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.
Highlights
INTRODUCTIONOver the past several years, new ideas have been developed in the high energy and nuclear physics community, which suggest a robust relation between the principle features of high energy scattering and entanglement properties of the hadronic wave function [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
We show that QCD at high energies leads to the multiplicity distribution ðσn=σinÞ 1⁄4 ð1=NÞ ðN − 1=NÞn−1 and to entanglement entropy S 1⁄4 ln N, confirming that the partonic state at high energy is maximally entangled
Over the past several years, new ideas have been developed in the high energy and nuclear physics community, which suggest a robust relation between the principle features of high energy scattering and entanglement properties of the hadronic wave function [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
Summary
Over the past several years, new ideas have been developed in the high energy and nuclear physics community, which suggest a robust relation between the principle features of high energy scattering and entanglement properties of the hadronic wave function [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. The main idea, which we explore in this paper, is the intimate relation between the entropy in the parton approach [18,19,20,21] and the entropy of entanglement in a proton wave function [5] This relation materialized as the resolution of the following difficulty in our understanding of high energy scattering: on one hand, the proton is a pure state, and it is described by a completely coherent wave function with zero entropy, but, on the other hand, the deep inelastic scattering (DIS) experiments are successfully described, treating the proton as a incoherent collection of quasifree partons. This ensemble has nonvanishing entropy, and Ref. In Ref. [44], it was shown that these two approaches are equivalent for the description of the scattering amplitude
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