Recent ATLAS results on flow measurements in lead-lead and proton-lead collisions

Recent measurements from the ATLAS experiment of the azimuthal anisotropy of charged hadron production in the relativistic p+Pb and Pb+Pb collisions at the Large Hadron Collider (LHC) are presented. We report on distributions of event-by-event flow harmonics vn, n = 2 − 4, for Pb+Pb collisions at energy of =2.76 TeV which provide a direct measure of flow harmonic fluctuations which may be related to fluctuations in the initial geometry of the interaction region. The relative event-by-event elliptic flow fluctuations are compared to the measurement based on the cumulant approach as well as to the model predictions. We also report on measurements of the two-particle correlations in Δϕ and Δη as a function of pT and the transverse energy (ΣEPbT) summed over 3.1 < η < 4.9 in the direction of the Pb beam in = 5.02 TeV p+Pb collisions. The recoil-corrected Δϕ-correlation exhibits flow-like modulations for all ΣEPbT ranges and particle pT. To study further the long-range correlations in p+Pb collisions, the elliptic flow has been measured with the cumulant approach and compared to the results from two-particle correlations. The presented p+Pb results exhibit features characteristic for collective anisotropic flow, similar to that observed in Pb+Pb collisions.


Introduction
The azimuthal anisotropy of hadron production is a key observable for understanding the properties of the hot and dense medium created in Pb+Pb collisions at the LHC. It is expected that this anisotropy is sensitive to conditions at the very early stage of evolution of the strongly coupled Quark-Gluon Plasma (sQGP) and is related to the spatial configuration of colliding nucleons as well as the energy density fluctuations in the initial overlap region of the two colliding nuclei [1]. The initial spatial asymmetry leads to asymmetric pressure gradients in the QGP, generating a significant azimuthal anisotropy in particle dN/dφ distributions which is usually described by means of a Fourier series with n th order flow harmonic, v n = cos n(φ − Φ n ) where φ is the particle azimuthal angle and Φ n represents the symmetry plane angle. The second order harmonic, called elliptic flow (v 2 ) characterizes the "elliptical" shape of the initial interaction region, while higher-order flow harmonics (v 3 , v 4 ,...) characterize more complicated configurations.
In ATLAS [2], flow phenomena are explored with charged particles reconstructed in each event within the inner detector consisting of a silicon pixel detector and a semiconductor microstrip tracker (SCT), immersed in a 2 T axial magnetic field and covering a wide pseudorapidity range (|η| <2.5). The transverse momenta of reconstructed particles are limited by a minimum p T of 0.5 GeV and 0.3 GeV in case of Pb+Pb and p+Pb collisions, respectively. For measurements, Figure 1. The event-by-event v n distributions in selected centrality bins for n = 2 (left panel), n = 3 (middle panel) and n = 4 (right panel) [5]. The solid curves represent radial projections of 2D Gaussian functions with the mean rescaled to the measured v n .
presented in this report, a minimum bias sample of ∼50M Pb+Pb collisions at an energy of √ s N N =2.76 TeV as well as ∼2M p+Pb collisions at an energy of √ s N N =5.02 TeV are used.

Event-by-event flow harmonic distributions
A detailed analysis of flow harmonics averaged over large Pb+Pb event samples has been recently performed in the ATLAS experiment [3,4]. Significant values of the higher order harmonics, v 3 − v 6 , imply presence of large event-by-event flow vector fluctuations. Benefiting from the large acceptance of the ATLAS detector for measurement of charged particles, the distribution of v 2 − v 4 measured event-by-event were also recently obtained [5]. In this analysis, the azimuthal distribution of charged particles in each event is expanded into a Fourier series with coefficients corresponding to the single event flow vector components. However, due to finite event multiplicity, indicated by M , the absolute value of the flow vector (corresponding to the true v n only in the limit M → ∞) is smeared randomly around the true v n . To correct for this smearing, the Bayesian unfolding procedure was applied [5]. The unfolded distributions represent the distributions of single event true flow harmonics and provide a direct measure of flow harmonic fluctuations. The unfolded distributions of v 2 , v 3 and v 4 , normalized to unity, are shown in Fig. 1 together with solid lines representing the radial projections of two-dimensional (2D) Gaussian functions with the mean adjusted to v n from the data. Figure 1 shows that the distributions of higher order harmonics, v 3 and v 4 , are consistent with the 2D Gaussian limit within the full measured centrality range. For the elliptic flow (n=2) the relative fluctuations, Fig. 2 as a function of centrality for three p T ranges: p T > 0.5 GeV, 0.5< p T <1 GeV and p T >1 GeV. It is observed that elliptic flow fluctuations strongly depend on centrality with the smallest fluctuations found in mid-central collisions (N part ≈ 200). The largest v 2 fluctuations are observed in the 2% most central collisions which are also consistent with the purely 2D Gaussian fluctuations. The relative fluctuations are nearly the same for p T > 1 GeV and 0.5 < p T < 1 GeV. The magnitude of event-by-event fluctuations of flow harmonics can also be estimated using the two-and four-particle cumulant method [8]. Assuming that non-flow effects and σ vn are small as compared to v n , then  for 0.5 < p T 2 GeV, extracted for mid-central collisions (20-30%) are at ∼0.35, which is similar to that measured with event-by-event method for a corresponding centrality of N part ≈200, shown in Fig. 2.

