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

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.