University of Birmingham Anisotropic flow in Xe–Xe collisions at sNN=5.44 TeV

The ﬁrst measurements of anisotropic ﬂow coeﬃcients v n for mid-rapidity charged particles in Xe– Xe collisions at √ s NN = 5 . 44 TeV are presented. Comparing these measurements to those from Pb–Pb collisions at √ s NN = 5 . 02 TeV, v 2 is found to be suppressed for mid-central collisions at the same centrality, and enhanced for central collisions. The values of v 3 are generally larger in Xe–Xe than in Pb–Pb at a given centrality. These observations are consistent with expectations from hydrodynamic predictions. When both v 2 and v 3 are divided by their corresponding eccentricities for a variety of initial state models, they generally scale with transverse density when comparing Xe–Xe and Pb–Pb, with some deviations observed in central Xe–Xe and Pb–Pb collisions. These results assist in placing strong constraints on both the initial state geometry and medium response for relativistic heavy-ion collisions.


Introduction
Relativistic heavy-ion collisions are believed to create a Quark-Gluon Plasma (QGP), a state of matter consisting of deconfined color charges. The pressure gradients in the QGP medium convert spatial anisotropies in initial conditions of the collision to momentum anisotropies of produced particles via multiple interactions, a phenomenon referred to as anisotropic flow [1]. The magnitude of anisotropic flow can be characterized by the flow coefficients (v n ), which are obtained from a Fourier expansion of the angular distribution of produced particles [2] dN dϕ ∝ 1 + 2 ∞ n=1 v n cos[n(ϕ − n )], (1) where ϕ is the azimuthal angle of the produced particle, n is the flow harmonic, and n is the corresponding symmetry plane angle. For the second and third order flow coefficients (v 2 and v 3 ), various hydrodynamical calculations have demonstrated the approximate relation [3][4][5][6][7] v n ≈ κ n ε n , (2) where ε n is the corresponding eccentricity coefficient, which governs the shape of the initial state. The variable κ n encodes the response of the medium, and in particular is sensitive to the shear E-mail address: alice -publications @cern .ch. viscosity over entropy density ratio (η/s) and the lifetime of the system. When values of η/s are finite, this inhibits the development of momentum anisotropies. It has also received a broader interest, as its lower bound is different for perturbative QCD [8] and AdS/CFT [9]. Experimental data from both the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC) [10-16], have implied values of η/s close to the AdS/CFT minimum of 1/4π [9], suggesting that the QGP behaves as a near perfect fluid. However, uncertainties in the modeling of the initial state have prevented the extraction of more precise information [17][18][19].
The data set from the LHC Xe-Xe run completed in 2017 may provide an opportunity to further constrain η/s. For mid-central collisions, various initial state models predict Xe-Xe collisions at √ s NN = 5.44 TeV and Pb-Pb collisions at √ s NN = 5.02 TeV have similar values of ε 2 at a given centrality [20,21]. However, at the same centrality the Xe-Xe system size is smaller than Pb-Pb, and the impact of a finite η/s suppresses κ 2 by 1/R, where R corresponds to the transverse size of the system [21]. Therefore, ratios of Xe-Xe/Pb-Pb v 2 coefficients in the mid-centrality range could be directly sensitive to η/s, with the influence of the initial state largely canceling out. Furthermore, hydrodynamical calculations have shown that v n /ε n increases monotonically with the transverse density 1/S dN ch /dη (dN ch /dη is the charged particle density and S is the transverse area) across different collision energies and systems [17,22,23]. Both ε n and S are quantities that are obtained from an initial state model. A violation of the scaling can be the result of incorrect modeling of the density (S) or the azimuthal geometry (ε n ). That being the case, such an exercise where one compares v n /ε n as a function of 1/S dN ch /dη for both Xe-Xe and Pb-Pb collisions can further constrain the initial state. Similar investigations using RHIC data from Cu-Cu and Au-Au collisions led to important refinements in this regard, such as the relevance of initial state fluctuations [24][25][26] and realization of finite values of ε n for higher order odd values of n (n ≥ 3) [27]. On the other hand, an observed violation of this scaling using experimental data (assuming the initial state predictions are accurate) may reveal deficiencies in the aforementioned hydrodynamical modeling. Addressing how the information from Xe-Xe collisions can shed more light on both the medium response and initial state, is the central goal of this Letter.