Azimuthal anisotropy in p+Pb collisions
An important tool to probe the collective phenomena in heavy ion collisions is the two-particle correlation function measured as a function of relative pseudorapidity (∆η) and azimuthal angle (∆φ) of particle pairs. Recently, a two-particle correlation (2PC) function was obtained in ATLAS [10] for p+Pb collisions in different centrality intervals measured by the transverse energy ΣE P b T . The 2D correlation functions for charged particles in peripheral and central collisions are shown in Fig. 4. For peripheral collisions the correlation function shows a sharp peak centered at (∆φ,∆η) = (0, 0) and a broad (in ∆η) structure at ∆φ ≈ π (called recoil) both predominantly originating from non-flow effects. In central collisions, in addition to the components observed in peripheral collisions, the correlation function reveals a broad (in ∆η) structure at ∆φ ≈ 0 (the "near-side ridge"). The distribution at ∆φ ≈ π is also broadened relative to peripheral collisions, consistent with the presence of a long-range component (the "away-side ridge").
The strength of the long-range component is commonly quantified by the "per-trigger yield", Y(∆φ), which measures the yield of particle pairs per the yield of trigger particles (1/N trig dN pair /d∆φ) [11]. Figure 5 shows the Y(∆φ) distributions for 2 < |∆η| < 5 in peripheral and central collisions as well as their difference (∆Y , solid points) which is symmetric around ∆φ = π/2 and consistent with flow-like modulations. The second order amplitude of these modulations, v 2 {2P C}, depicted in Fig. 6 as a function of p T is reminiscent of what is   Figure 6. Comparison of the p T dependence of the v 2 coefficient measured in p+Pb collisions with the four-particle cumulants v 2 {4} [12], and with the two-particle correlation method v 2 {2P C} [10] to v 2 obtained with the eventplane method for central and peripheral Pb+Pb collisions [3]. understood to be hydrodynamic flow in Pb+Pb collisions. To further study the collective flow in p+Pb collisions, the elliptic flow harmonics were obtained from cumulant method, v 2 {4} [12]. Figure 6 shows p T dependence of v 2 {4} which is consistent with v 2 {2P C} and, interestingly, with a magnitude between the values of v 2 obtained with the event-plane method [3] in the most central and most peripheral centrality intervals measured for Pb+Pb collisions.
In summary, ATLAS has presented event-by-event v 2 , v 3 and v 4 distributions in a wide centrality range of Pb+Pb collisions at the LHC energy of √ s N N = 2.76 TeV, which provide a direct insight into fluctuations in the initial geometry of the interaction region. The relative fluctuations of v 2 in the most central Pb+Pb collisions, and v 3 and v 4 within the full, measured centrality range are consistent with radially-projected 2D Gaussian distributions. In mid-central collisions, the relative fluctuations of v 2 are significantly smaller than the Gaussian limit. In √ s N N = 5.02 TeV p+Pb collisions, the two-particle correlation function clearly shows ridge structures resembling those observed in Pb+Pb collisions and suggesting that collective flow may also be present in p+Pb collisions. The flow interpretation of the p+Pb data is also supported by results from multi-particle azimuthal correlation measurements. This work was supported by National Science Centre grant number 2011/01/N/ST2/ 04042.