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Experiments with hydrogen confirm fundamental quantum theory up to the 13th decimal place and solve proton radius puzzle
Researchers at the Max Planck Institute for Quantum Optics (MPQ), Garching, in collaboration with Prof. Dr. Randolf Pohl from the Institute for Physics at Johannes Gutenberg University Mainz (JGU), have successfully conducted experiments on hydrogen atoms which allow testing of the Standard Model of particle physics up to the 13th decimal place. When it comes to measurements using hydrogen atoms, this is the most exact result to date. It allows researchers to, among other things, test predictions in hydrogen and solve the so-called proton radius puzzle. This puzzle has existed since measurements on two types of hydrogen indicated different proton radii. The new research results have recently been published in the journal Nature.
New benchmark for measuring the energy level of the hydrogen atom
The Standard Model of particle physics encompasses the smallest-scale physics in a model consisting of particles and forces. One of its foundational components is quantum electrodynamics (QED). It described how light and matter fundamentally interact with each other. “Because hydrogen is relatively simple, it is well-suited for calculation. This means we can use it to test QED, and thus the Standard Model”, explains Prof. Randolf Pohl. For their experiment, the researchers analyzed hydrogen’s energetic structure using high-precision laser spectroscopy. They examined two different energy levels and determined the energy needed to transition from one level to the other, or, more specifically, their transition frequency. The measured transition frequency confirms the Standard Model with a deviation of less than one trillionth (0.7 parts per trillion). With this, the researchers have set a new benchmark in measuring the energy levels of hydrogen atoms. “This measurement is as good as the anomalous magnetic moment of the electron – the current gold standard for the confirmation of the Standard Model”, says Pohl.
Thanks to this precision, the measurements taken confirm predictions made through the Standard Model which have never been confirmed in ordinary hydrogen before. “We are able to see very small, extremely interesting contributions that arise from the interaction with more complex particles called hadrons”, says Dr. Lothar Maisenbacher from the MPQ, lead author of the study. Dr. Vitaly Wirthl, co-author and also from the MPQ, expands on this: “In the contributions to the transition frequency, we see muons in the electronic hydrogen for the first time. In theory, muon-antimuon particle pairs contribute to vacuum polarization, which is relevant for the precision of our measurement.”
Solving an old discrepancy
In addition to testing the Standard Model and QED, the scientists also used the hydrogen measurement to investigate the inconsistency with earlier measurements in muonic hydrogen. These measurements, lead by Prof. Pohl, use muonic hydrogen that possesses a muon instead of an electron. This elementary particle is similar to an electron, since it carries the same charge. However, it is more than 200 times heavier and has a lifespan of just two microseconds. The new measurement data means that the discrepancy between the two hydrogen types can be significantly ruled out for the first time. Both types have a proton radius of 0.8406 femtometers. However, it remains unclear how the discrepancy measured earlier can be explained.
Expertise from Mainz
The MPQ, where Randolf Pohl worked from 2005 to his appointment to Mainz in 2017, was in charge of the current experiments. The experiments were prepared starting in 2011. After final measurements were taken in 2019, the researchers evaluated the data and quantified a large number of potential interference effects. Randolf Pohl is a member of the PRISMA ++ Cluster of Excellence as well as the Collaborative Research Centre “Hadrons and Nuclei as Discovery Tools” at JGU. His research group is investigating ordinary as well as muonic hydrogen and is currently working on a device that can measure tritium – hydrogen with two additional neutrons in its atomic nucleus.
Professor Randolf Pohl
Institute of Physics and
Cluster of excellence PRISMA++
Johannes Gutenberg University Mainz
55099 Mainz
Tel.: 06131 39-20517
pohl@uni-mainz.de
https://www.agpohl.physik.uni-mainz.de/
L. Maisenbacher et al, Sub-part-per-trillion test of the Standard Model with atomic hydrogen, Nature, February 11, 2026,
DOI: 10.1038/s41586-026-10124-3,
https://doi.org/10.1038/s41586-026-10124-3
The experimental setup for high-precision measurements on the hydrogen atom
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