On parton number fluctuations at various stages of the rapidity evolution

TL;DR

This paper models parton evolution as a branching-diffusion process to analyze fluctuations affecting QCD scattering amplitudes, deriving new results on saturation scales and geometric scaling at intermediate rapidities.

Contribution

It introduces a stochastic branching-diffusion framework for parton evolution, providing new insights into fluctuations and their impact on scattering amplitudes and saturation phenomena.

Findings

Derived new expressions for the saturation scale of large nuclei.

Identified a modified geometric scaling at intermediate rapidities.

Connected fluctuations in parton densities to observable scattering properties.

Abstract

Starting with the interpretation of parton evolution with rapidity as a branching-diffusion process, we describe the different kinds of fluctuations of the density of partons which affect the properties of QCD scattering amplitudes at moderately high energies. We then derive some of these properties as direct consequences of the stochastic picture. We get new results on the expression of the saturation scale of a large nucleus, and a modified geometric scaling valid at intermediate rapidities for dipole-dipole scattering.