Gravitational form factors of the proton in the improved holographic QCD model

TL;DR

The paper analyzes the gluonic contributions to the proton's gravitational form factors within the improved holographic QCD framework, modeling the proton as bulk Dirac fermions and extracting the form factors $\mathcal{A}(t)$ and $\mathcal{D}(t)$ from holographic couplings to metric fluctuations. By fitting $\mathcal{A}(t)$ to lattice data, the authors predict $\mathcal{D}(t)$, uncovering an infrared pole in the forward limit but showing that observable mechanical properties remain finite due to cancellations. Using these form factors, they derive the proton's mechanical structure, computing pressure and shear distributions and two radii, $\rho_{\text{mech}}$ and $\rho_{\text{mass}}$, finding $\rho_{\text{mech}} = 0.95$ fm and $\rho_{\text{mass}} = 0.61$ fm, in line with nonperturbative studies. The work illustrates how holographic methods yield nonperturbative insights into gluonic observables and motivates extensions to include quark degrees of freedom and connections to generalized parton distributions.

Abstract

We compute the gluonic contribution to the gravitational form factors of the proton using the improved holographic QCD model, in which the proton is described in terms of bulk Dirac fermions. Model parameters are constrained using lattice and phenomenological input, allowing us to obtain estimates for the gravitational form factors and to compare them with results from other approaches. The resulting $\mathcal{D}(t)$ form factor is found to exhibit an infrared pole in our framework. Using the extracted form factors, we analyze mechanical properties of the proton, including pressure and shear distributions. We obtain estimates of $ρ_\text{mech} = 0.95$ fm and $ρ_\text{mass} = 0.61$ fm for the mechanical and the mass radii of the proton, respectively, which are similar to values in other nonperturbative studies.

Figures (8)

• Figure 1: Two possible Witten diagrams for three-point functions including Dirac spinors.
• Figure 2: Results for the form factor $\mathcal{A}(t)$. Green data points and the green curve (Shanahan et al.) are based on lattice data from Shanahan:2018pib. Orange data points and the orange curve (Hackett et al.) are based on lattice data from Hackett:2023rif. The soft-wall-based result is from Mamo:2019mka. The black solid curve is our fit.
• Figure 3: Our prediction (solid black curve) compared to various results for the form factor $\mathcal{D}(t)$. Green data points and the green curve (Shanahan et al.) are based on lattice data from Shanahan:2018nnv, orange ones (Hackett et al.) are based on lattice data from Hackett:2023rif, and the purple ones (Burkert et al.) are based on the fit of Burkert:2021ith to DVCS data from CLAS:2007clmCLAS:2015uuo. Dashed curves are multipole fits (\ref{['eq:multipole']}) to the data points using the values given below this respective equation.
• Figure 4: Pressure distributions \ref{['eq:shearandpressure']} of a proton, as given by different models. The long-dashed black curve, as well as the violet and pink bands arise from a dipole fit analysis of DVCS data from Burkert et al., Burkert:2018bqq. The violet band shows the error estimate of Burkert:2018bqq, compared to a future projection (pink band). The dotted curve with green error band is a lattice fit result taken from Shanahan:2018nnv. The result labeled Hackett et al. is computed by us from the form of $\mathcal{D}(t)$ given in Hackett:2023rif.
• Figure 5: Shear force distributions \ref{['eq:shearandpressure']} of a proton, as given by different models. Notation as in Fig. \ref{['fig:pressureinproton']}.