skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Deep inelastic scattering as a probe of entanglement

Abstract

Using nonlinear evolution equations of QCD, we compute the von Neumann entropy of the system of partons resolved by deep inelastic scattering at a given Bjorken x and momentum transfer q 2 = - Q 2 . We interpret the result as the entropy of entanglement between the spatial region probed by deep inelastic scattering and the rest of the proton. At small x the relation between the entanglement entropy S ( x ) and the parton distribution x G ( x ) becomes very simple: S ( x ) = ln [ x G ( x ) ] . In this small x , large rapidity Y regime, all partonic microstates have equal probabilities—the proton is composed by an exponentially large number exp ( Δ Y ) of microstates that occur with equal and exponentially small probabilities exp ( - Δ Y ) , where Δ is defined by x G ( x ) ~ 1 / x Δ . For this equipartitioned state, the entanglement entropy is maximal—so at small x , deep inelastic scattering probes a maximally entangled state. Here, we propose the entanglement entropy as an observable that can be studied in deep inelastic scattering. Thismore » will then require event-by-event measurements of hadronic final states, and would allow to study the transformation of entanglement entropy into the Boltzmann one. We estimate that the proton is represented by the maximally entangled state at x ≤ 10 -3 ; this kinematic region will be amenable to studies at the Electron Ion Collider.« less

Authors:
 [1];  [2]
  1. Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy; Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center, Dept. of Physics
  2. Tel Aviv Univ., Ramat Aviv (Israel). Dept. of Particle Physics; Federico Santa María Technical Univ. and Science and Technology Center, Valparaiso (Chile). Dept. of Physics
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1392245
Alternate Identifier(s):
OSTI ID: 1363840
Report Number(s):
BNL-114269-2017-JA
Journal ID: ISSN 2470-0010; PRVDAQ; R&D Project: KB0301020
Grant/Contract Number:  
SC0012704; FG-88ER40388; AC02-98CH10886
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 95; Journal Issue: 11; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Kharzeev, Dmitri E., and Levin, Eugene M. Deep inelastic scattering as a probe of entanglement. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.95.114008.
Kharzeev, Dmitri E., & Levin, Eugene M. Deep inelastic scattering as a probe of entanglement. United States. doi:10.1103/PhysRevD.95.114008.
Kharzeev, Dmitri E., and Levin, Eugene M. Sat . "Deep inelastic scattering as a probe of entanglement". United States. doi:10.1103/PhysRevD.95.114008. https://www.osti.gov/servlets/purl/1392245.
@article{osti_1392245,
title = {Deep inelastic scattering as a probe of entanglement},
author = {Kharzeev, Dmitri E. and Levin, Eugene M.},
abstractNote = {Using nonlinear evolution equations of QCD, we compute the von Neumann entropy of the system of partons resolved by deep inelastic scattering at a given Bjorken x and momentum transfer q 2 = - Q 2 . We interpret the result as the entropy of entanglement between the spatial region probed by deep inelastic scattering and the rest of the proton. At small x the relation between the entanglement entropy S ( x ) and the parton distribution x G ( x ) becomes very simple: S ( x ) = ln [ x G ( x ) ] . In this small x , large rapidity Y regime, all partonic microstates have equal probabilities—the proton is composed by an exponentially large number exp ( Δ Y ) of microstates that occur with equal and exponentially small probabilities exp ( - Δ Y ) , where Δ is defined by x G ( x ) ~ 1 / x Δ . For this equipartitioned state, the entanglement entropy is maximal—so at small x , deep inelastic scattering probes a maximally entangled state. Here, we propose the entanglement entropy as an observable that can be studied in deep inelastic scattering. This will then require event-by-event measurements of hadronic final states, and would allow to study the transformation of entanglement entropy into the Boltzmann one. We estimate that the proton is represented by the maximally entangled state at x ≤ 10 -3 ; this kinematic region will be amenable to studies at the Electron Ion Collider.},
doi = {10.1103/PhysRevD.95.114008},
journal = {Physical Review D},
number = 11,
volume = 95,
place = {United States},
year = {2017},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Entanglement entropy and entropy production in the color glass condensate framework
journal, August 2015


