Multi-particle correlations and KNO scaling in the medium-induced jet evolution

TL;DR

This paper develops an exactly solvable model for medium-induced jet evolution, revealing strong gluon correlations, large multiplicities, and KNO scaling, with implications for heavy-ion collision experiments at the LHC.

Contribution

It provides the first exact analytic solutions for all n-point gluon correlation functions in medium-induced jet evolution, highlighting novel correlation structures and statistical properties.

Findings

Exact solutions for n-point correlation functions

Demonstration of KNO scaling in gluon multiplicities

Identification of a negative binomial distribution for gluon counts

Abstract

We study the gluon distribution produced via successive medium-induced branchings by an energetic jet propagating through a weakly-coupled quark-gluon plasma. We show that under suitable approximations the evolution of the jet can be described as a classical stochastic process, which is exactly solvable. For this process, we construct exact analytic solutions for all the n-point correlation functions (the n-body densities in the space of energy). The corresponding results for the one-point and the two-point functions were already known, but those for the higher-point functions are new. These results demonstrate strong correlations associated with the existence of common ancestors in the branching process. By integrating these n-point functions over the gluon energies, we deduce the mean gluon multiplicity $\langle N\rangle$ as well as the higher moments $\langle N^p\rangle$ with $p\ge 2$. We find that the multiplicities of the soft gluons are parametrically large and show a remarkable regularity, known as Koba-Nielsen-Olesen (KNO) scaling: the reduced moments $\langle N^p\rangle/\langle N\rangle^p$ are pure numbers, independent of any of the physical parameters of the problem. We recognize a special negative binomial distribution which is characterized by large statistical fluctuations. These predictions can be tested in Pb+Pb collisions at the LHC, via event-by-event measurements of the di-jet asymmetry.