What is the radius of a proton

Particle Physics Series: The True Size of the Proton

The advantage: muons are around 200 times heavier than electrons. Accordingly, they fly closer to the atomic nucleus and spend a lot more time inside the proton. So they are much better "sniffer dogs" for the proton and show a more pronounced shift in energy levels. "In addition, the electric field is much stronger this close to the proton," says Antognini. Therefore, muonic hydrogen is less sensitive to external disturbances than normal hydrogen. In principle, muonic hydrogen is ideal for measuring the proton radius. It should provide about ten times more accurate values ​​than previous methods.

For years the scientists looked in the wrong place: their apparatus was set to the literature value of the proton radius

The disadvantage: muons are unfortunately very unstable and decay into electrons on average in two millionths of a second. Within this darn short time span, the generated muons have to be collected and brought to a target, interact with it, slow down, bind to muonic hydrogen - and then the measurements on the muonic hydrogen have to take place before the muons decay again.

Only since the 1990s has experimental technology advanced enough to even be able to realize the idea of ​​muonic hydrogen. At the end of the 1990s, Randolf Pohl's working group began to set up such an experiment together with colleagues from Stuttgart, Switzerland, France and Portugal. For years, however, the scientists looked in the wrong place: their apparatus was set to the literature value of the proton radius. The experiment therefore remained fruitless for a long time. The researchers feared that their funding would be cut. It was only when they dared to measure beyond the expected range that their efforts were finally rewarded. "The new value is around four percent below the old one," says Pohl. That doesn't sound like much at first, but it is a significant deviation for precision measurements - so clear that normal measurement errors are no longer an explanation.

Four possible explanations

This surprising discrepancy has caused quite a stir; After all, such precision measurements on the simplest systems in nature are about the fundamentals of physics. Four possible explanations for the shrunk proton radius are currently in play. First, it could simply be a completely unexpected systematic measurement error. The researchers have tried for years to eliminate all sources of error. But with such a complex and new technology, a mistake can hardly be completely ruled out. If this turns out to be the cause, no new physics has been learned, but at least the state of the art has been improved.

Second, the muon could also have a surprisingly large effect on the proton. Since it flies so much closer around the proton and attracts it with its charge, the muon could compress the proton a little and thereby cause the smaller radius. This would be a surprise, since the proton is considered to be an extremely strongly bound system that should not be influenced so strongly by a muon - but this cannot currently be ruled out. Third, the value of the so-called Rydberg constant may be wrong. This natural constant is essential for all measurements on hydrogen and links some fundamental natural constants such as the fine structure constant, the Planck constant and the electron mass. The Rydberg constant is actually one of the most precisely known natural constants of all. However, previous regulations were always based on a whole series of requirements. The new measurements could now be an indication that all of this has to be tackled all over again.

A previously unknown particle could be responsible for the strange behavior of the muonic hydrogen

The fourth alternative is at the same time the most improbable, but also the most exciting: A previously unknown particle could be responsible for the strange behavior of the muonic hydrogen. According to some theories that go beyond the standard model of particle physics, such a particle could shift the energy states in such a way that the proton radius appears to change. Should this hypothesis prove to be true, it would be a sensation. It would be the first clear indication of a particle beyond the Standard Model and would provide particle physicists with valuable clues as to where to look for new physics. The problem here: These models are tailored to the problem of the proton radius - but not to other measurements. "If such a particle exists, it should also be noticeable in many other experiments," says Antognini. The new particle would have to have very specific properties in order to remain inconspicuous in other experiments.