Measurements of Multiparticle Correlations in $d+\mathrm{Au}$ Collisions at 200, 62.4, 39, and 19.6 GeV and $p+\mathrm{Au}$ Collisions at 200 GeV and Implications for Collective Behavior

Recently, multiparticle-correlation measurements of relativistic $p/d/{}^3\mathrm{He}+\mathrm{Au}$, $p+\mathrm{Pb}$, and even $p+p$ collisions show surprising collective signatures. Here, we present beam-energy-scan measurements of two-, four-, and six-particle angular correlations in $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$, 62.4, 39, and 19.6 GeV. We also present measurements of two- and four-particle angular correlations in $p+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We find the four-particle cumulant to be real valued for $d+\mathrm{Au}$ collisions at all four energies. We also find that the four-particle cumulant in $p+\mathrm{Au}$ has the opposite sign as that in $d+\mathrm{Au}$. Further, we find that the six-particle cumulant agrees with the four-particle cumulant in $d+\mathrm{Au}$ collisions at 200 GeV, indicating that nonflow effects are subdominant. These observations provide strong evidence that the correlations originate from the initial geometric configuration, which is then translated into the momentum distribution for all particles, commonly referred to as collectivity.

Figure 1

Components $⟪4⟫$ and $2⟪2{⟫}^2$ and cumulant $c_2\{4\}=⟪4⟫–2⟪2{⟫}^2$ as a function of $N_{\text{tracks}}^{\mathrm{FVTX}}$. (a) and (b) show the components and cumulant, respectively, in $p+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. (c) and (d) show the components and cumulant, respectively, in $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. (b) and (d) also show the cumulant as measured in the AMPT model for $p+\mathrm{Au}$ and $d+\mathrm{Au}$, respectively, indicated by the green line. The shaded green band indicates the statistical uncertainty on the AMPT values.

Figure 2

$v_2\{2\}$, $v_2\{2,|\mathrm{\Delta }\eta |>2\}$, and $v_2\{4\}$ as a function of $N_{\text{tracks}}^{\mathrm{FVTX}}$ in $d+\mathrm{Au}$ collisions with $\sqrt{s_{NN}}=$ (a) 200 GeV, (b) 62.4 GeV, (c) 39 GeV, and (d) 19.6 GeV; also shown in (a) is $v_2\{6\}$ for $\sqrt{s_{NN}}=200\mathrm{GeV}$. The arrowheads on the statistical uncertainties indicate cases where the standard $1\sigma$ uncertainty on the $c_2\{4\}$ crosses zero. For 19.6 GeV, the combined confidence interval for $v_2\{4\}$ to be real is 79%.

Figure 3

$v_2\{2\}$ and $v_2\{4\}$ as a function of $\sqrt{s_{NN}}$ in $d+\mathrm{Au}$ collisions. AMPT calculations are shown for comparison. For 19.6 GeV the confidence interval for $v_2\{4\}$ to be real is 79%.

Figure 4

Eccentricity distributions for $p+\mathrm{Au}$ and $d+\mathrm{Au}$ at $\sqrt{s_{NN}}=200\mathrm{GeV}$ as determined via Monte Carlo Glauber calculations. The exact values for the mean $⟨{ϵ}_2⟩$, standard deviation $\sigma$, skewness $s$, and kurtosis $k$ are listed on the figure in the caption for each distribution.