The Proton: A Baryonic Core Within express
The proton is not a solid ball. Its charge, mass, and other properties are distributed differently in space, and each property has its own radius. Physicists have long been able to measure where the proton's charge is concentrated and where its mass lies. Now they've tackled another property — the baryon number, which indicates how many heavy particles (baryons) are involved in a process. It turns out that the proton's baryon number lives in a very tight core.
To see this, researchers collided photons with protons and looked at which mesons were produced: rho mesons, omega mesons, pions. By measuring how strongly these mesons scatter sideways (their transverse momentum), they could reconstruct the region of the proton from which they emerged. The method is similar to using ripples on water to determine where a stone fell. They found that the baryon number is concentrated in a region with a radius of 0.33–0.53 femtometers. One femtometer is one millionth of one billionth of a meter, roughly the size of an atomic nucleus.
For comparison, the proton's charge and mass are spread noticeably wider: their radius is at least 0.67 femtometers. So the baryon number is like a dense kernel inside a looser cloud of charge and mass. This picture helps us better understand how the proton is structured and why nuclear forces behave the way they do.
This result is another step toward a complete map of the proton's interior. The more precisely we know where things are inside these tiny particles, the better we understand the matter around us.
Original abstract
as written by the authors arXiv:2603.03730
The spatial extent of the proton is a key factor in nuclear physics. Different measurement techniques probe different aspects of the proton, yielding different radii. The mass and charge radii depend on the parton and quark distributions respectively, while the mechanical radius depends on the mass/energy distribution. Here, we probe the spatial distribution of a new proton characteristic, studying the distribution of baryon number within the proton. We investigate the baryon number distribution by studying four exclusive meson production channels arising from photon-proton collisions ($$\gamma p \rightarrow p \rho^0$$, $$\gamma p \rightarrow p \omega$$, $$\gamma p \rightarrow n \pi^+$$, and $$\gamma p \rightarrow p \pi^0$$). The two-dimensional transverse sizes of the interacting systems are extracted by analyzing the transverse momentum, $$p_T$$, dependence of the meson production cross section, using Fourier-Bessel transformations. We find that baryon number is confined to a transverse radius of $$0.33 - 0.53$$~fm. In comparison, the transverse radius of the proton charge and mass distributions are considerably larger, at least 0.67~fm. The baryon number is concentrated in the center of the proton.
The radius of the proton's baryonic core is 0.33–0.53 femtometers. If the proton were the size of a football field, this core would be smaller than a ball.
In Liu Cixin's novel "The Three-Body Problem," protons are unfolded into multidimensional structures, but here we see that even an ordinary proton has a hidden internal structure with an unexpected distribution of properties.