We now have an accurate measurement of how large protons are.

Back in 2010, a team of physicists set their field (figuratively) on fire. They measured the radius of a proton and found it to be 4% smaller than expected. Physicists are very passionate about this kind of stuff and it sparked a huge debate. Now, researchers from York University have put the debate to rest by taking a precise measurement of the size of the proton.

How big is something very small?

“The level of precision required to determine the proton size made this the most difficult measurement our laboratory has ever attempted,” said Distinguished Research Professor Eric Hessels, Department of Physics & Astronomy, who led the study.

The exact size of the proton is an important unsolved problem in fundamental physics today, one which the present study addresses. The team reports that protons measure 0.833 femtometers in diameter (a femtometer is one-trillionth of a millimeter). This measurement is roughly 5% percent smaller than the previously-accepted radius value.

“After eight years of working on this experiment, we are pleased to record such a high-precision measurement that helps to solve the elusive proton-radius puzzle,” said Hessels.

The exact measurement of the proton’s radius would have significant consequences for the understanding of the laws of physics, such as the theory of quantum electrodynamics, which describes how light and matter interact. Hessels says that the study didn’t exist in a vacuum — three previous studies were pivotal in attempting to resolve the discrepancy between electron-based and muon-based determinations of the proton size.

The 2010 study was the first to use muonic hydrogen to determine the proton size (whereas previous experiments used regular hydrogen). Hydrogen atoms are made up of one proton and one electron In the 2010 experiment, the team replaced the electron with a muon, a related (but heavier) particle.

While a 2017 study using simple hydrogen agreed with the 2010 muon-based result, a 2018 experiment, also using hydrogen, supported the pre-2010 value. Hessels and his team spent the last eight years trying to get to the bottom of the issue and understand why researchers were getting different results when measuring with muons rather than electrons.

The team carried out a high-precision measurement using a technique they developed for this purpose, the frequency-offset separated oscillatory fields technique (FOSOF). In essence, they used a fast beam of hydrogen atoms created by shooting protons through hydrogen molecules. Their result agrees with the value found in the 2010 study.

The paper “A measurement of the atomic hydrogen Lamb shift and the proton charge radius” has been published in the journal Science.