Extraction of the color dipole amplitude with physics-informed neural networks

TL;DR

This paper introduces Physics-Informed Neural Networks (PINNs) to extract a process-independent color dipole amplitude in QCD, successfully predicting exclusive J/ψ photoproduction without retuning.

Contribution

It presents a novel PINN-based method that combines theoretical evolution equations with experimental data to determine the dipole amplitude independently of initial assumptions.

Findings

The PINN approach accurately predicts J/ψ photoproduction cross-sections.

The method demonstrates the process-independence of the gluon saturation scale.

It achieves model-independent extraction without geometric adjustments.

Abstract

The process-independence of the color dipole amplitude is a cornerstone of high-energy Quantum Chromodynamics (QCD). However, standard phenomenological approaches typically rely on rigid parametric ansatzes and often require ad-hoc geometric adjustments to reconcile inclusive and diffractive measurements. To resolve this tension, we introduce Physics-Informed Neural Networks (PINNs) employing a ``Teacher--Student'' strategy. The physics-based momentum-space Balitsky-Kovchegov evolution dynamics act as the ``Teacher,'' constraining the solution manifold, while the network ``Student'' is refined against inclusive HERA $F_2$ data. This approach extracts a model-independent dipole amplitude without assuming initial states. Strikingly, we demonstrate that this amplitude -- without parameter retuning or geometric rescaling -- successfully predicts the absolute normalization and kinematic dependence of exclusive $J/\psi$ photoproduction cross-sections. This parameter-free prediction of the saturation dynamics provides promising evidence for the process-independence of the gluon saturation scale and establishes PINNs as a transformative paradigm for uncovering non-perturbative QCD structures.