Letter
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Deep inelastic scattering as a probe of entanglement: Confronting experimental data

Dmitri E. Kharzeev ^1,2,* and Eugene Levin ^3,4,†

¹Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University, New York 11794-3800, USA
²Department of Physics and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
³Department of Particle Physics, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
⁴Departamento de Física, Universidad Técnica Federico Santa María and Centro Científico-Tecnológico de Valparaíso, Casilla 110-V, Valparaiso, Chile

^*Dmitri.Kharzeev@stonybrook.edu
^†leving@tauex.tau.ac.il,eugeny.levin@usm.cl

Phys. Rev. D 104, L031503 – Published 30 August, 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L031503

Abstract

Parton distributions can be defined in terms of the entropy of entanglement between the spatial region probed by deep inelastic scattering and the rest of the proton. For very small $x$ , the proton becomes a maximally entangled state. This approach leads to a simple relation $S = \ln N$ between the average number $N$ of color-singlet dipoles in the proton wave function and the entropy of the produced hadronic state $S$ . At small $x$ , the multiplicity of dipoles is given by the gluon structure function, $N = x G (x, Q^{2})$ . Recently, the H1 collaboration analyzed the entropy of the produced hadronic state in deep inelastic scattering, and studied its relation to the gluon structure function; poor agreement with the predicted relation was found. In this paper we argue that a more accurate account of the number of color-singlet dipoles in the kinematics of H1 experiment (where hadrons are detected in the current fragmentation region) is given not by $x G (x, Q^{2})$ but by the sea quark structure function $x Σ (x, Q^{2})$ . Sea quarks originate from the splitting of gluons, so at small $x$ $x Σ (x, Q^{2}) \sim x G (x, Q^{2})$ , but in the current fragmentation region this proportionality is distorted by the contribution of the quark-antiquark pair produced by the virtual photon splitting. In addition, the multiplicity of color-singlet dipoles in the current fragmentation region is quite small, and one needs to include $\sim 1 / N$ corrections to $S = \ln N$ asymptotic formula. Taking both of these modifications into account, we find that the data from the H1 collaboration in fact agree well with the prediction based on entanglement.

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References (15)

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Phys. Rev. D 104, L031503– Published 30 August, 2021

Vol. 104, Iss. 3 — 1 August 2021

Received 22 February 2021
Accepted 10 August 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L031503

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Deep inelastic scattering as a probe of entanglement: Confronting experimental data

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