Imaging baryon number density within the proton

Abstract

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 ($γp \rightarrow p ρ^0$, $γp \rightarrow p ω$, $γp \rightarrow n π^+$, and $γp \rightarrow p π^0$). 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.

Figures (5)

• Figure 1: Diagrams for (a) forward production and (b, c) two possible processes for backward production. In forward production, (a), $|t|$ is small while $|u|$ is maximized. Backward production can occur via one of two processes, as shown in (b) and (c). In (b), production occurs via the exchange of a Reggeon that carries baryon number but small momentum while in (c), the Reggeon carries no baryon number but large momentum.
• Figure 2: Diffractive $\pi^+$ photoproduction off a proton. The green and blue dashed lines are the $u$ and $t$-channel contributions respectively. The solid black line is the sum of the $t$ and $u$-channel fits to the data. The different slopes of the $u$ and $t$-channel processes are obvious. The red vertical dash-dotted lines represent the maximum kinematically allowed values of $|t|$ and $|t|_{\rm max}$, on the right with maximum $p_T$ and $p^{\rm kin}_{T\,{\rm max}}$ near the center of the plot. Adapted from Ref. anderson1976measurements.
• Figure 3: The HWHM of the $F(b)$ distributions. Blue circles display the $t$-channel results while the green squares denote those for the $u$-channel. Open markers are the HWHM with no extrapolation used in the Fourier transform. The solid markers indicate the results using extrapolations.
• Figure 4: Cross section measurements for meson photoproduction off proton targets. The hollow green points correspond to $u$-channel processes. The solid blue points represent $t$-channel reactions. Exponential function fits to the tails of the distribution, indicated by the solid lines, are used to estimate the incompleteness of the integration. The number of points used in the fit, chosen to best represent the shape of the tail, varies with each dataset.
• Figure 5: Normalized $F(b)$ distributions obtained via Fourier-Bessel transforms, as discussed in the supplemental material, for the two different finite-window control methods. In (a) no extrapolation is used, only an incompleteness uncertainty. The incompleteness uncertainty and statistical uncertainty are added in quadrature and drawn as shaded bands around the central curves. The results in (b) use an extrapolation to $p^{\rm kin}_{T, \, \rm max}$. Minor finite window effects still exist in (b) since the integral is formally defined from $p_T = 0$ to $p_T = \infty$, and $p^{\rm kin}_{T, \, \rm max}$ is finite.