Entanglement entropy production in deep inelastic scattering

TL;DR

This paper models deep inelastic scattering as a local quench in Lipatov's spin chain, revealing a logarithmic growth of entanglement entropy over time and linking it to the small-x behavior of gluon distributions.

Contribution

It introduces a novel representation of DIS as a local quench in Lipatov's spin chain and calculates the entanglement entropy evolution, connecting it to gluon distribution growth.

Findings

Entanglement entropy grows logarithmically with time, S(t)=1/3 ln(t/τ).

The central charge of Lipatov's spin chain is c=1.

Gluon structure function scales as 1/x^{1/3} at small x.

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 $xG(x) \sim 1/x^{1/3}$.