The proton is one of the fundamental building blocks of matter and the basis of important natural constants. But so far there have always been discrepancies when measuring the proton radius. Now physicists have measured this value for hydrogen atoms more precisely than ever before using a newly developed method. Their measurement result shows that the proton is smaller than long assumed, but confirms measurements with muonic hydrogen and the reference value for this value that was adjusted a few years ago. This clarifies some of the previous discrepancies. At the same time, the team was also able to use the measured energy transfer to check fundamental predictions of the Standard Model of particle physics – accurate to 13 decimal places.
Protons, together with neutrons, form the nucleus of an atom and are therefore the basic building blocks of all matter. Their properties not only shape the behavior of atoms, but also form the basis for natural constants such as the Rydberg constant. For example, it can be used to assign spectral lines to specific elements. The energy at which atoms assume certain excitation states is also described by quantum electrodynamics (QED) – one of the pillars of the physical standard model. It is therefore important to know the mass and charge radius of the proton as accurately as possible. However, for years, various measurement methods and experiments for the proton radius have produced values that deviate from each other and from the long-term reference value. In 2022, this reference value was therefore reduced to 0.841 femtometers. However, there are still some discrepancies.
Proton measurement on excited hydrogen
That’s why physicists led by Lothar Maisenbacher from the Max Planck Institute for Quantum Optics in Garching have now checked the proton radius of atomic hydrogen again – using the most precise measurement method to date. To do this, they used so-called Doppler-free one-photon spectroscopy. This allows hydrogen energy transitions to be measured very precisely with little distortion due to the Doppler effect. The basis for this measurement is a beam of hydrogen atoms cooled down to 4.6 Kelvin, which are brought into an excited state by a laser pulse – the so-called 2S-6P level. In the test chamber, the hydrogen atoms fall back into two different lower energy states. The physicists determined the energy released in the form of photons using spectroscopy. By comparing these values with another frequency transition, they were able to determine the proton radius.
The result: According to the new measurements, the charge radius of the proton is 0.8406 femtometers. “This measurement is 2.5 times more precise than the next best for atomic hydrogen and six times more precise than our own measurement using the 2S-4P transition,” write Maisenbacher and his colleagues. According to them, the resolution of the spectroscopic measurement is so high that it shows the transition frequency down to one 15,000th of the spectral line width. “As far as we know, this is unprecedented for laser spectroscopy,” said the team. More importantly, however, the new value corresponds to the proton radius measured with muonic hydrogen and is very close to the official reference value of 2022. This result therefore confirms that the proton radius is lower than long thought, but supports the results of more recent measurements and the new reference value.
Standard model confirmed down to the trillionth
In the next step, the physicists used their measurements to check the standard model of particle physics and, in particular, quantum electrodynamics. This predicts the energy at which atomic transitions between different quantum states would have to take place. “Because hydrogen is relatively simple and can therefore be calculated very easily, we were able to use it to test QED and thus the standard model,” explains co-author Randolf Pohl from the University of Mainz. The analyzes showed that the measured frequency for the 2S-6P transition of hydrogen agrees almost perfectly with the predictions of the Standard Model. Both values only differ from each other in the 13th decimal place. “This corresponds to a test of the standard model with the precision of 0.7 parts per trillion (ppt),” write Maisenbacher and his team. This is a new benchmark for measuring the energy levels in the hydrogen atom.
As the physicists explain, the method they developed can now also be used to check other energy transitions in atomic hydrogen or deuterium. “Together with complementary approaches, we expect this to provide substantial progress for testing quantum electrodynamics in bound states,” says the team.
Source: Lothar Maisenbacher (Max Planck Institute for Quantum Optics, Garching) et al., Nature, doi: 10.1038/s41586-026-10124-3