High energy QCD: multiplicity distribution and entanglement entropy

TL;DR

This paper demonstrates that high-energy QCD predicts a specific multiplicity distribution and maximal entanglement entropy, with the distribution fitting LHC data for low multiplicities and adjustments needed for higher multiplicities.

Contribution

It introduces a model linking multiplicity distribution and entanglement entropy in high-energy QCD, and compares predictions with experimental data, refining assumptions about parton density.

Findings

Multiplicity distribution matches LHC data for low multiplicities

Entanglement entropy at high energy is maximally entangled

Model adjustments improve fit for high multiplicity events

Abstract

In this paper we show that QCD at high energies leads to the multiplicity distribution $\frac{\sigma_n}{\sigma_{ \rm in}}\,\,=\,\,\frac{1}{N}\,\Lb \frac{N\,-\,1}{N}\Rb^{n - 1}$, (where $N$ denotes the average number of particles), and to entanglement entropy $S \,=\,\ln N$, confirming that the partonic stat at high energy is maximally entangled. However, the value of $N$ depends on the kinematics of the parton cascade. In particular, for DIS$N = xG(x,Q)$ , where $xG$ is the gluon structure function, whil for hadron-hadron collisions, $N \propto Q^2_S(Y)$, where $Q_s$ denotes the saturation scale. We checked that this multiplicity distribution describes the LHC data for low multiplicities $n \,<\,(3 \div 5)\,N$, exceeding it for larger values of $n$. We view this as a result of our assumption, that the system of partons in hadron-hadron collisions atc.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.