Probing Proton Structure via Physics-Guided Neural Networks in Holographic QCD

TL;DR

This paper introduces a physics-guided neural network integrating holographic QCD to model proton structure functions, achieving accurate fits and revealing the transition between different scattering mechanisms.

Contribution

It presents a novel neural network framework that embeds QCD equations, enabling data-driven analysis of proton structure without relying on empirical models.

Findings

Achieved a fit with χ²/d.o.f. ≈ 0.91 to deep inelastic scattering data.

Identified a kinematic crossover near x ≈ 0.19 between resonance and diffractive regimes.

Recovered a Pomeron intercept of approximately 1.0786 and modeled higher-twist effects.

Abstract

Describing the proton structure function $F_2$ in the non-perturbative and transition regimes of quantum chromodynamics (QCD) remains a significant theoretical challenge. In this work, we introduce a Physics-Guided Neural Network (PGNN) that integrates Holographic QCD with deep learning. By embedding the five-dimensional $\text{AdS}_5$ Dirac equation and the string diffusion kernel directly into the computational graph, the network is strictly constrained to the physical proton mass ($M_p \equiv 0.938 \text{ GeV}$). Applying this framework to high-precision SLAC deep inelastic scattering data yields a global fit of $\chi^2/\text{d.o.f.} \simeq 0.91$. Rather than relying on predetermined empirical forms, the network dynamically extracts the transition between the $s$-channel bulk fermion mechanism (hadronic resonance excitations) and the $t$-channel holographic Pomeron exchange (diffractive background), identifying a kinematic crossover near $x \approx 0.19$. Furthermore, the optimization naturally recovers a Pomeron intercept of $\alpha_0 \approx 1.0786$ and generates higher-twist scale-breaking effects through the evolution of resonance mass spectra. This demonstrates that embedding analytical differential equations into neural networks provides an interpretable, data-driven approach for phenomenological studies of strongly coupled systems.