Two- and Multi-particle Azimuthal Correlations in Small Collision Systems with the ATLAS Detector

Abstract The recent ATLAS results on two- and multi-particle azimuthal correlations of charged particles are presented for s = 5.02  TeV and 13 TeV pp, s NN = 5.02  TeV  p + Pb and s NN = 2.76  TeV low-multiplicity Pb + Pb collisions. To suppress the “non-flow” contribution from the correlations, a template fitting procedure is used in the two-particle correlations (2PC) measurements, while for multi-particle correlations the cumulant method is applied. The correlations are expressed in the form of Fourier harmonics v n ( n = 2 , 3 , 4 ) measuring the global azimuthal anisotropy of produced particles. The measurements presented hereafter confirm the evidence for collective phenomena in high-multiplicity p + Pb and low-multiplicity Pb + Pb collisions. For pp collisions the results on four-particle cumulants do not demonstrate a similar collective behaviour.


Introduction
The large azimuthal anisotropy observed in particles produced in heavy ion collisions at RHIC and LHC, is one of the main signatures of the formation of strongly interacting Quark-Gluon Plasma. Interestingly, significant long range azimuthal correlations were also observed at the LHC for the first time in pp and p+Pb collisions. This observation leads to puzzling questions related to the origin of this phenomenon as well as indicates a possible presence of the Quark-Gluon Plasma in light nuclei collisions. Since the first measurements, the collective phenomena in small systems are under extensive theoretical and experimental study. In this report, the recent ATLAS [1] results on Fourier coefficients v n , based on a novel template fitting 2-Particle Correlation (PC) method, are shown for pp collisions at √ s = 5.02 TeV and 13 TeV and p+Pb collisions at √ s NN = 5.02 TeV [2]. For the same systems and additionally for low-multiplicity √ s NN = 2.76 TeV Pb+Pb collisions measurements of multi-particle cumulants and corresponding flow harmonics are also presented [3].

The 2PC method
The azimuthal anisotropy in small systems is studied using the two-particle correlation function [4], which is also commonly applied to probe collective phenomena in heavy ion collisions [5]. Recently, a two-particle correlation analysis was performed in ATLAS [2,6] for pp collisions at √ s = 2.76 TeV, 5.02 TeV and 13 TeV and for p+Pb collisions at √ s NN = 5.02 TeV. The correlation function for low-multiplicity pp or p+Pb collisions, measured in the relative pseudorapidity (∆η) and azimuthal angle (∆φ) of correlated particle pairs, is dominated by non-flow effects including particle pairs from the same jet, Bose-Einstein correlations, resonance decays or momentum conservation. The non-flow correlations are suppressed by requiring |∆η| > 2. The two-particle correlation function shows a sharp peak centred at (∆φ,∆η) = (0, 0) and a broad structure (in ∆η) at ∆φ ≈ π. In high-multiplicity collisions, an additional long-range structure (in ∆η) at ∆φ ≈ 0, called "near-side ridge", is clearly seen. Also the correlation function at ∆φ ≈ π is broadened relative to the low-multiplicity collisions, revealing a presence of the "away-side ridge". The strength of the long-range component is commonly quantified by the "per-trigger yield", Y(∆φ), which measures the average number of particle pairs associated with a trigger particle. The per-trigger yield is fitted by a template function consisting of two components: a scaled per-trigger yield for low multiplicity interactions,Y periph (∆φ), and an azimuthal modulation term describing the "ridge". In this approach no "ZYAM" subtraction procedure is performed on Y(∆φ) or Y periph (∆φ) [2]. The azimuthal modulation parameters v n,n obtained from the fitting procedure were found to factorize into a product of single particle flow harmonics v n v n , hence v n = √ v n,n . Figure 1 (the left column) shows measurements of v 2 , v 3 and v 4 harmonics in 5 and 13 TeV pp, and 5 TeV p+Pb collisions as a function of the event multiplicity, N rec ch .  One can see that all three v n harmonics in 5.02 and 13 TeV pp data are N rec ch -independent, while the p+Pb v 2 , v 3 and v 4 increase with increasing N rec ch . The p T -dependence of v n in 5.02 and 13 TeV pp, and 5.02 TeV p+Pb collisions for N rec ch ≥ 60 is also shown in Fig. 1 (the right column). Similar v 2 harmonics are observed in pp collisions at both collision energies. As a function of p T , v 2 harmonics rise reaching a maximum near 3 GeV and then they drop, reaching almost 0 at p T ≈ 7 GeV. In p+Pb collisions a more rapid increase of v 2 is measured, but generally a similar trend is observed in both systems. The v 3 harmonic in 13 TeV pp increases with p T over the measured p T range. For p+Pb collisions, larger v 3 values are observed than in pp for p T < 3 GeV. At higher p T , v 3 in p+Pb data saturates. The v 4 in 13 TeV pp and 5.02 TeV p+Pb collisions increases with p T and larger v 4 values are measured in p+Pb collisions than in pp data.

