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 ≥ 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.

Jet evolution in a dense medium: event-by-event fluctuations and multi-particle correlations

“…D (2) fulfills an evolution equation similar to the one in eq. (2) , under the same approximations leading to eq.…”

“…(2) , under the same approximations leading to eq. (3) the evolution equation of D (2) has the solution…”

“…If we want to have more detailed information on the energy loss and the distribution of particles we need to compute higher order n-point functions D (n) . They fulfill an evolution equation similar to the one of D (2) , they can be analytically solved using the same approximations [2]. We can use this result to compute the ratio of the moments of the distribution of soft particles inside the jet with respect to the mean number of these particles…”

“…as the difference between the in-medium path lengths of the two jets). We compute the higher moments of the multiplicity distribution and identify a remarkable regularity known as Koba-Nielsen-Olesen (KNO) scaling [2]. These predictions could be tested via eventby-event measurements of the di-jet asymmetry.…”

“…We show that under suitable approximations, the jet evolution is a Markovian stochastic process, which is exactly solvable. For this process, we construct exact analytic solutions for all the n-point correlation functions describing the gluon distribution in the space of energy [1,2]. Using these results, we study the event-by-event distribution of the energy lost by the jet at large angles and of the multiplicities of the soft particles which carry this energy.…”