Imaging baryon number density within the proton

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.