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DOE OSTI · 1866113

Entanglement entropy production in deep inelastic scattering

Zhang, Kun·Hao, Kun·Kharzeev, Dmitri·Korepin, Vladimir
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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 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 $τ = 1/m for 1/m ≤ t ≤ (mx)^{–1}$, where m is the proton mass and $\textit{x}$ is the Bjorken $\textit{x}$. The central charge c of Lipatov’s spin chain is determined here to be $\textit{c}$ = 1; using the proposed relation between the entanglement entropy and parton distributions, this corresponds to the gluon structure function growing at small $\textit{x}$ as $xG(x) ~ 1/x^{1/3}$.

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS97 MATHEMATICS AND COMPUTING

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Zhang, Kun, Hao, Kun, Kharzeev, Dmitri, Korepin, Vladimir. 2022-01-04. Entanglement entropy production in deep inelastic scattering. https://doi.org/10.1103/physrevd.105.014002

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