Traveling wave solution of the Reggeon Field Theory (EPS proceedings)

TL;DR

This paper models the impact-parameter evolution in Reggeon Field Theory as a stochastic Fisher-KPP equation, revealing universal traveling wave solutions that depend only on noise strength and have implications for high-energy collider cross-sections.

Contribution

It identifies a stochastic Fisher-KPP equation in impact-parameter space for Reggeon Field Theory, providing a unitarity-preserving model with universal traveling wave solutions.

Findings

Traveling wave solutions depend only on noise strength.

Predictions for different noise regimes are provided.

Implications for collider cross-section measurements.

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 and 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" behavior 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 different regimes corresponding to zero, weak and strong noise, respectively. They have phenomenological implications for total and differential hadronic cross-sections at colliders.