Physics-Informed Global Extraction of the Universal Small-$x$ Dipole Amplitude
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
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2026
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| author | Dai, Si-Wei Li, Fu-Peng Pang, Long-Gang Qin, Guang-You Wei, Shu-Yi Zhang, Han-Zhong Zhao, Wenbin |
| author_facet | Dai, Si-Wei Li, Fu-Peng Pang, Long-Gang Qin, Guang-You Wei, Shu-Yi Zhang, Han-Zhong Zhao, Wenbin |
| contents | We extract the universal small-$x$ dipole scattering amplitude $N(r,x_B)$ from a global analysis based on a physics-informed neural network (PINN), without imposing a priori MV-type parametrization of the initial condition. The network provides a smooth and differentiable surrogate for $N(r,x_B)$, whose rapidity dependence is constrained by the collinearly improved Balitsky--Kovchegov evolution equation, while its functional form is simultaneously constrained by Deep Inelastic Scattering (DIS) data for the reduced total and charm cross sections, exclusive $J/ψ$ photoproduction measurements, and a positivity requirement for the momentum-space dipole amplitude. The resulting single universal amplitude consistently describes all fitted observables within a unified framework, alleviating the long-standing tension between total and charm channels encountered in conventional small-$x$ fits based on rigid parametric ansätze. Within the fitted kinematic domain, the best extracted PINN solution yields a smooth, non-negative momentum-space dipole over the full transverse-momentum range examined. Our results provide a robust and well-behaved input for Color Glass Condensate phenomenology across a broad class of high-energy processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08008 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Physics-Informed Global Extraction of the Universal Small-$x$ Dipole Amplitude Dai, Si-Wei Li, Fu-Peng Pang, Long-Gang Qin, Guang-You Wei, Shu-Yi Zhang, Han-Zhong Zhao, Wenbin High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Experiment Nuclear Theory We extract the universal small-$x$ dipole scattering amplitude $N(r,x_B)$ from a global analysis based on a physics-informed neural network (PINN), without imposing a priori MV-type parametrization of the initial condition. The network provides a smooth and differentiable surrogate for $N(r,x_B)$, whose rapidity dependence is constrained by the collinearly improved Balitsky--Kovchegov evolution equation, while its functional form is simultaneously constrained by Deep Inelastic Scattering (DIS) data for the reduced total and charm cross sections, exclusive $J/ψ$ photoproduction measurements, and a positivity requirement for the momentum-space dipole amplitude. The resulting single universal amplitude consistently describes all fitted observables within a unified framework, alleviating the long-standing tension between total and charm channels encountered in conventional small-$x$ fits based on rigid parametric ansätze. Within the fitted kinematic domain, the best extracted PINN solution yields a smooth, non-negative momentum-space dipole over the full transverse-momentum range examined. Our results provide a robust and well-behaved input for Color Glass Condensate phenomenology across a broad class of high-energy processes. |
| title | Physics-Informed Global Extraction of the Universal Small-$x$ Dipole Amplitude |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2603.08008 |