A complex logistic equation for universal energy evolution in hadronic elastic scattering

TL;DR

This paper presents a universal, analytically solvable evolution equation for hadronic elastic scattering amplitudes, rooted in Regge theory, that respects fundamental physical bounds and unitarity across a wide energy spectrum.

Contribution

It introduces a complex logistic-based evolution equation derived from Regge field theory, providing a minimal, predictive framework for saturation and unitarization in elastic scattering.

Findings

Reproduces differential cross sections and integrated quantities across energies

Ensures unitarity, Froissart-Martin bound, and dispersion relations

Fits parameters at a single energy for broad applicability

Abstract

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 $\epsilon_{\mathcal{P}}$ and the nonlinear coupling $\lambda$, 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.