High energy QCD: Multiplicity distribution and entanglement entropy

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<(35)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.