Nuclei in the toy world: beyond the Pomeron in zero transverse dimensions

TL;DR

This paper extends high energy evolution models in zero transverse dimensions by allowing multiple dipole emissions per step, analyzing the resulting particle multiplicity and the onset of saturation effects in a toy hadron model.

Contribution

It introduces a generalized model that permits multiple dipole emissions, maintaining unitarity and low-density limits, and studies its impact on particle multiplicity and saturation behavior.

Findings

Saturation occurs after a specific rapidity range where multiple emissions dominate.

In the saturation regime, the entropy scales as S ≈ ln N, with N being the mean multiplicity.

The model preserves unitarity and correctly reproduces low-density limits.

Abstract

We explore possible extensions of the $t$-channel and $s$-channel unitary model of high energy evolution in zero transverse dimensions appropriate to very high energy/atomic number where the dipole density in a toy hadron is parametrically high.We suggest that the appropriate generalization is to allow emission of more than one dipole in a single step of energy evolution. We construct explicitly such a model that preserves the $t$-channel and s-channel unitarity and have the correct low density limit, and study the particle multiplicity distribution resulting from this evolution. We consider initial conditions of a single dipole and many dipoles at initial rapidity. We observe that the saturation regime in this model is preceded by a parametric range of rapidities $\frac{1}{\alpha_s}\ln\frac{1}{\alpha_s}<Y<\frac{1}{\alpha_s}\ln\frac{1}{\alpha_s^2}$, where the saturation effects are still unimportant, but multiple emissions determine the properties of the evolution. We also discuss the influence of the saturation on the parton cascade and, in particular, find that in the saturation regime the entropy of partons becomes $S \approx \h \ln N$ where $N$ is the mean multiplicity.