Traveling wave solution of the Reggeon Field Theory

TL;DR

This paper models the impact-parameter evolution in Reggeon Field Theory using a stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation, revealing universal traveling wave solutions that depend solely on noise strength.

Contribution

It introduces a novel stochastic PDE framework for the supercritical Pomeron, capturing unitarity and universal impact-parameter profiles at high energies.

Findings

Traveling wave solutions exhibit universal behavior.

Impact-parameter profiles depend only on noise strength.

Predictions for zero, weak, and strong noise regimes.

Abstract

We identify the nonlinear evolution equation in impact-parameter space for the "Supercritical Pomeron" in Reggeon Field Theory as a 2-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to an high energy traveling wave solution corresponding to an ""universal" behaviour of the impact-parameter front profile of the elastic amplitude; Its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the non-linear terms restoring unitarity. Theoretical predictions are presented for the three typical distinct regimes corresponding to zero, weak and strong noise.