Multi-particle cumulants
The multi-particle cumulant method of measuring flow harmonics [7,8] is a commonly used approach, which efficiently suppresses the non-flow correlations. In the first step of the cumulant method, the 2kparticle azimuthal correlations, corr n {2k}, are calculated. Then, the multi-particle cumulants c n {2k} are obtained by subtracting from corr n {2k} all correlations between fewer number of particles, which include most of non-flow correlations. The cumulant method was used for Pb+Pb [9] and p+Pb collisions [10] and recently, for pp collisions [11]. In this report, the ATLAS measurements of multi-particle cumulants are presented for pp collisions at √ s = 5.02 TeV and 13 TeV, for √ s NN = 5.02 TeV p+Pb and for lowmultiplicity Pb+Pb collisions at √ s NN = 2.76 TeV [3].   A comparison of the v 2 harmonic obtained with different cumulants, v 2 {2, |∆η| > 2} calculated with the requirement of pseudorapidity separation |∆η| > 2, v 2 {4}, v 2 {6} and v 2 {8}, is shown in Fig. 3 for p+Pb and low-multiplicity Pb+Pb collisions. All derived v 2 harmonics have larger magnitudes in Pb+Pb collisions than in p+Pb collisions with the same multiplicity. For both systems, v 2 {2k} are similar for k = 2, 3 and 4 while v 2 {2, |∆η| > 2} is systematically larger than the second order Fourier component calculated with more than two-particle cumulants due to fluctuations in the initial-state geometry.
The third and fourth order flow harmonics, v 3 and v 4 , calculated with two-particle cumulants with the |∆η| > 2 requirement for reference particles with 0.3 < p T < 3.0 GeV are shown in Fig. 4. For p+Pb and Pb+Pb collisions the v 3 {2, |∆η| > 2} values are similar, and much larger as compared to the 13 TeV pp data. The v 3 increases with increasing multiplicity. A weaker increase is observed for v 4 {2, |∆η| > 2}, but systematically larger values for Pb+Pb collisions are measured at high multiplicities as compared to p+Pb measurements. For multiplicities below 100, where the v 4 {2, |∆η| > 2} is also available for pp collisions, there is no visible system-dependence.

Summary
A two-particle correlation function method was used to obtain single-particle v n harmonics (n=2, 3,4) in pp collisions at multiplicity and transverse momentum. The measurement shows that v 2 in pp collisions weakly depends on multiplicity and collision energy. The p+Pb v 2 values are larger than the pp v 2 for all multiplicities and are observed to increase with N rec ch . As a function of p T , the p+Pb v 2 is larger than v 2 in pp collisions but similar p T dependence is observed, which also resembles the trend seen in Pb+Pb collisions.
Multi-particle cumulants were measured for the same pp and p+Pb collision systems as well as in low-multiplicity Pb+Pb collisions at √ s NN = 2.76 TeV. The collective nature of multi-particle correlations is well confirmed for p+Pb and Pb+Pb collisions for charged-particle multiplicities above 100. For pp collisions, the four-particle cumulants are positive or consistent with zero over the full range of particle multiplicities. Therefore, these measurements in pp collisions, do not satisfy the requirement of being negative, indicating that c 2 {4} cumulants may still be biased by residual non-flow correlations. It should be noted that, to estimate and limit the effect of non-flow correlations, ATLAS has recently proposed a novel sub-event cumulant method [12], in which particles from different sub-events separated in pseudorapidity are used for cumulant calculations. The measured v 2 harmonics from multi-particle cumulants have larger values for Pb+Pb collisions as compared to p+Pb collisions and for each system v 2 {2k} are similar for k = 2, 3 and 4, while v 2 {2, |∆η| > 2} is systematically larger than the second order Fourier component calculated with more than two-particle cumulants. This observation is consistent with models assuming fluctuation-driven initial-state anisotropies.