Cut Reggeon Field Theory as a Stochastic Process

TL;DR

This paper interprets cut Reggeon field theory as a stochastic process, linking it to population models and directed percolation, and clarifies the probabilistic meaning of AGK cutting rules.

Contribution

It provides a novel probabilistic interpretation of cut RFT, connecting it to population dynamics and percolation models, and elucidates the AGK rules within these frameworks.

Findings

Cut RFT can be viewed as a population model with two genotypes.

It can be interpreted as a bicolor directed percolation problem.

AGK rules correspond to specific limiting cases in these models.

Abstract

Reggeon field theory (RFT), originally developed in the context of high energy diffraction scattering, has a much wider applicability, describing, for example, the universal critical behavior of stochastic population models as well as probabilistic geometric problems such as directed percolation. In 1975 Suranyi and others developed cut RFT, which can incorporate the cutting rules of Abramovskii, Gribov and Kancheli for how each diagram contributes to inclusive cross-sections. In this note we describe the corresponding probabilistic interpretations of cut RFT: as a population model of two genotypes, which can reproduce both asexually and sexually; and as a kind of bicolor directed percolation problem. In both cases the AGK rules correspond to simple limiting cases of these problems.