Reconstruction of Gravitational Form Factors using Generative Machine Learning

Abstract

We develop a generative framework based on denoising diffusion for the model-independent reconstruction of hadronic form factors from sparse and noisy data. The generative prior is built from a large ensemble of synthetic curves drawn from ten distinct functional classes rooted in different theoretical approaches to hadron structure. Applied to the proton gravitational form factors $A(t)$, $J(t)$, and $D(t)$, the framework yields non-parametric reconstructions consistent with lattice QCD across the full kinematic range $0\le -t\le 2{\mathrm{GeV}}^2$, remaining robust even when only one or two conditioning points are retained. The densely sampled output enables a direct extraction of the chiral low-energy constants $c_8=-4.6\pm 0.8{\mathrm{GeV}}^{-1}$ and $c_9=-0.61\pm 0.19{\mathrm{GeV}}^{-1}$. Using these values at the physical pion mass, we obtain $D(0)=-4.3\pm 0.8$ for the nucleon $D$-term.

Cited by in corpus (1)

• Energy-momentum tensor form factors and spin density distribution in the nucleon calculated in a quantized Skyrme model with vector mesons