long-standing anomaly in particle physics.
The Standard Model, forming the core theoretical framework of particle physics, articulates the behavior and interaction of fundamental particles and forces. Within it lies quantum electrodynamics (QED), a theory that elucidates the interaction between light particles (photons) and matter. Hydrogen, being the simplest atom with only one proton and one electron, provides an ideal platform for precision tests of QED’s predictions. The experimental team harnessed state-of-the-art high-precision laser spectroscopy to selectively probe two distinct energy levels of atomic hydrogen. By measuring the exact frequency associated with electron transitions between these energy levels, the team was able to affirm the Standard Model’s predictions with extraordinary accuracy — diverging by less than one part in a trillion, or 0.7 parts per trillion to be precise.
This formidable level of precision establishes a new benchmark in the measurement of atomic hydrogen’s energy states and equals the accuracy of the most celebrated validation of the Standard Model to date — the anomalous magnetic moment of the electron. Prof. Randolf Pohl notes that this breakthrough brings ordinary hydrogen studies in line with the most stringent tests of quantum theory, affirming the Standard Model in an unprecedented way.
The new level of sensitivity in the measurements has facilitated the detection of subtle quantum effects arising from the involvement of hadrons, complex particles composed of quarks. These weak contributions to the transition frequency historically remained beyond observational reach. The team further identified contributions stemming from transient muon-antimuon pairs emerging within the quantum vacuum — a subtle form of vacuum polarization that enters calculations when considering quantum fluctuations surrounding the hydrogen atom’s electron.
This novel observation sheds light on an intricate quantum phenomenon wherein virtual particle pairs briefly flicker into existence, influencing the atom’s energy dynamics. Dr. Vitaly Wirthl from MPQ emphasized that such quantum effects were detected in electronic hydrogen for the very first time, an achievement only possible due to the extraordinary resolution of their experimental setup.
Alongside testing QED, the experiment addresses the long-standing “proton radius puzzle.” This puzzle emerged due to discrepancies between proton size measurements obtained from ordinary hydrogen atoms and those inferred from muonic hydrogen — atoms where the electron is replaced by a much heavier muon. Since muons are roughly 200 times more massive than electrons, their proximity to the proton nucleus amplifies interactions sensitive to the proton’s charge distribution, permitting proton radius measurements with distinct systematic effects.
The new measurements of transition frequencies in electronic hydrogen agree with prior muonic hydrogen data, both yielding a proton radius estimated at 0.8406 femtometers. This revelation significantly narrows previously observed inconsistencies and suggests the discrepancy may be attributable to as-yet-undiscovered systematic or theoretical effects rather than fundamental physics. However, despite this convergence, the precise origin of the earlier disagreement remains enigmatic, encouraging renewed theoretical inquiry.
The MPQ led this research endeavor, with groundwork laid since 2011 and final measurements culminating in 2019. Following meticulous data analysis that carefully accounted for various potential interference and systematic errors, the experiment achieved a level of precision that pushes the frontier of atomic physics. Prof. Pohl, now primarily based at Mainz University, remains closely engaged in these investigations through his affiliation with the PRISMA++ Cluster of Excellence and the Collaborative Research Centre “Hadrons and Nuclei as Discovery Tools” at JGU.
Looking forward, the research team is expanding their scope beyond ordinary and muonic hydrogen to investigate tritium — a hydrogen isotope containing two added neutrons alongside its single proton. Measuring energy transitions in this isotope could yield new insights into nuclear forces and interactions, further refining fundamental constants and deepening our understanding of atomic physics.
Beyond the fundamental insights, this research exemplifies the powerful synergy of cutting-edge experimental techniques and theoretical precision. The use of ultra-stable lasers and sophisticated spectroscopy instruments enables probing atomic transitions with hitherto unimagined accuracy. This paves the way not only for validating existing physical laws but also for potentially uncovering deviations that hint at new physics beyond the Standard Model.
The findings highlight the remarkable capacity of atomic hydrogen, despite its simplicity, to remain a critical tool for probing the fabric of the quantum world. By discerning minuscule energy shifts and quantum vacuum phenomena, these experiments open fresh avenues in both fundamental physics and applied sciences, including the refinement of atomic clocks and quantum metrology.
In essence, this research not only consolidates our confidence in the Standard Model and QED but also invigorates the quest to resolve outstanding anomalies in particle physics. As experimental precision climbs ever higher, the humble hydrogen atom continues to serve as a luminous beacon guiding physicists through the subtle underpinnings of matter and the universe.
Subject of Research: Not applicable
Article Title: Sub-part-per-trillion test of the Standard Model with atomic hydrogen
News Publication Date: 11-Feb-2026
Web References: 10.1038/s41586-026-10124-3
References: The results were published in the journal Nature.
Image Credits: Photo/© Vitaly Wirthl, MPQ
Keywords
Standard Model, Quantum Electrodynamics, Hydrogen Atom, Proton Radius Puzzle, Muonic Hydrogen, High-Precision Laser Spectroscopy, Atomic Energy Levels, Vacuum Polarization, Muon-Antimuon Pairs, Particle Physics, Fundamental Constants, Quantum Metrology
