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)PRVDAQ2470-001010.1103/PhysRevD.95.114008], 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)=1/3ln(t/τ) with τ=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)∼1/x1/3.