Analysis details
The two data sets analyzed were recorded by the ALICE detector at the LHC during the Xe-Xe (2017) and Pb-Pb (2015) runs at the center of mass energies of √ s NN = 5.44 TeV and √ s NN = 5.02 TeV, respectively. A more detailed description of the ALICE detector and its performance can be found elsewhere [28][29][30]. Charged-particle tracks at mid-rapidity are reconstructed using the Time Projection Chamber (TPC) [28,31], the primary tracking detector. Information from the Inner Tracking System (ITS) [28,32] is used to improve the spatial and momentum resolution of the TPC tracks. This helps to reject the background from secondaries, which originate from weak decays, conversions, secondary hadronic interactions in the detector material, and pile-up. The two innermost layers of the ITS, the Silicon Pixel Detector (SPD), are employed for triggering and event selection. The two V0 counters [28,33], each containing 32 scintillator tiles and covering 2.8 < η < 5.1 (V0A) and −3.7 < η < −1.7 (V0C), provide information for triggering, event selection, the determination of centrality and the symmetry plane angle [34]. The trigger conditions and the event selection criteria are described elsewhere [29]. An offline event selection is applied to remove beam-induced background (i.e., beam-gas events) and pile-up events, which are rejected using information from the ITS and V0 detectors. Primary vertex information is provided by tracks reconstructed in the ITS and TPC. Only events with a reconstructed primary vertex within 10 cm from the center of the detector along the beam axis (that position is denoted by P V z ) are used in the analysis to ensure a uniform acceptance in η. The resulting event sample available for analysis consisted of ∼ 1.0M Xe-Xe events in the 0-70% centrality range, and ∼ 67M events for Pb-Pb collisions in the same centrality interval. The charged tracks at mid-rapidity used to determine the flow coefficients have the kinematic values 0.2 < p T < 10 GeV/c and |η| < 0.8. The track fit uses an SPD hit if one exists within the trajectory, if not, they are constrained to the primary vertex. Such a configuration leads to a relatively flat azimuthal acceptance. Track quality is ensured by requiring tracks to have at least 70 TPC space points out of a maximum of 159 with an average χ 2 per degreeof-freedom for the track fit lower than 2. In addition, the distances of closest approach to the primary vertex in the xy plane and z direction are required to be less than 2.4 cm and 3.2 cm, respectively. The charged particle track reconstruction efficiency is estimated from HIJING simulations [35,36] combined with a GEANT3 [37] transport model. In order to extract the flow coefficients from charged particles produced in either Xe-Xe or Pb-Pb collisions, the Scalar Product [38] and Generic Framework [39,40] methods are used, which evaluate m particle flow coefficients v n {m}. The v n {m} coefficients characterize flow fluctuations, and are sensitive to correlations not related to the common symmetry planes n ("non-flow"), such as those due to resonances and jets. The contribution from flow fluctuations was shown to decrease v n {m ≥ 4} and increase v n {2} relative to v n [41]. In the absence of flow fluctuations and nonflow, v n {m} is independent of m. Both methods feature calculations involving the Q n -vector which is defined as where M is the number of particles used to build the Q n -vector in a single event, and ϕ i is the azimuthal angle of particle i. For the Scalar Product method, the flow coefficients v n (denoted as where u n,k = exp(inϕ k ) is the unit flow vector of the particle of interest k. The brackets · · · denote an average over all events, the double brackets · · · an average over all particles in all events, and * the complex conjugate. The vector Q n is calculated from the azimuthal distribution of the energy deposition measured in the V0A. Its x and y components are given by where the sum runs over all channels j of the V0A detector ( j = 1 − 32), ϕ j is the azimuthal angle of channel j, and w j is the amplitude measured in channel j. The vectors Q A n and Q B n are determined from the azimuthal distribution of the energy deposition measured in the V0C and the azimuthal distribution of the tracks reconstructed in the ITS and TPC, respectively. The large gap in pseudo-rapidity (| η| > 2.0) between the charged particles in the TPC used to determine v n and those in the V0A greatly suppresses non-flow effects. The course ϕ segmentation of the V0 leads to a deterioration of resolution for higher order flow coefficients (n ≥ 4), and prevents their measurements.
