Universality of Koba-Nielsen-Olesen scaling in QCD at high energy and entanglement

Abstract

Using Mueller's dipole formalism for deep inelastic scattering in QCD, we formulate and solve the evolution for the generating function for the multiplicities of the produced particles, in hadronic processes at high energy. The solution for the multiplicities satisfies Koba-Nielsen-Olesen (KNO) scaling, with good agreement with the recently re-analyzed data from the H1 experiment at HERA (DESY), and the old ALEPH data for hadronic $Z$ decay at LEP (CERN). The same scaling function with KNO scaling, carries to the hadronic multiplicities from jets in electron-positron annihilation. This agreement is {\it a priori} puzzling, since in Mueller's dipole evolution, one accounts for virtual dipoles in a wave function, whereas in electron-positron annihilation, one describes cross-sections of real particles. We explain the origin of this similarity, pointing at a particular duality between the two processes. Finally, we interpret our results from the point of view of quantum entanglement between slow and fast degrees of freedom in QCD, and derive the entanglement entropy pertinent to electron-positron annihilation into hadronic jets.