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

Zigeng Ding, Fan Lin, Xinyang Wang

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.

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

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 and the quark anomalous magnetic moment (AMM) ratio , 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 and . 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.

Paper Structure

This paper contains 5 sections, 13 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework: NJL Model with Field-Dependent Parameters
  3. Machine Learning Methodology
  4. Numerical Results
  5. Conclusion and Outlook

Figures (5)

  • Figure 1: Schematic architecture of the differentiable physics-informed inversion framework for extracting the magnetic field-dependent parameters $G(eB)$ and $v_2(eB)$ from lattice QCD data. The framework integrates a neural network with feature-expanded inputs, the gap equation as a hard physics solver, and a multi-objective loss function that incorporates both data-fidelity and physical-prior constraints.
  • Figure 2: Estimated value ranges for the coupling constant $G$ (left) and the AMM ratio $v_{2}$ (right) as functions of the magnetic field $eB$. The shaded regions indicate the spread of values obtained across 100 independent training runs, illustrating the robustness of the learned parameter distributions.
  • Figure 3: The mean value of the coupling constant $G$(left) and the AMM constant $v_2$(right) as a function of $eB$.
  • Figure 4: The chiral condensate and constituent mass of quarks with the mean value of our running parameters.
  • Figure 5: The normalized pseudo-critical temperature as a function of the magnetic field. The results from the physics-informed framework (red shade and red line for mean value) are compared against lattice QCD data(gray shade).