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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.22751 |
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Table of Contents:
- We introduce a universal evolution equation for elastic scattering of hadrons, derived from Regge field theory (RFT) and solved in closed analytical form. The equation emerges from a complex logistic structure and evolves initial amplitude profiles taken from existing models at fixed energy, reproducing both the differential cross sections and the integrated quantities in a broad energy range. We prove that it admits a unique solution for each initial condition and rigorously satisfies unitarity, the Froissart-Martin bound, and dispersion relations. The dynamics are governed by two physically meaningful parameters: the effective Pomeron mass $ε_{\mathcal{P}}$ and the nonlinear coupling $λ$, both fitted at a single energy. Our approach offers a minimal, yet predictive framework for saturation and unitarization in elastic scattering and may provide a useful bridge toward small-$x$ QCD evolution.