PHENIX results on multiparticle correlations in small systems

We present measurements of 2- and 4-particle correlations in d+Au collisions at four different center-of-mass energies: 200, 62.4, 39, and 19.6 GeV. The data were collected in 2016 by the PHENIX experiment at RHIC. The second Fourier coefficient $v_2$ of the particle azimuthal distributions is measured using the Q-cumulant method as a function of event multiplicity. The results give a strong indication of collective behavior down to the lowest energy.


Introduction
The study of collective behavior in small systems, like p+Pb at the LHC and d+Au at RHIC, is one of the major pillars of heavy-ion physics research. Measurements of collectivity in small systems are testing the limits of collectivity and the applicability of hydrodynamics. In 2016, RHIC delivered a beam energy scan of d+Au collisions at four different collisions energies: 200 GeV, 62.4 GeV, 39 GeV, 19.6 GeV. Table 1 shows the number of events analyzed for each collision energy. We used a central trigger that greatly enhanced the high multiplicity data sample. Measurements of multiparticle correlations in small systems at the LHC (see e.g. Reference [1,2,3]) are considered very strong evidence for collective behavior, as by mathematical construction they reduce contributions from few particle correlations like resonance decays, quantum correlations, Coulomb interactions, momentum conservation effects, etc, generally referred to as non-flow. In this proceedings, we present PHENIX results on multiparticle correlations in the 2016 d+Au beam energy scan. We will also present results from simulations using A Multi-Phase Transport model (AMPT) [4] to aid interpretations of the data as needed.

Analysis
The azimuthal distribution of particles produced in a heavy-ion collision can be described with a Fourier expansion with coefficients v n [5]. In this analysis we focus on the second harmonic coefficient v 2 . To study multiparticle correlations, we use the Q-cumulant method [6]. To briefly summarize the salient features, the 2-particle cumulant can be described as c 2 {2} = v 2 2 and the 4-particle cumulant can be described as  [7], where σ 2 is the variance of the v 2 distribution. We also expect fewer particle correlations to be more subject to non-flow, so that [7], where δ 2 parameterizes the non-flow contribution. In this way, the study of correlations with different numbers of particles can potentially elucidate the relationship between v 2 , the fluctuations, and the non-flow effects.
We use the PHENIX forward vertex (FVTX) detector for this analysis. The FVTX has a nominal pseudorapidity coverage of 1 < |η| < 3. Reconstructed tracks are required to have hits and at least 3 of the 4 layers and to have a distance of closest approach to the vertex of |DCA| < 2 cm. Events with a collision vertex of |z vertex | < 10 cm are selected. We plot all quantities as a function of the number of reconstructed tracks, N FVTX tracks .  We observe real valued v 2 {4} at all four energies (albeit with 79% confidence interval for the 19.6 GeV). Additionally, we observe that although v 2 {2} > v 2 {4} for all energies, the difference decreases as the collision energy decreases. This result may be regarded as surprising, because naively it would appear to indicate that the variance of the distribution is decreasing significantly with decreasing collision energy (we note that there are other possibilities, beyond the scope of these proceedings).

Results
Because AMPT has had significant success in describing collective observables in both large and small systems, we can check if AMPT shows a similar trend. Figure 2 shows trend. The AMPT simulations are scaled by a factor of 1.18 to account for the p T dependence of the FVTX efficiency. To try to assess how the interplay of fluctuations and non-flow effects influence the relationship between v 2 {2} and v 2 {4}, we can also look at 2-particle v 2 with a pseudorapidity gap to reduce the non-flow. Figure 1 also shows v 2 {2, |∆η| > 2}, where |∆η| > 2 indicates that the minimum pseudorapidity separation (gap) is 2 units. To achieve this pseudorapidity gap, we require one particle to be in the south (backward pseudorapidity) arm of the FVTX and the other to be in the north (forward pseudorapidity) arm. We find that v 2 {2, |∆η| > 2} < v 2 {4} for all four energies, with the difference increasing as the collision energy decreases. This can be understood as arising from the fact that v 2 {2} and v 2 {4} are weighted averages of the backward pseudorapidity v B 2 and the forward pseudorapidity v F 2 whereas the v 2 {2, |∆η| > 2} gives equal weight to each, In asymmetric collisions, dN ch /dη [8] and v 2 [9] are larger at backward pseudorapidity. As an illustrative example, Figure 3 shows AMPT simulations of dN ch /dη (left panel) and v 2 (right panel) as a function of η. Based on this alone, we can plausible expect v 2 {2, |∆η| > 2} < v 2 {4}. However, it is likely that longitudinal decorrelations [10] play a role in further reducing v 2 {2, |∆η| > 2}, where we have ), where ψ B 2 and ψ F 2 indicate the 2 nd harmonic event planes at backward and forward pseudorapidity, respectively. To corroborate the interpretation of real valued v 2 {4} as indicative of collective behavior, Figure 4 shows the individual components 2 2 2 and 4 (upper panels) and the cumulant c 2 {4} = 4 − 2 2 2 (lower panels) in the data (left plot), AMPT (middle plot), and AMPT with no scattering (right plot). When turning off the scattering, the transport from initial geometry to final state interactions doesn't take place, so that only non-flow effects remain. Comparing the middle plot and the right plot, the case with scattering shows a negative c 2 {4}, meaning real-valued v 2 {4}, whereas the case without scattering shows a c 2 {4} that's near zero but positive, indicating complex-valued v 2 {4}.

Summary
In summary, we have presented measurements of multiparticle correlations in d+Au collisions at 200, 62.4, 39, and 19.6 GeV. We find real-valued v 2 {4} for all energies, providing strong evidence of collective behavior in small systems at RHIC energies down to the lowest energies.