A data-driven method was applied to measurements of Au+Au collisions at $\sqrt{s_{_{\rm NN}}} =$ 200 GeV made with the STAR detector at RHIC to isolate pseudorapidity distance $\Delta\eta$-dependent and $\Delta\eta$-independent correlations by using two- and four-particle azimuthal cumulant measurements. We identified a component of the correlation that is $\Delta\eta$-independent, which is likely dominated by anisotropic flow and flow fluctuations. It was also found to be independent of $\eta$ within the measured range of pseudorapidity $|\eta|<1$. The relative flow fluctuation was found to be $34\% \pm 2\% (stat.) \pm 3\% (sys.)$ for particles of transverse momentum $p_{T}$ less than $2$ GeV/$c$. The $\Delta\eta$-dependent part may be attributed to nonflow correlations, and is found to be $5\% \pm 2\% (sys.)$ relative to the flow of the measured second harmonic cumulant at $|\Delta\eta| > 0.7$.
The second harmonic two-particle cumulants for ($\eta_{\alpha}$, $\eta_{\beta}$ pairs for 20-30% central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
The third harmonic two-particle cumulants for ($\eta_{\alpha}$, $\eta_{\beta}$ pairs for 20-30% central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
The second harmonic four-particle cumulant for ($\eta_{\alpha}$, $\eta_{\alpha}$, $\eta_{\beta}$, $\eta_{\beta}$) quadruplets for 20-30% central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the presence of global azimuthal correlations. The Pb-Pb values are higher than the p-Pb values at similar multiplicities. In both systems, the second harmonic four-particle cumulants exhibit a transition from positive to negative values when the multiplicity increases. The negative values allow for a measurement of $v_{2}\{4\}$ to be made, which is found to be higher in Pb-Pb collisions at similar multiplicities. The second harmonic six-particle cumulants are also found to be higher in Pb-Pb collisions. In Pb-Pb collisions, we generally find $v_{2}\{4\} \simeq v_{2}\{6\}\neq 0$ which is indicative of a Bessel-Gaussian function for the $v_{2}$ distribution. For very high-multiplicity Pb-Pb collisions, we observe that the four- and six-particle cumulants become consistent with 0. Finally, third harmonic two-particle cumulants in p-Pb and Pb-Pb are measured. These are found to be similar for overlapping multiplicities, when a $|\Delta\eta| > 1.4$ gap is placed.
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