Determining the NJL Coupling and AMM in Magnetized QCD Matter via Machine Learning

TL;DR

This paper uses machine learning to determine how the NJL model's parameters depend on magnetic fields, fitting lattice QCD data to better understand QCD matter under strong magnetic fields.

Contribution

It introduces a physics-informed neural network approach to extract functional forms of NJL parameters from lattice data, capturing the inverse magnetic catalysis effect.

Findings

Magnetic field suppresses both the NJL coupling and AMM ratio.

The neural network accurately reproduces the inverse magnetic catalysis effect.

The method bridges effective models with lattice QCD data.

Abstract

In this study, we investigate the phase structure of magnetized QCD matter by determining the field-dependent parameters of the Nambu-Jona-Lasinio (NJL) model through a physics-informed machine learning framework. Specifically, we focus on extracting the optimal functional forms for the running coupling constant $G(eB)$ and the quark anomalous magnetic moment (AMM) ratio $v_2(eB)$, utilizing lattice QCD-computed quark condensate data as the ``ground truth". By embedding the NJL gap equation as a differentiable physics-constrained module, our neural network pipeline identifies continuous parameter functions that accurately reproduce the inverse magnetic catalysis (IMC) effect. Our results demonstrate that the magnetic field smoothly suppresses both $G$ and $v_2$. This approach not only bridges the gap between effective models and lattice data but also provides new microscopic insights into the response of the QCD vacuum to strong magnetic fields.