Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD

TL;DR

This paper investigates zero-dimensional reaction-diffusion models as simplified representations of high-energy QCD evolution, finding that only reversible processes exhibit expected amplitude growth and that certain modifications slow evolution.

Contribution

It compares different reaction-diffusion models as toy models for QCD, highlighting the unique behavior of reversible processes and effects of various modifications.

Findings

Reversible processes show increasing scattering amplitude with rapidity.

Recombination, quantum loops, and running couplings slow down evolution.

Only reversible processes match expected high-energy QCD behavior.

Abstract

We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined -- Reggeon Field Theory, Directed Percolation and Reversible Processes -- only the latter shows the behaviour commonly expected, namely an increase of the scattering amplitude with increasing rapidity. Further, we find that increasing recombination terms, quantum loops and the heuristic inclusion of a running of the couplings, generically slow down the evolution.