Momentum fraction and hard scale dependence of double parton scattering in heavy-ion collisions
In a previous work, we studied the momentum fraction and hard--scale dependence of double parton scattering (DPS) in proton--proton collisions and the resulting dependence of the effective cross section on the final--state observables. In this paper, we extend those results to heavy--ion ($pA$ and $AA$) collisions, accounting for nuclear effects in the relevant kinematic region, namely shadowing and antishadowing. In addition to modifying the longitudinal parton distributions, these effects also alter the transverse parton distribution of the nucleus, for which we propose a simple new nuclear profile. We further hypothesize that partons inside a bound nucleon are more widely separated than in a free proton. We compute the effective cross section for the available $p$Pb data, obtaining reasonable agreement, and provide predictions for future measurements at the LHC. The observed dependence of our predictions on the final state indicates that DPS in heavy--ion collisions can be used to probe the transverse profile of the free proton and the bound nucleon, primarily in $pA$ collisions, as well as the transverse structure of the nucleus, mainly in $AA$ collisions.