The flow coefficients v n {m} from two-and multi-particle cumulants can also be obtained using the Generic Framework. The calculations using the Q n -vector are generally much more complex than those shown in Eq. (4), and can be found elsewhere [40]. This approach provides a capability for the necessary corrections of systematic biases from non-uniform detector acceptance and tracking inefficiencies, and it has been used in other measurements [16, 42,43]. It can also be used to suppress non-flow by placing an η-gap between various Q n -vectors. The non-flow contribution to v n {m ≥ 4} in this framework is strongly suppressed by construction without the use of an η-gap. The newly developed sub-event methods [44,45], provide additional means of sup- and v n {m ≥ 4} (including v 2 {4, 3 sub-event}) from charged tracks in the TPC acceptance only. When constructing Eq. (3) from charged particles to determine v n {m}, particle-wise weights are placed to account for nonuniformities in the ϕ acceptance and p T dependent efficiencies.
The systematic uncertainties for v n {m} have three sources: event selection, track type/selection, and the Q n -vector correction procedure. The event selection contributions were determined by varying the P V z ranges, not applying the pile-up rejection criteria, and using a different detector system (ITS) for centrality determination. The track type/selection uncertainties were determined by using tracks with TPC information only or tracks that always have an ITS hit (which changes the contributions from secondary particles), changing the track quality cuts (such as the minimum number of TPC space points), and comparing any differences between determining Q n or u n,k from positive or negative only TPC tracks (both charge signs are used to build a flow vector for the final results). Finally, the uncertainties in Q n -vector correction procedure contribution are due to uncertainties in the p T dependent efficiencies. The individual sources of systematic uncertainty are assumed uncorrelated and are added in quadrature to obtain the overall estimated systematic uncertainties. For the p T -integrated v n {m} coefficients, the total systematic uncertainties are typically 2-3%, and smaller than the marker size in the corresponding figures. The systematic uncertainties for the p T -differential coefficients can be larger, and are denoted by boxes in the relevant figures.

Results
The top panel of Fig. 1 shows two-and multi-particle p T -inte-  all those observations regarding non-flow, one can interpret differ- to be largely driven by flow fluctuations [41]. To quantify these differences, in the bottom panel of Fig. 1, which is found to decrease for central collisions. The results are compared to a hydrodynamic calculation in the same panel, which uses an η/s = 0.047 to model the medium response [21]. For these hydrodynamic calculations, the T R ENTo initial condition model [46] is used to determine the eccentricities. The justification for using p = 0 is described later in the Letter. The initial condition model implements a 129 Xe β 2 deformation (β 2 = 0.162), which is predicted for the 129 Xe nucleus [47], but has never been measured directly. It modifies the Woods-Saxon distribution as follows [48] ρ(r, θ) where ρ 0 is the density at the center of the nucleus, R 0 the nuclear radius, r is the distance away from the center, Y 20 is a Bessel function of the second kind, and a is the skin depth. According to Eq. (2), the ratio of flow coefficients v 2 {4}/v 2 {2} should be identical to the ratio of initial state eccentricities ε 2 {4}/ε 2 {2}. To test this relation, the bottom panel of Fig. 1 also shows the flow coefficient ratios and the eccentricity ratios from the same model. The difference between the two curves shows that Eq. (2) only holds approximately. The hydrodynamic calculations generally predict lower ratios compared to the data, with the largest deviations being in the semi-central region (10-50%).  for both the Xe and Pb nuclei is zero [47], with both models assuming such a value. In Fig. 3, similar comparisons are made in finer centrality bins as compared with Fig. 2 for central collisions. The transition where Xe-Xe v 2 {2} becomes larger than the Pb-Pb values occurs for a centrality of ∼15%. For 0-1% central collisions, where the overlap geometry is expected to play a minimal role for both systems, v 2 {2} is ∼60% larger for Xe-Xe collisions. In terms of the initial state, this is expected for two reasons. The first relates to the fact that the 129 Xe nucleus is deformed while the 208 Pb nucleus is not, and the second relates to the role of initial state fluctuations and the number of sources that contribute to ε n {2}. It has been previously shown that ε n {2} decreases as the number of sources increases for a spherical system [49], and if the number of sources were infinite, then ε n {2} would be zero in this centrality range.
