Long range two-particle rapidity correlations in A+A collisions from high energy QCD evolution

TL;DR

The paper derives a compact, leading-logarithmic expression for long-range two-gluon correlations in A+A collisions in terms of unintegrated gluon distributions, linking early-time Glasma dynamics to small-$x$ evolution via the BK equation with running coupling. By factorizing the Glasma observables into Wilson-line distributions and solving BK for the dipole amplitude, the authors express the two-gluon spectrum as convolutions of $Φ_A(y,k_⊥)$ for the two nuclei, with a central result for the correlation $C(p,q)$ explicitly depending on these distributions at the relevant rapidities. Initial conditions are constrained by fixed-target $e+A$ data, and predictions are confronted with RHIC data (PHOBOS) and extended to LHC kinematics, where a large rapidity window enhances sensitivity to nonlinear small-$x$ evolution. The work provides a quantitative bridge between high-energy QCD evolution and early-time multi-particle correlations, offering a new avenue to study multiparton correlations in nuclear wavefunctions.

Abstract

Long range rapidity correlations in A+A collisions are sensitive to strong color field dynamics at early times after the collision. These can be computed in a factorization formalism \cite{GelisLV5} which expresses the $n$-gluon inclusive spectrum at arbitrary rapidity separations in terms of the multi-parton correlations in the nuclear wavefunctions. This formalism includes all radiative and rescattering contributions, to leading accuracy in $α_sΔY$, where $ΔY$ is the rapidity separation between either one of the measured gluons and a projectile, or between the measured gluons themselves. In this paper, we use a mean field approximation for the evolution of the nuclear wavefunctions to obtain a compact result for inclusive two gluon correlations in terms of the unintegrated gluon distributions in the nuclear projectiles. The unintegrated gluon distributions satisfy the Balitsky-Kovchegov equation, which we solve with running coupling and with initial conditions constrained by existing data on electron-nucleus collisions. Our results are valid for arbitrary rapidity separations between measured gluons having transverse momenta $p_\perp,q_\perp\gtrsim \qs$, where $\qs$ is the saturation scale in the nuclear wavefunctions. We compare our results to data on long range rapidity correlations observed in the near-side ridge at RHIC and make predictions for similar long range rapidity correlations at the LHC.

Figures (9)

• Figure 1: 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 2: 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 3: Unintegrated gluon distribution in the adjoint representation at $Y=0,2,6,10,15$ (from left curve rightwards) with the Balitsky prescription for the kernel in eq. (\ref{['eq:NLO-BFKL-kernel']}) as well as for the fixed coupling case. The distribution is in units of $N_c \pi R_A^2/\alpha_s$.
• Figure 4: The $x$ and $Q^2$ dependence of the normalized ratio of structure functions $F_2$ in nuclei. The curves in the left figure includes effects due to the small $x$ evolution of the dipole cross-section described by the BK evolution with the modified kernel in eq. (\ref{['eq:NLO-BFKL-kernel']}). The curve in the right figure is sensitive to the $Q^2$ dependence of the initial condition alone because it is evaluated at relatively large $x$. Details regarding the parameters of the initial condition are discussed in appendix B. The data are from the NMC collaboration AmaudA1.
• Figure 5: The $A$ dependence of the ratio of structure functions given by data from the NMC collaboration ArneoA1. The corresponding curves for other initial conditions are in appendix B.