In this paper, we show that QCD at high energies leads to the multiplicity distribution ${(\sigma }_n/{\sigma }_{\mathrm{in}})=(1/N){(N-1/N)}^{n-1}$ (where $N$ denotes the average number of particles) and to entanglement entropy $S=\ln N$, 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, $N\propto Q_S^2(Y)$, where $Q_s$ 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.

• Received 4 July 2020
• Accepted 22 September 2020

DOI:https://doi.org/10.1103/PhysRevD.102.074008

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Published by the American Physical Society