Physics-Informed Neural Network Approach to Quark-Antiquark Color Flux Tube

TL;DR

This paper presents a physics-informed neural network framework that models chromodynamic fields in quark-antiquark systems, integrating physical laws directly into the learning process to accurately reconstruct flux tube profiles from lattice QCD data.

Contribution

It introduces a novel PINNs-based method that incorporates differential equations and boundary conditions to analyze non-perturbative QCD phenomena without predefined models.

Findings

Accurately reconstructs colour field distributions from lattice data.

Extracts physical observables like string tension and flux tube width.

Provides insights into the dual Meissner effect and confinement mechanism.

Abstract

We introduce a physics-informed neural network (PINNs) framework for modelling the spatial distribution of chromodynamic fields induced by quark-antiquark pairs, based on lattice Monte Carlo simulations. In contrast to conventional neural networks, PINNs incorporate physical laws-expressed here as differential equations governing type-II superconductivity-directly into the training objective. By embedding these equations into the loss function, we guide the network to learn physically consistent solutions. Adopting an inverse problem approach, we extract the parameters of the superconducting equations from lattice QCD data and subsequently solve them. To accommodate physical boundary conditions, we recast the system into an integro-differential form and extend the analysis within the fractional PINNs framework. The accuracy of the reconstructed field distribution is assessed via relative $L_2$-error norms. We further extract physical observables such as the string tension and the mean width of the flux tube, offering quantitative insight into the confinement mechanism. This method enables the reconstruction of colour field profiles as functions of quark-antiquark separation without recourse to predefined parametric models. Our results illuminate aspects of the dual Meissner effect and highlight the promise of data-driven strategies in addressing non-perturbative challenges in quantum chromodynamics.