Deep inelastic scattering as a probe of entanglement

Kharzeev, Dmitri E.; Levin, Eugene M.

doi:10.1103/PhysRevD.95.114008

Title: Deep inelastic scattering as a probe of entanglement

Journal Article · Sat Jun 03 00:00:00 EDT 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.95.114008· OSTI ID:1392245

Kharzeev, Dmitri E. ^[1]; Levin, Eugene M. ^[2]

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
Tel Aviv Univ., Ramat Aviv (Israel). Dept. of Particle Physics; Federico Santa MarÃÂa Technical Univ. and Science and Technology Center, Valparaiso (Chile). Dept. of Physics

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.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0012704; FG-88ER40388; AC02-98CH10886

OSTI ID:: 1392245

Alternate ID(s):: OSTI ID: 1363840

Report Number(s):: BNL-114269-2017-JA; PRVDAQ; R&D Project: KB0301020

Journal Information:: Physical Review D, Vol. 95, Issue 11; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 96 works

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