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

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 $⟨N⟩$ as well as the higher moments $⟨N^p⟩$ 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 $⟨N^p⟩/⟨N{⟩}^p$ 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.

arXiv comment31 pages, 7 figures

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