Entanglement entropy of the proton in coordinate space

Abstract

We calculate the entanglement entropy of a model proton wave function in coordinate space by integrating out degrees of freedom outside a small circular region $\bar{A}$ of radius $L$, where $L$ is much smaller than the size of the proton. The wave function provides a nonperturbative distribution of three valence quarks. In addition, we include the perturbative emission of a single gluon and calculate the entanglement entropy of gluons in $\bar{A}$. For both, quarks and gluons we obtain the same simple result: $S_E=-\int \frac{dx}{\Delta x}{N}_{L^2}(x)\log [N_{a^2}(x)]$, where $a$ is the UV cutoff in coordinate space and $\Delta x$ is the longitudinal resolution scale. Here $N_S(x)$ is the number of partons (of the appropriate species) with longitudinal momentum fraction $x$ inside an area $S$. It is related to the standard parton distribution function (PDF) by $N_S(x)=\frac{S}{A_p}\Delta xF(x)$, where $A_p$ denotes the transverse area of the proton.

arXiv comment24 pages, 1 figure

References in corpus (27)

• A computable measure of entanglement
• The logarithmic negativity: A full entanglement monotone that is not convex
• Impact Parameter Space Interpretation for Generalized Parton Distributions
• Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation
• Deep inelastic scattering as a probe of entanglement
• The EPR paradox and quantum entanglement at sub-nucleonic scales
• Relativistic Constituent Quark Model of Electroweak Properties of Baryons
• Wavefunction-Independent Relations between the Nucleon Axial-Coupling g_A and the Nucleon Magnetic Moments
• Gluon Tomography from Deeply Virtual Compton Scattering at Small-x
• The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional
• Deep inelastic scattering as a probe of entanglement: confronting experimental data
• Entanglement entropy and entropy production in the Color Glass Condensate framework
• Classical and quantum entropy of parton distributions
• Entanglement entropy, entropy production and time evolution in high energy QCD
• Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon
• Evidence for the maximally entangled low $x$ proton in Deep Inelastic Scattering from H1 data
• Maximally entangled proton and charged hadron multiplicity in Deep Inelastic Scattering
• Investigating entanglement entropy at small-x in DIS off protons and nuclei
• Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model
• Rapidity evolution of the entanglement entropy in quarkonium: parton and string duality
• Quark and gluon entanglement in the proton on the light cone at intermediate $x$
• Entanglement between Valence and Sea Quarks in Hadrons of 1+1 Dimensional QCD
• High-energy dipole scattering amplitude from evolution of low-energy proton light-cone wave functions
• Hadronic structure on the light-front IV: Heavy and light Baryons
• Investigating the QCD dynamical entropy in high-energy hadronic collisions
• Page Entropy of Proton System in Deep-Inelastic-Scattering at Small-$x$
• Quantum Entanglement and the Thermal Hadron

Cited by in corpus (6)

• QCD evolution of entanglement entropy
• Quantum simulation of entanglement and hadronization in jet production: lessons from the massive Schwinger model
• Entanglement as a probe of hadronization
• Quantum entanglement correlations in double quark PDFs
• Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models
• Quantum entanglement between partons in a strongly coupled quantum field theory