High energy QCD: Multiplicity distribution and entanglement entropy
E. Gotsman, E. Levin
Abstract
In this paper, we show that QCD at high energies leads to the multiplicity distribution ${(\ensuremath{\sigma}}_{n}/{\ensuremath{\sigma}}_{\mathrm{in}})=(1/N){\text{ }(N\ensuremath{-}1/N)}^{n\ensuremath{-}1}$ (where $N$ denotes the average number of particles) and to entanglement entropy $S=\mathrm{ln}N$, 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, $N\ensuremath{\propto}{Q}_{S}^{2}(Y)$, where ${Q}_{s}$ denotes the saturation scale. We checked that this multiplicity distribution describes the LHC data for low multiplicities $n<(3\textdiv{}5)N$, 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.