Anomalous centrality evolution of two-particle angular correlations from Au-Au collisions at $\sqrt{s_{\mathit{NN}}}=62$ and 200 GeV

We present two-dimensional (2D) two-particle angular correlations measured with the STAR detector on relative pseudorapidity $\eta$ and azimuth $\varphi$ for charged particles from Au-Au collisions at $\sqrt{s_{\mathit{NN}}}=62$ and 200 GeV with transverse momentum $p_t\ge 0.15$ GeV/$c$, $\left|\eta \right|\le 1$, and $2\pi$ in azimuth. Observed correlations include a same-side (relative azimuth $<$$\pi /2$) 2D peak, a closely related away-side azimuth dipole, and an azimuth quadrupole conventionally associated with elliptic flow. The same-side 2D peak and away-side dipole are explained by semihard parton scattering and fragmentation (minijets) in proton-proton and peripheral nucleus-nucleus collisions. Those structures follow $N$-$N$ binary-collision scaling in Au-Au collisions until midcentrality, where a transition to a qualitatively different centrality trend occurs within one $10\%$ centrality bin. Above the transition point the number of same-side and away-side correlated pairs increases rapidly relative to binary-collision scaling, the $\eta$ width of the same-side 2D peak also increases rapidly ($\eta$ elongation), and the $\varphi$ width actually decreases significantly. Those centrality trends are in marked contrast with conventional expectations for jet quenching in a dense medium. The observed centrality trends are compared to perturbative QCD predictions computed in hijing, which serve as a theoretical baseline, and to the expected trends for semihard parton scattering and fragmentation in a thermalized opaque medium predicted by theoretical calculations and phenomenological models. We are unable to reconcile a semihard parton scattering and fragmentation origin for the observed correlation structure and centrality trends with heavy-ion collision scenarios that invoke rapid parton thermalization. If the collision system turns out to be effectively opaque to few-GeV partons the present observations would be inconsistent with the minijet picture discussed here.

Figure 1

Perspective views of 2D charge-independent angular correlations $\Delta \rho /\sqrt{{\rho }_{\mathrm{ref}}}$ on $({\eta }_{\Delta },{\varphi }_{\Delta })$ for Au-Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ and 62 GeV (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84\%$–$93\%$, $55\%$–$64\%$, $18\%$–$28\%$, and $0\%$–$5\%$ for the 200-GeV data and $84\%$–$95\%$, $56\%$–$65\%$, $18\%$–$28\%$, and $0\%$–$5\%$ for the 62 GeV data (see Tables 3 and 4).

Figure 2

Fit decomposition of the $46\%$–$56\%$ centrality data for 62-GeV Au-Au collisions. The top panels show from left to right the corrected data, model fit, fit residuals (data $-$ model), and same-side 2D Gaussian. The bottom panels similarly show the away-side azimuth dipole, the nonjet azimuth quadrupole, the 1D ${\eta }_{\Delta }$ Gaussian, and the 2D exponential. This centrality is just below the sharp transition at ${\nu }_{\text{trans}}=3$. Fit residuals (c) are scaled up eightfold relative to the data.

Figure 3

Fit parameters for $({\eta }_{\Delta },{\varphi }_{\Delta })$ correlation data from Au-Au collisions at $\sqrt{s_{\mathit{NN}}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy (200 GeV). The SS 2D Gaussian amplitudes, ${\eta }_{\Delta }$ widths, and ${\varphi }_{\Delta }$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio ${\sigma }_{{\eta }_{\Delta }}/{\sigma }_{{\varphi }_{\Delta }}$. Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62- and 200-GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $\nu$ equivalents for $N$-$N$ collisions and $b=0$ Au-Au collisions.

Figure 4

(a) 2D data histogram from $0\%$–$5\%$ central 200 GeV Au-Au collisions [$(0,0)$ bin suppressed]. (b) Additional model component fitted to the 2D histogram and consisting of an AS azimuth dipole modulated by function $F\left({\eta }_{\Delta }\right)$ described in the text. (c) Fit residuals including the new model component. (d) Data histogram in the first panel minus the additional model component and fitted offset. Remaining structure is described accurately by an AS dipole and SS 2D Gaussian.

