High energy factorization in nucleus-nucleus collisions III. Long range rapidity correlations

TL;DR

The paper develops a leading-logarithmic resummation framework for inclusive multi-gluon production in high-energy nucleus-nucleus collisions within the Color Glass Condensate, showing that all leading rapidity logarithms factorize into universal Wilson-line distributions $W$ that evolve via the JIMWLK equation. This establishes a factorized, process-general description of long-range rapidity correlations and strongly supports the Glasma flux-tube picture as the origin of near-side ridge structures. Explicit expressions for single- and double-gluon spectra are given as convolutions over Wilson-line functionals and a Green's function that propagates JIMWLK evolution between produced gluons, enabling quantitative studies across wide rapidity separations. The work also clarifies the limitations in dilute-dense regimes, highlighting the need to include pomeron-splitting contributions beyond the JIMWLK framework for a complete interpolation to dilute systems, and outlines paths for numerical implementation via BK/Gaussian approximations and extensions to asymmetric collisions and LHC energies.

Abstract

We obtain a novel result in QCD for long range rapidity correlations between gluons produced in the collision of saturated high energy hadrons or nuclei. This result, obtained in a high energy factorization framework, provides strong justification for the Glasma flux tube picture of coherent strong color fields. Our formalism can be applied to "near side ridge" events at RHIC and in future studies of long range rapidity correlations at the LHC.

Figures (4)

• Figure 1: Initial space-time surface $\Sigma$ used in the initial value problem for the retarded classical field ${\cal A}^\mu$.
• Figure 2: Diagrammatic representation of the various building blocks in the factorized formula for the inclusive single gluon spectrum. The lower part of the figure, representing nucleus 2, is made up of identical building blocks.
• Figure 3: Diagrammatic representation of the various building blocks in the factorized formula for the inclusive 2-gluon spectrum. As in the previous figure, the corresponding evolution from nucleus 2 at the bottom of the figure is not shown explicitly.
• Figure 4: Order of magnitude of various contributions to the 2-gluon spectrum as a function of the color charge density $\rho_2$ in the small projectile (the color charge density in the large projectile is held fixed $\rho_1={\cal O}(g^{-1})$). Large logarithms of the energy, which become relevant in the leading logarithmic resummation, are not considered here.