KNO scaling from a nearly Gaussian action for small-x gluons

TL;DR

This paper links KNO scaling in small-x gluons to a nearly Gaussian effective theory of color charge fluctuations, emphasizing the importance of saturation and running coupling in QCD evolution.

Contribution

It demonstrates that KNO scaling arises from a Gaussian approximation of color charge fluctuations and highlights the necessity of saturation and running coupling effects in QCD evolution.

Findings

KNO scaling is consistent with a Gaussian effective theory of color charges.

Evolution with the QCD eta;-function satisfies KNO scaling.

Fixed-coupling evolution does not produce KNO scaling.

Abstract

Transverse momentum integrated multiplicities in the central region of pp collisions at LHC energies satisfy Koba-Nielsen-Olesen scaling. We attempt to relate this finding to multiplicity distributions of soft gluons. KNO scaling emerges if the effective theory describing color charge fluctuations at a scale on the order of the saturation momentum is approximately Gaussian. From an evolution equation for quantum corrections which includes both saturation as well as fluctuations we find that evolution with the QCD \beta-function satisfies KNO scaling while fixed-coupling evolution does not. Thus, non-linear saturation effects and running-coupling evolution are both required in order to reproduce geometric scaling of the DIS cross section and KNO scaling of virtual dipoles in a hadron wave function.