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  • Open Access

Complex logistic equation for universal energy evolution in hadronic elastic scattering

Anderson Kendi Kohara*

  • *Contact author: anderson.kendi@gmail.com
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Phys. Rev. D 113, 116041 – Published 29 June, 2026

DOI: https://doi.org/10.1103/xz23-bqg9

Abstract

We introduce a universal evolution equation for elastic scattering of hadrons, derived from Reggeon field theory and solved in closed analytical form. The equation has a complex logistic structure and evolves initial amplitude profiles from existing models at a fixed energy, reproducing both differential cross sections and integrated quantities over a broad energy range. 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 εP and the nonlinear coupling λ, both fitted at a single energy. By decoupling the nonperturbative input from the universal energy evolution, the framework enables model-independent extrapolations and provides a minimal predictive alternative to eikonal resummation. Moreover, the structure of the equation—featuring rapidity evolution, saturation, and impact-parameter dependence—shares qualitative features with nonlinear QCD equations at small-x, such as Balitsky-Kovchegov and Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, and Kovner, suggesting a possible bridge between Regge-based and QCD-based approaches to high-energy scattering.

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Phys. Rev. D 113, 116041– Published 29 June, 2026
  • Received 16 February 2026
  • Accepted 5 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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