Long-Range Rapidity Correlations in Heavy-Light Ion Collisions

TL;DR

The paper investigates the origin of long-range two-particle rapidity correlations (ridge) in heavy-light ion collisions within the Color Glass Condensate framework, calculating the two-gluon production cross section with all-order saturation in the heavy nucleus and minimal rescattering in the light nucleus. Using light-cone perturbation theory and Wilson-line interactions, the authors derive the corresponding cross sections, including geometric, HBT, away-side, and near-side correlations, and show that away- and near-side structures have identical amplitudes and lie in an even-harmonics azimuthal expansion. The analysis, performed in the MV/GM regime with large-Nc, reveals that initial-state, non-flow correlations can be long-range in rapidity and may mimic elliptic flow observables if not properly isolated. The results emphasize the importance of accounting for these CGC-based correlations in the interpretation of flow measurements and provide a framework for further quantitative comparisons with data.

Abstract

We study two-particle long-range rapidity correlations arising in the early stages of heavy ion collisions in the saturation/Color Glass Condensate framework, assuming for simplicity that one colliding nucleus is much larger than the other. We calculate the two-gluon production cross section while including all-order saturation effects in the heavy nucleus with the lowest-order rescattering in the lighter nucleus. We find four types of correlations in the two-gluon production cross section: (i) geometric correlations, (ii) HBT correlations accompanied by a back-to-back maximum, (iii) away-side correlations, and (iv) near-side azimuthal correlations which are long-range in rapidity. The geometric correlations (i) are due to the fact that nucleons are correlated by simply being confined within the same nucleus and may lead to long-range rapidity correlations for the produced particles without strong azimuthal angle dependence. Somewhat surprisingly, long-range rapidity correlations (iii) and (iv) have exactly the same amplitudes along with azimuthal and rapidity shapes: one centered around Δφ=π with the other one centered around Δφ=0 (here Δφ is the azimuthal angle between the two produced gluons). We thus observe that the early-time CGC dynamics in nucleus-nucleus collisions generates azimuthal non-flow correlations which are qualitatively different from jet correlations by being long-range in rapidity. If strong enough, they have the potential of mimicking the elliptic (and higher-order even-harmonic) flow in the di-hadron correlators: one may need to take them into account in the experimental determination of the flow observables.

Figures (13)

• Figure 1: Transverse plane geometry of the two-particle production in the collision of a smaller projectile nucleus ($A_1$) with a larger target nucleus ($A_2$). The two smaller circles represent two nucleons in the nucleus $A_1$ (see text for details).
• Figure 2: Diagrams describing the two-gluon production in the heavy-light ion collision. Two horizontal solid lines denote valence quarks inside the two nucleons in the projectile nucleus. Vertical dashed line denotes the interaction with the target nucleus, while the vertical dotted lines denote intermediate states.
• Figure 3: Diagrams contributing to the square of the scattering amplitude for the single gluon production in $pA$ collisions. The cross denotes the measured produced gluon.
• Figure 4: Diagrams contributing to the two-gluon production cross section in the heavy--light ion collision. For clarity the diagrams are shown as a direct product of gluon production processes in collisions of the two interacting nucleons from the projectile nucleus with the target nucleus.
• Figure 5: Diagrams contributing to the two-gluon production cross section, with the gluon emitted by each nucleon in the amplitude absorbed by another nucleon in the complex conjugate amplitude. The top cross denotes the gluon with momentum ${\bm k}_1$, while the bottom one denotes the gluon with momentum ${\bm k}_2$.