Protons Are Probably Even Smaller Than We Thought

Different methods for measuring the size of protons give conflicting results, but it looks like the smaller estimates are right. DOE's Jefferson Lab

It's not easy to measure the size of subatomic particles. Besides being tiny there is the whole thing about being simultaneously a wave and a particle. In the case of protons, different methods have produced conflicting results, but upgraded measuring techniques have gone a long way to resolving this.

Although high-school atomic models present protons as little balls, they, like everything else that small, lack exact boundaries. Physicists use a measure called the “charge radius” or area over which the positive charge is distributed.

To measure this radius, physicists fired electrons at protons and used the angle of deviation for scattered electrons to calculate the proton's size. An alternative technique uses the wavelengths of photons released as electrons bounce between energy levels in hydrogen or deuterium atoms. The error bars for these methods usually overlapped at 0.88 femtometers (fm) – or almost a trillionth of a millimeter, and until 2010 everyone was happy.

Then some troublemakers tried something new, replacing orbiting electrons with muons (heavier particles with an electron's charge) and instead got 0.84 fm – a difference of just 4 percent, but enough to give particle physicists a decade of doubt. It's this discrepancy Professor Ashot Gasparian of North Carolina A & T State University believes he has resolved.

In Nature, Gasparian has described a more precise electron-scattering technique, flowing cold hydrogen into a stream of fast-moving electrons without the metal covers used in previous electron-scattering measurements. His set-up also measured the positions of the scattered electrons with greater accuracy than the magnetic spectrometers used in the past, and removed cases where electrons interacted with each other, rather than with the target protons, muddying the data.

These advances allowed Gasparian and co-authors to observe much smaller scattering angles than ever before, and from these calculate a radius of 0.831 fm.

"When we started this experiment, people were searching for answers. But to make another electron-proton scattering experiment, many skeptics didn't believe that we could do anything new,” Gasparian said in a statement

Now, instead of the muon measurements being inconsistent with other techniques, it is the spectroscopy that is out of step with the other two methods. The paper notes, however, that recent spectroscopy results differ from each other.

The exact size of a particle a billion times too small to see might seem to be the modern equivalent of asking how many angels can dance on the head of a pin, but the proton's radius is needed to calculate some of the fundamental constants of the universe.

Important advances in physics can come out of these studies. "When the initial proton radius puzzle came out in 2010, 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," co-author Professor Dipangkar Dutta of the Mississippi State University said. "But the PRad experiment seems to shut the door on that possibility."

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