How big is the proton — the positively charged particle found in atomic nuclei?

At first glance, this seems like a straightforward question that should have a straightforward answer. In real life, however, the situation is slightly more complicated.

In 2010, a team of scientists observed something that still can’t be explained. While trying to improve the accuracy of measurement of a proton’s radius — which had long back been pinned down at 0.877 femtometres — they found that if the electron in a hydrogen atom is replaced by its heavier cousin — the muon — the proton seems to shrink. When this was done, the radius of the proton came out to be 0.84 femtometre — 4 percent smaller than the average measured through other means.

These findings were confirmed by new measurements in 2013.

The reason why this is puzzling is because the Standard Model of particle physics — which describes three of the four fundamental forces in nature — tells us that the interaction between a proton and muon should be identical to that between a proton and an electron.

This “proton radius puzzle” has since left particle physicists scratching their heads, as it suggests, pessimistically, that there is an undiscovered error in the Standard Model, or, optimistically, that it is the tell-tale sign of a previously unknown fundamental force — one that acts between protons and muons but not between protons and electrons.

Now, a fresh effort to gain new insights into the perplexing phenomenon has only deepened the mystery. It turns out that even when the hydrogen atom — which has just one proton in its nucleus — is replaced with a deuterium atom — a hydrogen isotope with one proton and one neutron in the nucleus — and the measurement problem still refuses to go away.

The deuteron — nucleus with one proton and one neutron — is smaller than expected too.

“Mirroring the proton radius puzzle, the radius of the deuteron was several standard deviations smaller than the value inferred from previous spectroscopic measurements of electronic deuterium,” the researchers, led by Randolf Pohl from the Max Planck Institute of Quantum Optics in Germany — who led the 2010 experiment — wrote in a new study published Friday in the journal Science. “This independent discrepancy points to experimental or theoretical error or even to physics beyond the standard model.”

So, does this enduring discrepancy point toward a new force of nature? Or is it a result of limitations of our current measurement techniques? No one knows, and the authors of the new study do not venture an explanation beyond acknowledging that it amplifies the proton radius puzzle.

“It tells us that there’s still a puzzle,” Evangeline Downie from the George Washington University in Washington D.C., who was not involved in the study, told New Scientist. “It’s still very open, and the only thing that’s going to allow us to solve it is new data.”