Review of Particle Physics
journal, October 2016


Decoherence and entropy production in relativistic nuclear collisions
journal, March 2009


Geometric and renormalized entropy in conformal field theory
journal, August 1994


Very High-Energy Collisions of Hadrons
journal, December 1969


Semihard processes in QCD
journal, November 1983


The Color Glass Condensate
journal, November 2010


Entanglement entropy of scattering particles
journal, July 2016


Chaos in the color glass condensate
journal, October 2005


Event by event analysis and entropy of multiparticle systems
journal, March 2000


Universal upper bound on the entropy-to-energy ratio for bounded systems
journal, January 1981


Asymptotic Sum Rules at Infinite Momentum
journal, March 1969


Inelastic Electron-Proton and γ -Proton Scattering and the Structure of the Nucleon
journal, September 1969


“Bottom-up” thermalization in heavy ion collisions
journal, March 2001


From color glass condensate to quark–gluon plasma through the event horizon
journal, May 2005


Ultraviolet Behavior of Non-Abelian Gauge Theories
journal, June 1973


Toward equilibration in the early stages after a high energy heavy ion collision
journal, April 2000


Hadron production in nuclear collisions at RHIC and high-density QCD
journal, May 2001


Multiparticle production and thermalization in high-energy QCD
journal, April 2007


Entropy Analysis in π+p and K+p Collisions at s = 22 GeV
conference, January 2006

  • Li, Zhiming
  • MULTIPARTICLE DYNAMICS: XXXV International Symposium on Multiparticle Dynamics; and Workshop on Particle Correlations and Femtoscopy, AIP Conference Proceedings
  • DOI: 10.1063/1.2197406

Reliable Perturbative Results for Strong Interactions?
journal, June 1973


QCD coherence in high-energy reactions
journal, April 1988


Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006


Asymptotic freedom in parton language
journal, August 1977


A covariant entropy conjecture
journal, July 1999


A linear evolution for non-linear dynamics and correlations in realistic nuclei
journal, January 2004


Soft gluons in the infinite-momentum wave function and the BFKL pomeron
journal, March 1994


AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks
journal, July 2011

  • Albacete, Javier L.; Armesto, Néstor; Milhano, José Guilherme
  • The European Physical Journal C, Vol. 71, Issue 7
  • DOI: 10.1140/epjc/s10052-011-1705-3

F 2 and F L at small x using a collinearly improved BFKL resummation
journal, April 2013


Dynamical entropy of dense QCD states
journal, February 2013


A covariant holographic entanglement entropy proposal
journal, July 2007

  • Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
  • Journal of High Energy Physics, Vol. 2007, Issue 07
  • DOI: 10.1088/1126-6708/2007/07/062

Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all
journal, September 2016


Momentum-space entanglement and renormalization in quantum field theory
journal, August 2012

  • Balasubramanian, Vijay; McDermott, Michael B.; Van Raamsdonk, Mark
  • Physical Review D, Vol. 86, Issue 4
  • DOI: 10.1103/PhysRevD.86.045014

Collinearly-improved BK evolution meets the HERA data
journal, November 2015


Unitarity and the BFKL pomeron
journal, March 1995


Entanglement Entropy and Quantum Field Theory: a Non-Technical Introduction
journal, June 2006

  • Calabrese, Pasquale; Cardy, John
  • International Journal of Quantum Information, Vol. 04, Issue 03
  • DOI: 10.1142/S021974990600192X

Solution to the evolution equation for high parton density QCD
journal, May 2000


Gluon distribution functions for very large nuclei at small transverse momentum
journal, April 1994


Charged particle multiplicities in pp interactions at $ \sqrt {s} = 0.9 $, 2.36, and 7 TeV
journal, January 2011

  • Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.
  • Journal of High Energy Physics, Vol. 2011, Issue 1
  • DOI: 10.1007/JHEP01(2011)079

Possible non-Regge behavior of electroproduction structure functions
journal, September 1974


Manifestations of high density QCD in the first RHIC data
journal, December 2001