Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reconstruction of gravitational form factors using generative machine learning

Herzallah Alharazin, Julia Yu. Panteleeva

TL;DR

A generative framework based on denoising diffusion for the model-independent reconstruction of hadronic form factors from sparse and noisy data, which yields non-parametric reconstructions consistent with lattice QCD across the full kinematic range.

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 $c_8=-4.6\pm 0.8$ and $c_9=-0.61\pm 0.19$. Using these values at the physical pion mass, we obtain $D(0)=-4.3\pm 0.8$ for the nucleon $D$-term.

Reconstruction of gravitational form factors using generative machine learning

TL;DR

A generative framework based on denoising diffusion for the model-independent reconstruction of hadronic form factors from sparse and noisy data, which yields non-parametric reconstructions consistent with lattice QCD across the full kinematic range.

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 , , and , the framework yields non-parametric reconstructions consistent with lattice QCD across the full kinematic range , 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 and . Using these values at the physical pion mass, we obtain for the nucleon -term.
Paper Structure (15 sections, 16 equations, 5 figures)

This paper contains 15 sections, 16 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Training data: classes of functional forms
  3. Denoising Diffusion Probabilistic Model
  4. Forward process and v-prediction
  5. Reverse sampling
  6. Conditioning and error propagation
  7. Model-independent reconstruction of the proton GFFs at unphysical pion mass
  8. Reconstruction of symmetry-constrained form factors $A(t)$ and $J(t)$
  9. Reconstruction of D form factor
  10. Extracting the unknown LECs $c_8$ and $c_9$
  11. Summary and Outlook
  12. Network architecture
  13. Network training
  14. Ablation studies
  15. The proton GFFs at physical pion mass

Figures (5)

  • Figure 1: Model-independent reconstruction of $A(t)$ and $J(t)$. In each column, the four panels correspond to progressively sparser conditioning: the top panel uses the largest subset of lattice data points (red markers), and successive panels remove points until only a single datum remains. The green marker denotes the constraint imposed by the Poincaré algebra. Gray dashed and dotted curves are the dipole and $z$-expansion fits of Ref. Hackett:2023nkr.
  • Figure 2: Reconstruction of the $D(t)$ under two physics-informed criteria. (a) Only D-term is negative. (b) Negativity is enforced at every point on the spacelike grid: $D(t)<0$. Panel layout, markers, and bands are as in Fig. (\ref{['fig:AJ_reconstruction']}).
  • Figure 3: Training diagnostics for the $v$-prediction DDPM.
  • Figure 4: $N$ denotes the number of conditioning points. Rows 1--4 progressively remove high-$|t|$ conditioning points; row 5 keeps only high-$|t|$ points for contrast. The bottom row (red) uses the same number of points as the third row but retains only high-$|t|$ measurements, demonstrating the disproportionate importance of forward-region data.
  • Figure 5: Diffusion-model reconstruction of the proton GFFs at the physical pion mass ($m_\pi\approx139$ MeV), conditioned on ChPT data points evaluated with the LECs extracted in Sec. \ref{['sec:LEC_extraction']}. Panel layout follows the data-ablation protocol: top panels use the most conditioning points, successive panels progressively remove them.