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10-Year Proton Measurement Mystery Is Probably Solved

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JLab’s experimental Hall B where the experiment is located
JLab’s experimental Hall B where the experiment is located
Photo: Jefferson Lab

A precise new measurement of the size of the proton shows a decade-long problem may now have a solution.

The proton is arguably the most important particle to our everyday lives, forming one of the three core components of atoms and determining elements’ identities. That makes the values of its various properties extra important. Experimental disagreement over one of those properties, called the charge radius, kicked off a decade of increasingly precise measurements. Scientists have now released the results of a new measurement method, and they suggest the uncertainty is approaching an end.

Scientists measure the proton’s size using a value called the charge radius, a measure of how electric charge is distributed in the particle. Until 2010, scientists measured the radius in one of two ways: either by scattering electrons off of the proton or by using something called the Lamb shift, which calculated the value based on the difference between two energy levels in an atom consisting of just one proton and one electron (remember from chemistry class that electrons prefer certain places around an atom, called energy levels). These two methods were in approximate agreement on a charge radius value of around 0.877 femtometers, where a femtometer is 100 quintillionths of a meter.


But two measurements in 2010 sort of ruined everything. Both measured the Lamb shift of an atom consisting of a proton and a muon, which is kind of like a heavier, rarer version of the electron. The muon sits much closer to the proton than the electron does, making the method more accurate. Both results agreed with one another and were much smaller than previous measurements, at around 0.842 femtometers—so much smaller, in fact, that some physicists wondered whether there were undiscovered physical effects to explain the difference.


Physicists continued re-measuring the charge radius throughout the 2010s. Then, earlier this year, the puzzle seemed solved, without any unexpected new physics. A team at York University in Canada led by professor Eric Hessels observed a harder-to-measure Lamb shift, using a hydrogen atom consisting of both a proton and an electron, as well as the Lamb shift of an atom with a proton and a muon. Both measurements agreed, and the team measured a charge radius of 0.833 femtometers. Perhaps something was simply wrong with the pre-2010 measurements.

But this is science, and puzzles don’t get solved by single papers—other experiments were ongoing, and scientists typically want to see independent verification of important measurements. Today, another team of scientists working in the United States, Ukraine, Russia, and Armenia forming the PRad collaboration at Jefferson Lab in Virginia revisited the measurement using a new proton-electron scattering experiment. “We decided to design a new kind of experiment that addresses the problem from a whole new approach,” Ashot Gasparian, professor at North Carolina A&T State University and PRad spokesperson, told Gizmodo.


The experiment consists of a beam of electrons striking cryogenically cooled hydrogen gas, followed by a series of detectors that measure where the electrons end up after scattering as well as their energies, and finally a hole through which the unscattered electrons pass. This measurement improves on past scattering experiments by more accurately measuring the electrons only slightly scattered by the protons, and it uses different detectors to measure the electrons’ energies. Various other strategies to increase the experiment’s precision included taking into account electrons scattering off of themselves and building the hydrogen gas container without entrance and exit windows that might produce extra noise.

Scientists were able to extract another measurement of the radius: 0.831 femtometers, in agreement with the Hessels measurement, according to the new paper published in Nature.


“In my opinion, the problem is closed after this experiment,” Krzysztof Pachucki, a professor at the University of Warsaw who reviewed the new study but was not involved in it, told Gizmodo.

What went wrong back in 2010? How did one measurement overturn decades of prior measurements? It’s still not clear, Pachucki said. Perhaps another incorrect value made its way into the mathematics used to turn the data into the measurement of the proton radius. Conclusively solving the radius problem will require figuring out if something was wrong with these past experiments and what it was, physicists Jean-Philippe Karr at Sorbonne Université and Dominique Marchand is at the Université Paris-Sud wrote in a Nature commentary about the new work.


The authors behind this paper don’t think the problem has been completely solved (I mean, what kind of scientist would go out and say, “The problem I work on is done, now I don’t have to work on it anymore.”?). Several more experiments will join the PRad experiments, looking for new ways to increase the precision and confirm the lower value. And even if people agree on a value, perhaps more precise measurements will reveal other charge radius discrepancies just beyond the abilities of current experiments. You’ll continue to see these kinds of precision measurements from particle physics, like the muon g-2 experiment, for example, as researchers hunt for new discrepancies that might hold the key to undiscovered physics.

“What we wanted to do is really to push the limit of the precision of this kind of measurement,” Haiyan Gao, a professor at Duke University and a PRad spokesperson, told Gizmodo. “Maybe down the road, if there’s new physics, we can uncover it.”