Figure 5

Fit parameters for $({\eta }_{\Delta },{\varphi }_{\Delta })$ correlation data from Au-Au collisions at $\sqrt{s_{\mathit{NN}}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ illustrating a sharp transition in centrality trends at ${\nu }_{\text{trans}}\approx 3$. The dashed curves labeled GLS are calculated predictions corresponding to linear superposition of $N$-$N$ collisions (binary collision scaling). The bold solid lines illustrate slope changes by factors of 3.5 in panels (a) and (b) and 5 in panel (c) within one centrality bin on $\nu$. The dotted line in panel (b) simply continues the slope trend from below the transition. Panel (a) shows that 62- and 200-GeV SS 2D peak amplitudes $A_1$ are related by a $\log \left(\sqrt{s_{\mathit{NN}}}\right)$ factor $\approx$$0.6$ [72], whereas panel (c) demonstrates that the AS 1D peak amplitude $A_D$ is approximately independent of collision energy.

Figure 6

Same-side 2D peak width trends for $({\eta }_{\Delta },{\varphi }_{\Delta })$ correlation data from Au-Au collisions at $\sqrt{s_{\mathit{NN}}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy (200 GeV). The SS 2D Gaussian ${\eta }_{\Delta }$ and ${\varphi }_{\Delta }$ widths are shown in panels (a) and (b), respectively. Panel (c) shows the SS peak width aspect ratio ${\sigma }_{{\eta }_{\Delta }}/{\sigma }_{{\varphi }_{\Delta }}$. The hatched regions indicate GLS trends based on p-p collision data. The bold curves are explained in the text.

Figure 7

Same-side 2D peaks from $38\%$–$46\%$ central (left panel) and $9\%$–$18\%$ central (right panel) 200-GeV Au-Au collisions. These histograms were obtained by subtracting the AS dipole ($A_D$), quadrupole ($A_Q$), and offset ($A_3$) elements of the 2D model fits from the data histograms.

Figure 8

(Left) 2D histogram from Fig. 4 (fourth panel) projected onto ${\varphi }_{\Delta }$ (light histogram). The bold histogram with near-zero amplitude is a projection of 2D residuals from Fig. 4 (third panel). The dash-dotted and dashed curves represent components of the model fit from the present analysis. (Right) The bold histogram is the 1D data histogram in the left panel minus the fitted AS dipole component (dashed curve). The dash-dotted curve is the 1D projection of the fitted 2D Gaussian from this analysis. The bold dotted curves represent multipoles $m=1,...,4$ derived from the SS 1D Gaussian (see the text).

Figure 9

(a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from p-p data (dashed curve) and from the hijing Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from p-p data (dashed curve, GLS), and from more-central Au-Au data (solid line) and hijing (dash-dotted line, open points). (c) Single-particle hard-component production per $N$-$N$ binary collision from p-p data, from more-central Au-Au data and from hijing (open points). (d) Jet-correlated pair production (SS 2D peak) per $N$-$N$ binary collision extrapolated from p-p data (GLS), and from Au-Au data (solid points) and hijing (open points).

Figure 10

(Left) The data histogram is the 2D histogram in Fig. 7 (right panel) projected onto 1D ${\eta }_{\Delta }$. The narrow peak at the center is BEC $+$ electron pairs. The dash-dotted curve through the data histogram is a single 1D Gaussian with parameters $(A,{\sigma }_{\eta })$. The dashed curve is the sum of a 1D Gaussian $(A^{\prime },{\sigma }_{\eta }^{\prime })$ plus constant offset $A_{1D}$. The two curves are barely resolved at the $\eta$ acceptance limits. The dotted line is the constant offset. (Right) The second difference of the data histogram in the left panel corresponds to its local curvature. The calculated curvature $A/{\sigma }_{\eta }^2$ of the 1D Gaussian in the left panel (dash-dotted curve) is the dash-dotted line in this panel.

Figure 11

(Left) Uncorrected angular correlations from 62-GeV $37\%$–$46\%$ central Au-Au collisions showing pileup distortions, especially evident as the W-shaped nonuniformity of the AS ridge on ${\eta }_{\Delta }$. (Right) The same data with pileup correction applied.