High energy QCD: multiplicity distribution and entanglement entropy

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, $N\propto Q_S^2(Y)$, 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 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.