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arXiv · 2110.04881

Entanglement entropy production in deep inelastic scattering

Kun Zhang·Kun Hao·Dmitri Kharzeev·Vladimir Korepin
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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, $\mathcal S(t)=1/3 \ln{(t/τ)}$ with $τ= 1/m$ 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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Kun Zhang, Kun Hao, Dmitri Kharzeev, Vladimir Korepin. 2022-01-04. Entanglement entropy production in deep inelastic scattering. https://doi.org/10.1103/physrevd.105.014002

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