Entanglement entropy production in deep inelastic scattering

Abstract

Deep inelastic scattering (DIS) samples a part of the wave function of a hadron in the vicinity of the light cone. Lipatov constructed a spin chain which describes the amplitude of DIS in leading logarithmic approximation. Kharzeev and Levin proposed the entanglement entropy as an observable in DIS [Phys. Rev. D 95, 114008 (2017)], and suggested a relation between the entanglement entropy and parton distributions. Here we represent the DIS process as a local quench in the Lipatov's spin chain, and study the time evolution of the produced entanglement entropy. We show that the resulting entanglement entropy depends on time logarithmically, $\mathcal{S}(t)=1/3\ln (t/\tau )$ with $\tau =1/m$ for $1/m\le t\le (mx{)}^{-1}$, where $m$ is the proton mass and $x$ is the Bjorken $x$. The central charge $c$ of Lipatov's spin chain is determined here to be $c=1$; using the proposed relation between the entanglement entropy and parton distributions, this corresponds to the gluon structure function growing at small $x$ as $xG(x)\sim 1/x^{1/3}$.

Published version, 8 pages, 1 figure

References in corpus (7)

• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Operator space entanglement entropy in transverse Ising chain
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Description of F2 and FL at small x using a collinearly-improved BFKL resummation
• Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
• Bethe Ansatz for XXX chain with negative spin

Cited by in corpus (20)

• Maximally entangled proton and charged hadron multiplicity in Deep Inelastic Scattering
• Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium
• Rapidity evolution of the entanglement entropy in quarkonium: parton and string duality
• Quantum simulation of entanglement and hadronization in jet production: lessons from the massive Schwinger model
• Quark and gluon entanglement in the proton on the light cone at intermediate $x$
• Investigating the QCD dynamical entropy in high-energy hadronic collisions
• Page Entropy of Proton System in Deep-Inelastic-Scattering at Small-$x$
• Quark pair angular correlations in the proton: entropy versus entanglement negativity
• Quantum Entanglement and the Thermal Hadron
• From locality to irregularity: Introducing local quenches in massive scalar field theory
• Universal rapidity scaling of entanglement entropy inside hadrons from conformal invariance
• 1+1D Hadrons Minimize their Biparton Renyi Free Energy
• Quantum Entanglement in Top Quark Pair Production
• Classical information entropy of parton distribution functions and an application in searching gluon saturation
• Threshold and infrared singularities: time evolution, asymptotic state and entanglement entropy
• Yangian symmetry applied to Quantum chromodynamics
• Quantum entanglement between partons in a strongly coupled quantum field theory
• Chirality distributions inside baryons in $\mathrm{QC}{\mathrm{D}}_2$
• Small $x$ behavior in QCD from maximal entanglement and conformal invariance
• On the conformal spin dependence of the perturbative QCD vacuum singularity