A Comprehensive holographic Study of Proton Structure: From Spectroscopy and Form Factors to the $γp\rightarrow J/ψp$ Scattering Cross Section

TL;DR

The paper addresses the challenge of a unified, non-perturbative description of proton structure by employing a soft-wall holographic QCD model with a dilaton profile $Φ(z)=k_1^2 z^2 \tanh\left(\frac{k_2^4 z^2}{k_1^2}\right)$ to compute the proton mass spectrum, electromagnetic form factors $F_1$, $F_2$, and Sachs form factors $G_E$, $G_M$, as well as gravitational form factors $A(Q^2)$ and $D(Q^2)$. It then uses the gravitational form factors to predict the gluon-driven photoproduction cross section for $\gamma p \rightarrow J/\psi p$, comparing with GlueX data. The results show proton masses within a few percent of data, EMFFs in close agreement with measurements and lattice, and GFFs that align with lattice results, yielding consistent radii and internal mechanical distributions. The predicted $\gamma p \rightarrow J/\psi p$ cross section agrees with experiment, providing a direct validation of the holographic description of the proton’s gravitational structure and linking spectroscopy, static structure, and scattering in a single framework.

Abstract

Understanding the internal structure of the proton-including its mass spectrum, electromagnetic and gravitational form factors, and mechanical properties-remains a central challenge in hadronic physics. While lattice QCD and experimental measurements provide valuable insights, a unified holographic framework capable of simultaneously describing these diverse observables and connecting them to measurable scattering processes is still lacking. Here, we employ the soft wall model, a holographic approach that incorporates gluon condensation and linear confinement, to systematically compute the proton mass spectrum, electromagnetic form factors (EMFFs), and gravitational form factors (GFFs). Our results show good agreement with recent experimental data and lattice QCD calculations. We further derive the corresponding proton radii and mechanical properties, such as pressure and shear force distributions. Finally, using the obtained GFFs as input, we calculate the cross-section for the photoproduction process $γp\rightarrow J/ψp$. Our calculations demonstrate that the soft wall model consistently reproduces key proton structure observables and predicts a scattering cross-section in agreement with experimental measurements.

Figures (12)

• Figure 1: Elastic electron-proton scattering mediated by virtual photon exchange.
• Figure 2: The proton electric form factor $G_E^P(Q^2)$. The solid blue line is our result and the red crosses represent experimental data from Ref. Arrington:2007ux.
• Figure 3: The proton magnetic form factor $G_M^p(Q^2)$. The solid blue line is our result and the red crosses represent experimental data from Ref. Arrington:2007ux.
• Figure 4: The proton GFF $A(Q^2)$. The red crosses represent the lattice results Hackett:2023rif, the dotted and dashed lines denote the predictions from other models Abidin:2009hrGuidal:2004nd, and the solid black line is our result.
• Figure 5: The proton GFF $D(Q^2)$. The red crosses represent the lattice results Hackett:2023rif and the solid black line is our result.