System size dependence of cluster properties from two-particle angular correlations in Cu+Cu and Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV

TL;DR

This work analyzes two-particle angular correlations in Cu+Cu and Au+Au collisions at √sNN = 200 GeV using the PHOBOS detector to extract effective cluster size K_eff and decay width δ across centralities. It models the correlations with a cluster-emission framework, corrects for detector acceptance and high occupancy, and investigates near- and away-side differences, revealing a centrality-dependent decrease in K_eff and a geometric scaling with b/2R between systems. After extrapolating to full η coverage, the inferred cluster parameters are substantially larger, posing challenges to conventional hadronization pictures and suggesting strong medium or geometric effects. The results provide new constraints for heavy-ion collision dynamics and underscore the importance of acceptance corrections in correlation analyses.Overall, the study connects cluster-based descriptions of particle production to the evolving geometry and density of the created medium, informing both theory and future experiments.

Abstract

We present results on two-particle angular correlations in Cu+Cu and Au+Au collisions at a center of mass energy per nucleon pair of 200 GeV over a broad range of pseudorapidity ($η$) and azimuthal angle ($φ$) as a function of collision centrality. The PHOBOS detector at RHIC has a uniquely-large angular coverage for inclusive charged particles, which allows for the study of correlations on both long- and short-range scales. A complex two-dimensional correlation structure in $Δη$ and $Δφ$ emerges, which is interpreted in the context of a cluster model. The effective cluster size and decay width are extracted from the two-particle pseudorapidity correlation functions. The effective cluster size found in semi-central Cu+Cu and Au+Au collisions is comparable to that found in proton-proton collisions but a non-trivial decrease of the size with increasing centrality is observed. Moreover, a comparison between results from Cu+Cu and Au+Au collisions shows an interesting scaling of the effective cluster size with the measured fraction of total cross section (which is related to the ratio of the impact parameter to the nuclear radius, $b/2R$), suggesting a geometric origin. Further analysis for pairs from restricted azimuthal regions shows that the effective cluster size at $Δφ\sim 180^{\circ}$ drops more rapidly toward central collisions than the size at $Δφ\sim 0^{\circ}$. The effect of limited $η$ acceptance on the cluster parameters is also addressed, and a correction is applied to present cluster parameters for full $η$ coverage, leading to much larger effective cluster sizes and widths than previously noted in the literature. These results should provide insight into the hot and dense medium created in heavy ion collisions.

Figures (8)

• Figure 1: (a) $dE/dx$ distribution for hits registered in the Octagon in the 0 $<\eta<$ 0.3 range (open circles) fitted by a sum (solid line) of predicted $dE/dx$ distributions for various number of particles hitting a single pad (dashed lines) for the most central 3% of 200 GeV Au+Au collisions. A MIP is defined as the energy deposited by a single minimum-ionizing particle at normal incidence. (b) Estimated average number of particles per silicon pad as a function of $\eta$ and $dE/dx$ for the most central 3% of 200 GeV Au+Au collisions.
• Figure 2: Two-particle angular correlation functions in $\Delta \eta$ and $\Delta \phi$ for (a) p+p, the most central 10% (b) Cu+Cu and (c) Au+Au collisions at $\sqrt{s}$ or $\sqrt{s_{_{NN}}}$ = 200 GeV.
• Figure 3: Two-particle pseudorapidity correlation functions, averaged over the $\Delta \phi$ range from $0^{\circ}$ to $180^{\circ}$, in Cu+Cu (upper row) and Au+Au (lower row) collisions for five different centrality classes at $\sqrt{s_{_{NN}}}$ = 200 GeV. The solid curves (black) correspond to Eq.~\ref{['2pcorr_clusterfitting_incl']} with the final values of the parameters (see text for discussion). The error bars and bands (grey) correspond to point-to-point systematic errors and overall scale errors respectively with 90% C.L. The statistical errors are negligible.
• Figure 4: (a) $K_{\rm eff}$ and (b) $\delta$ as a function of fractional cross section (1-$\sigma$/$\sigma_{0}$=1 for the most central collisions) for PHOBOS data (open symbols) and from the AMPT model (lines) in Cu+Cu (squares) and Au+Au (circles) collisions for $|\eta|<$ 3 at $\sqrt{s_{_{NN}}}$ = 200 GeV. The error bars for data points represent systematic errors with 90% C.L. Results from p+p collisions at $\sqrt{s}$ = 200 GeV~phobos_pp are shown by the shaded band.
• Figure 5: Near-side (left column) and away-side (right column) $K_{\rm eff}$ (upper row) and $\delta$ (lower row) as a function of fractional cross section (1-$\sigma$/$\sigma_{0}$=1 for the most central collisions) for PHOBOS data (open symbols) and from the AMPT model (lines) in Cu+Cu (squares) and Au+Au (circles) collisions for $|\eta|<$ 3 at $\sqrt{s_{_{NN}}}$ = 200 GeV. The error bars for data points represent systematic errors with 90% C.L. Results from p+p collisions at $\sqrt{s}$ = 200 GeV~phobos_pp are shown by the shaded band.