Entanglement entropy production in deep inelastic scattering

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, $\mathcal{S}(t)=1/3\ln (t/\tau )$ 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 $xG(x)\sim 1/x^{1/3}$.

Figure 1

Feynman diagram describing DIS at small Bjorken $x$. The virtual photon $\gamma *$ emitted by the scattered lepton (not shown) splits into a virtual quark-antiquark pair. The Reggeized gluons are exchanged between the virtual quark-antiquark pair and the hadron.