Momentum fraction and hard scale dependence of double parton scattering in heavy-ion collisions

Abstract

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 model. 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.

Figures (7)

• Figure 1: Schematic diagrams of double parton scattering (DPS) contributions in $pA$ collisions, where the two nuclear partons originate either (a) from the same nucleon, labelled 1x1, or (b) from two different nucleons, labeled 1x2.
• Figure 2: Our proposed two-dimensional nuclear profile for different values of the nuclear gluon modification factor $R_g$. Compared to the baseline Woods--Saxon distribution at $R_g=1$, larger shadowing (antishadowing) leads to a broadening (narrowing) of the profile.
• Figure 3: Comparison between available experimental results and theoretical predictions for the DPS effective cross section in $p$Pb collisions at $\sqrt{s}=8.16$ TeV for various final states $CD$. The CMS data point corresponds to the central rapidity ("ce") double $J/\psi$ result CMS:2024wgu. The LHCb results correspond to $J/\psi + D^0$ and double $D^0$ production in the forward ("fw") and backward ("bw") rapidity configurations LHCb:2020jse. Theoretical predictions are shown for bound nucleons with transverse profiles the same as ($\gamma_A=0$, black empty circles) or wider than ($\gamma_A=1$ mb, blue filled circles) those of free protons. Solid vertical bars represent the combined $1\sigma$ theoretical uncertainties, while dashed bars indicate the additional variation obtained by varying $\gamma_A$ in the range $0.5$--$1.5$ mb.
• Figure 4: Theoretical predictions for the DPS effective cross section in $\sqrt{s} = 8.16$ TeV $p$Pb collisions for final states with identical observables ($C=D$), considering backward, central, and forward rapidity configurations.
• Figure 5: Theoretical predictions for the DPS effective cross section in $\sqrt{s} = 8.16$ TeV $p$Pb collisions for final states with different observables ($C\neq D$), considering backward, central, and forward rapidity configurations.