PHENIX results on collectivity in high-multiplicity p + Au, d + Au and 3He + Au collisions

We present recent PHENIX results for long-range two-particle correlation functions across a large pseudorapidity(η) gap in high-multiplicity p+Au, d+Au and 3He+Au collisions. Enhanced correlations are observed for particles with small azimuthal separation. Measurements of the second order Fourier coefficients (v2) in p/d/3He+Au collisions, and the third order Fourier coefficient (v3) in 3He+Au collision are performed using the event plane method. Scaling of v2 with the initial eccentricity (ɛ2) is performed in each system to investigate the role of the initial geometry in the development of a final-state anisotropy in the particle emission. The v2 coefficients for identified π±, K± and (anti-)proton are measured as a function of transverse kinetic energy (KET) and their magnitudes are found to scale approximately with the number of constituent quarks in the hadron.


Introduction
Collective flow is one of the defining signatures of quark-gluon plasma (QGP) formation in high-energy nucleus-nucleus (AA) collisions. It has long been considered that a large volume, in which a thermal equilibrium can be achieved, is a prerequisite for QGP formation. However, a number of recent measurements from high-multiplicity collisions in small systems at RHIC [1,2,3] and LHC [4,5,6,7] have found strong correlations between the produced particles reminiscent of those observed in the AA collisions. In AA collisions, the final-state particles anisotropies are well described by hydrodynamics models with small specific viscosity. In these models, the anisotropies are driven by the pressure gradients in the initial energy density. There are different initial state models, some of which, such as the IP-glasma model [8], involve gluon saturation. Alternatively, the system evolution can be described on a microscopic level with partonic and hadronic scatterings, such as in the AMPT model [9]. These models have different sensitivity to the initial geometry in the collisions [10]. To investigate if QGP can be formed in small system, and if the observed correlations can be attributed to collective hydrodynamic flow, the PHENIX experiment has conducted a series of geometry-controlled experiments using 0-5% central p/d/ 3 He + Au collision at √ s N N = 200 GeV. The two-particle correlations and the Fourier coefficients in the single-particle azimuthal distributions are studied as a function of transverse momentum.

Experiment Details
In the PHENIX detector [11], charged particle trajectories are reconstructed with the two central arm using the drift chambers (DC) and multi-wire proportional chambers (PC) [11], covering TOF is comprised of two arms: east arm (TOFe) and west arms (TOEw). Identification of π ± , K ± and (anti-)proton in a momentum range up to 3 GeV/c is achieved over 99% purity [12,13]. The beam-beam counters (BBC) [11] consist two arrays of 64 photomultiplier tubes (PMTs) each, covering 2π in azimuth and 3.1 < |η| < 3.9 in pseudorapidity. The Forward Silicon Vertex Detector (FVTX) consists of two identical end-cap assemblies, covering 1.0 < |η| < 3.0. The event planes are measured in the Au-going direction using the charge deposited in the south BBC (BBC-S), as well as the reconstructed clusters in the south end-cap of FVTX (FVTX-S).
The p+Au, d+Au and 3 He+Au data sets were collected in year 2015, 2008, and 2014, respectively. In p+Au and 3 He+Au collisions, high multiplicity (HM) triggers were implemented to enrich the central events. The high multiplicity trigger is based on the minimum bias trigger, but imposes additional requirement of more than 48 photomultiplier tubes firing in the BBC-S in p+Au collisions, which corresponds approximately to the 5% most central events. A similar high multiplicity trigger was used on 2014 run for 3 He+Au collisions. The HM trigger increases the recorded central event samples, in comparison to the minimum bias sample, by 40 times in p+Au and 10 times in 3 He+Au collisions.
Centrality classes are determined as a percentile of the total multiplicity measured in the BBC-S, following the procedure documented in Ref. [14]. In this analysis we select the 0-5% most central events. The initial geometry for the corresponding centrality is computed and characterized by a standard Monte Carlo (MC) Glauber model [15] with a Gaussian smearing of the nucleon distributions with σ = 0.4 fm.

Analysis method
The two-particle azimuthal correlations are measured between tracks in the PHENIX central arm at a given transverse momentum(p T ) and charge measured in the PMTs in the BBC-S, which is on Au-going side. The correlation function is constructed as a function of relative azimuthal angle ∆φ and p T using pairs from the same event S(∆φ, p T ) and normalized to the correlations in mixed events M (∆φ, p T ), where the particles in the pair come from different events, following the same procedure as in [3]: where the w pmt is taken from the total charge from the BBC-S PMTs. We measure the flow coefficient with the event plane method [16].
The event plane is determined by detectors at large pseudorapidity, and the standard re-centering and flattering procedures are applied to calibrate the event-plane distributions [16]. To determine the event plane resolution, the three sub-event method is used: Res(Ψ n,BBCs ) =< cos(n(Ψ n,BBCs − Ψ RP )) >= < cos(n(Ψ n,BBCs − Ψ n,CN T )) >< cos(n(Ψ n,BBCs − Ψ n,F V T Xs )) > < cos(n(Ψ n,CN T − Ψ n,F V T Xs )) > Here, Ψ n,CN T is the event plane angle determined by the central arm tracking detectors, Ψ n,BBCs is the event plane angle determined by the BBC-S PMTs. Ψ n,F V T Xs is the event plane angle determined by the south end-caps of the FVTX.

