The puzzle of a proton’s proportions

We are built of protons – there are around 10 octillion (1028) of them in the centre of the atoms that make up our bodies – but scientists are still not sure how big they are. 

Two recent experiments have given more cause for confusion.

One was undertaken at the Thomas Jefferson National Accelerator Facility in the US and reported in the journal Nature

The other, from York University in Canada, is published in Science

Both seem to show that the proton is 4% smaller than previously thought – a difference of about four quintillionths (0.04 femtometres) of a metre.

Not much, but enough to represent a significant puzzle in the world of physics.

These results point to a proton radius of about 0.83 femtometres, in contrast with other measurements which – as recently as 2018 from Sorbonne Université in France – suggest that suggest a radius closer to 0.88 femtometres, similar to the value that has been accepted for decades. 

The discrepancy is well outside the uncertainty limits of either set of measurements, so it seems unlikely improving the precision of existing experiments will solve the puzzle. 

Protons, along with neutrons, are the components of all nuclei in the centre of atoms. Protons and neutrons are in turn each comprised of three quarks, held together by gluons that flit back and forth between the quarks. 

Quarks are much smaller than the protons, but like electrons in orbitals, smear out into a cloud to form a proton. The extent of the quark cloud defines the edge of the protons the scientists are seeking to identify, from the interaction between the charge of the quark cloud with charged particles such as electrons or muons. 

The Jefferson Lab’s approach, called PRad, was to shoot electrons across a chilled gas jet full of protons – like shooting ping pong balls across a stream of bowling balls careering down a bowling alley and measuring the angles they bounce off at.

While a very successful experiment with low uncertainty, the latest result from the Jefferson Lab has put a hole in an exciting hypothesis that could have explained the puzzle. 

Because the lower value had initially come out of a measurement method that used modified hydrogen atoms that replaced the electron with a heavier cousin of the electron called a muon, scientists wondered if a possible explanation could be that muons were interacting differently to electrons. 

If there were a new, additional force that muons were subject to – unlike electrons that merely interact with protons through their electrical charge – then that could be the source of the discrepancy. And a darn exciting discovery too! 

“There was hope in the community that maybe we have found a fifth force of nature, that this force acts differently between electrons and muons,” says Dipangkar Dutta, a member of the Jefferson Lab team from Mississippi State University in the US. 

“But the PRad experiment seems to shut the door on that possibility.”

The scientists had to put away their champagne when the Jefferson Lab experiment – using a non-muon approach – came up with a low value for the proton radius that more closely matched the muon experiments at York than the electron-based experiments at the Sorbonne, giving no evidence for a new force. 

The Jefferson Lab had effectively widened the gulf between its results and those from the Sorbonne by reducing their uncertainty in a number of ways. For example, they improved sensitivity in their detectors so they could pick up the electrons that barely grazed the surface of the protons. And they believe they can improve their precision further, says Haiyan Gao, a member of the Jefferson Lab team from Duke University, US.

“There is a very good chance we can improve our measurements by a factor of two or maybe even more.” 

More experiments that are in the pipeline will combine different features from each experiment and hopefully help explain the discrepancy in the next few years. 

But for now, we just have to be content with walking around with octillions of puzzles in our bodies.

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