Probing Proton Structure via Physics-Guided Neural Networks in Holographic QCD
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arXiv
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| Format: | Preprint |
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2026
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| author | Kou, Wei Chen, Xurong |
| author_facet | Kou, Wei Chen, Xurong |
| contents | 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 $χ^2/\text{d.o.f.} \simeq 0.91$. 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 $α_0 \approx 1.0786$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02906 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Probing Proton Structure via Physics-Guided Neural Networks in Holographic QCD Kou, Wei Chen, Xurong High Energy Physics - Phenomenology High Energy Physics - Theory 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 $χ^2/\text{d.o.f.} \simeq 0.91$. 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 $α_0 \approx 1.0786$ 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. |
| title | Probing Proton Structure via Physics-Guided Neural Networks in Holographic QCD |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.02906 |