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, S(t) = 1/3 ln(t/tau) with tau = 1/m for 1/m <= t <= (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) similar to 1/x(1)(/3).

Automated summary

This study investigates the entanglement entropy in deep inelastic scattering (DIS) and its relation with parton distributions. By analyzing the local quench in Lipatov's spin chain, the time evolution of the produced entanglement entropy is studied, revealing a logarithmic dependence on time.