Entanglement entropy production in deep inelastic scattering

• URL: http://arxiv.org/abs/2110.04881v2
• Date: Tue, 4 Jan 2022 22:00:23 GMT
• Title: Entanglement entropy production in deep inelastic scattering
• Authors: Kun Zhang, Kun Hao, Dmitri Kharzeev, Vladimir Korepin
• Abstract summary: Deep inelastic scattering (DIS) samples a part of the wave function of a hadron in the vicinity of the light cone. We show that the resulting entanglement entropy depends on time logarithmically, $mathcal S(t)=1/3 ln(t/tau)$ with $tau = 1/m$ for $1/m le tle (mx)-1$, where $m$ is the proton mass and $x$ is Bjorken $x$.
• Score: 6.359294579761927
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $xG(x) \sim 1/x^{1/3}$.

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