# High energy QCD: Multiplicity distribution and entanglement entropy

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## Abstract

In this paper, we show that QCD at high energies leads to the multiplicity distribution (σn/σin)=(1/N) (N-1/N)n-1 (where N denotes the average number of particles) and to entanglement entropy S=lnN, confirming that the partonic state at high energy is maximally entangled. However, the value of N depends on the kinematics of the parton cascade. In particular, for deep inelastic scattering, N=xG(x,Q), where xG is the gluon structure function, while for hadron-hadron collisions, N∝QS2(Y), where Qs denotes the saturation scale. We checked that this multiplicity distribution describes the LHC data for low multiplicities n<(3÷5)N, exceeding it for larger values of n. We view this as a consequence of our assumption that the system of partons in hadron-hadron collisions at c.m. rapidity Y=0, is dilute. We show that the data can be described at large multiplicities in the parton model, if we do not make this assumption.

Original language English 074008 Physical Review D 102 7 https://doi.org/10.1103/PhysRevD.102.074008 Published - Oct 2020

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