Correlation function in p+Au, d+Au and 3 He+Au collisions
The correlation functions C(∆φ, p T ) for 0-5% central events in p+Au, d+Au and 3 He+Au collisions in selected p T bins, , and compared to the correlation functions measured in minimum bias p+p collisions at the same center-of-mass energy. We analyze these shapes by fitting each correlation function to a four-term Fourier cosine expansion, f (∆φ) = 1+Σ 4 n=1 c n (p T ) cos(n∆φ). The fitting results are plotted in Fig. 1 for each distribution. Central 3 He+Au and d+Au collisions show a clearly visible enhancement of near-side pairs; central p+Au collisions show a flat distribution in near-side area. In both cases, a sizable second order Fourier term is needed to describe the correlations. In contrast, the p+p collisions can be described almost completely by the dipole term, as expected from back-to-back jets contribution and transverse momentum conservation.

Charged hadron v 2 comparison in three systems
To better understand the origin of the near-side peaks and the azimuthal anisotropy in particle production in small system, we compare the v 2 vs p T in the three systems for 0-5% central event, as shown in Fig. 2. The data clearly indicate that v 2 in p+Au collisions is significant, but smaller than that measured in d+Au [2] and 3 He+Au [3]. Given that from Glauber MC, the initial eccentricity ε 2 in central p+Au collisions is smaller than in d+Au and 3 He+Au collisions, it supports the hypothesis that the initial geometry plays a major role in determining these anisotropies. The data are compared to the predictions of the SONIC hydrodynamics model [17], which translates the initial state geometry to final-state momentum anisotropies. The SONIC model [17] can describe the data well in all the three systems.

Charged hadron v 2 and v 3 compared to models
Various models have predicted the anisotropy in small systems with different physics mechanism, including hydrodynamics models with [18] or without pre-flow [17], AMPT model [9], and gluon saturation [8]. In Fig. 3, we compared our results with the predictions of these models. SONIC model [17] and superSONIC [18] predict the v 2 values well in all three systems. Within the current systematics, we cannot tell one from another. AMPT model [9] can predict the three systems up to 1.5 GeV/c. IPGlasma+Hydrodynamic [8] model underpredicts the p+Au results but overpredicts the d/ 3 He+Au results. Clear v 3 signal is observed in central 3 He+Au events.
The v 3 measured in 3 He+Au provides an additional constrain.

Eccentricity scaling
The quantity v 2 /ε 2 is shown in the Fig. 4 in p/d/ 3 He+Au collisions at same energy. The quantity ε 2 of these three systems are from the standard Glauber model calculations [15]. The Glauber model predicts that the initial eccentricity in d+Au collisions is similar to that in 3 He+Au collisions but larger than in p+Au collisions. The measured v 2 follows the same order, however, the scaling of the values of v 2 with the corresponding eccentricities in these three system would not collapse to a common pattern. The larger v 2 /ε 2 in p+Au collisions may indicate that the substructure of the proton also plays a role. The second order flow coefficients for identified π ± , K ± and (anti-)proton are presented in the left panel of Fig. 5. Mass-ordering is observed in 3 He+Au collisions. The trend is consistent with hydrodynamic flow in which the heavier particles are boosted to higher p T even with same expanding velocity of the medium. The right panel of the Fig. 5 shows that the v 2 values for identified particles can be described by a universal curve when scaled by number of quarks in the hadron. Such scaling previously observed in Au+Au collisions is also seen in the small 3 He+Au system, which is consistent with viscous hydro calculations or the quark coalescence models [19,20].

Conclusions
We have presented measurements of long-range azimuthal correlations between tracks at midrapidity |η| < 0.35, and charges in BBC Au-going direction in p/d/ for mid-rapidity particles with the event plane method. The v 2 of 0-5% p+Au is sizable and found to be smaller than that of d/ 3 He+Au and indicates that the initial geometry plays an important role in describing system evolution. A sizable v 3 is seen in 3 He+Au collisions. Hydrodynamics models with initial conditions from the Glauber model describe v 2 and v 3 quite well. These values of η/s at or near the conjectured lower bound 1/4π [21] are similar to the ones needed to describe collective flow in large systems, such as Au+Au or Pb+Pb collisions. The measurements of v 2 for identified hadrons in 0-5% 3 He+Au collisions are found to scale with the number of quarks, as expected in systems where the flow develops at the partonic level.