The eccentricity in heavy-ion collisions from Color Glass Condensate initial conditions

TL;DR

The paper demonstrates that initial conditions based on Color Glass Condensate (CGC) physics within a $k_\perp$-factorization framework produce a significantly larger midrapidity eccentricity $\varepsilon$ than Glauber-based models, a result that persists across diverse unintegrated gluon distributions and is not solely due to edge effects. The authors attribute the large $\varepsilon$ to the scaling with the smaller saturation scale $\min(Q_{s,1}^2, Q_{s,2}^2)$ and show that extended geometric scaling and leading-twist shadowing have limited impact on this outcome, while revealing a nontrivial longitudinal dependence of the initial CGC density. They further show nonzero odd moments of the energy-density distribution with rapidity and discuss how high-$p_\perp$ partons and jet quenching could probe this initial density, underscoring the importance of 3D hydrodynamic modeling and the role of large-$x$ effects for quantitative predictions. Overall, the work highlights the robustness of CGC-driven eccentricity enhancements and their potential to shape final-state azimuthal anisotropy in heavy-ion collisions.

Abstract

The eccentricity in coordinate-space at midrapidity of the overlap zone in high-energy heavy-ion collisions predicted by the $k_\perp$-factorization formalism is generically larger than expected from scaling with the number of participants. We provide a simple qualitative explanation of the effect which shows that it is not caused predominantly by edge effects. We also show that it is quite insensitive to ``details'' of the unintegrated gluon distribution functions such as the presence of leading-twist shadowing and of an extended geometric scaling window. The larger eccentricity increases the azimuthal asymmetry of high transverse momentum particles. Finally, we point out that the longitudinal structure of the Color Glass Condensate initial condition for hydrodynamics away from midrapidity is non-trivial but requires understanding of large-$x$ effects.

Figures (7)

• Figure 1: (Color online) Centrality dependence of the multiplicity in Au+Au collisions as compared to PHOBOS data phobos for $\sqrt{s_{NN}}=130$ and 200 GeV. Running (fixed) coupling is used in the upper (lower) panel. $\lambda$ denotes the growth rate of the saturation momentum with $\log\,1/x$. The curves correspond to various parameterizations of the unintegrated gluon distribution function, see text for detailed explanations.
• Figure 2: (Color online) Initial spatial eccentricity $\varepsilon$ at midrapidity as a function of the number of participants for 200 $A$ GeV Au+Au collisions from various models. For comparison, we also show initial conditions where the initial parton density at midrapidity scales with the transverse density of wounded nucleons (full line) and of binary collisions (dotted line) Kolb:2001qz.
• Figure 3: Along the line $\vec{l}_x$, the density of gluons in the CGC case falls off more rapidly than in Glauber type models. Along $\vec{l}_y$, the collision is symmetric and the CGC gluon density behaves similar to the Glauber model. See text for explanation.
• Figure 4: (Color online) Moments ${\langle(r_x-\langle r_x\rangle)^n\rangle}$ (in fm$^n$) of the coordinate-space distribution of produced gluons as a function of rapidity. Open (closed) symbols correspond to the Ansatz (\ref{['eq:uninteg']}) with (without) the additional factor of $(1-x)^4$. The $n=1,3$ moments have been scaled up by a factor of 10.
• Figure 5: Top: suppression factor $R_{AA}(p_\perp;b)$ at $p_\perp\simeq10$ GeV as a function of centrality for CGC/KLN and $\sim N_{\rm part}$ bulk density distributions, respectively. PHENIX data phenixRaa correspond to hadron transverse momenta $p_\perp>4.5$ GeV. Bottom: second harmonic coefficient of $R_{AA}(p_\perp,\varphi;b)/R_{AA}(p_\perp;b)$.