Given that a very central Pb-Pb collision is expected to have more sources than a very central Xe-Xe collision, fluctuations would be expected to give rise to larger values of ε 2 {2} for the latter. The same line of reasoning can explain why v 3 {2} is observed to be larger in Xe-Xe compared to Pb-Pb in the same centrality interval. Fig. 4 shows comparisons of two-particle p T -differential  various centrality bins. As mentioned, the larger | η| gap measurements use both the TPC and the V0 detectors, which maximizes the number of particles used to build the Q n -vectors. The corresponding reduction in statistical uncertainties is particularly useful for the higher p T measurements. As expected, the centrality dependence of v 2 {2, | η| > 2} from Xe-Xe collisions follows that observed in Fig. 1. Compared with Pb-Pb collisions in the semicentral bins, it appears the differences observed in Fig. 2 are larger in the mid-p T region, and this will be investigated more quantitatively. Fig. 5 shows the same comparison for p T -differential v 3 {2, | η| > 2} coefficients. The Xe-Xe coefficients are typically larger than from Pb-Pb collisions at a given centrality at low p T , whereas the larger statistical uncertainties for the Xe-Xe coefficients at higher p T make it difficult to establish whether there are any differences between the two systems.
which is defined such that the sources that contribute to the ec- and S for a given V0 based centrality class were extracted using a method described in a previous publication [34]. The multiplicity of charged particles in the acceptance of the V0 detector is generated according to a negative binomial distribution, based on the number of participant nucleons and binary collisions from each initial state model. The parameters used for this approach can be found elsewhere [52,54], and were optimized to describe the multiplicity distribution from the data. Regarding the T R ENTo model, following other approaches [21,46], the multiplicity in the acceptance of the V0 detector was modeled by scaling the entropy production, again to match the multiplicity distribution from the data.
The top left panel shows an investigation of such a scaling with the MC Glauber model [57,58], which uses nucleon positions as the sources. In particular, for v 2 {2} in central Xe-Xe and Pb-Pb collisions, this model does not provide a clear scaling, and was already observed for v 2 from Au-Au and U-U collisions at RHIC using the same model [59]. The scaling using the MC KLN model (version 32) [51,60], which assumes gluon sources and uses a Color Glass Condensate approach to determine the gluon spatial distribution, is shown in the top middle panel. The MC KLN scaling appears to work well for v 3 {2}, but fails for v 2 {2} with the Xe-Xe points being above Pb-Pb for more central collisions. A sudden rise is also observed for central Pb-Pb collisions. This behavior is in contrast to the MC Glauber nucleon model, where the Xe-Xe points are below Pb-Pb for central collisions. The top right panel investigates the scaling using the T R ENTo initial state model [46]. In this model, the distribution of nuclear matter within the collision zone of A-A collisions is controlled by the p parameter, with p = 0 mimicking IP-Glasma initial conditions [61,62]. The choice of parameter was determined using Bayesian statistics from a simultaneous fit of charged hadron multiplicity distributions, mean transverse momentum measurements, and integrated flow coefficients v n in Pb-Pb collisions at √ s NN = 2.76 TeV [63]. The IP-Glasma approach uses Color Glass Condensate calculations to determine the distribution of gluons in the initial state. This model provides a better scaling compared with the previous two other models. However for central Pb-Pb collisions, a drop is observed The drop is also observed in the MC Glauber nu- The bottom panels show ratios derived from constituent quark MC Glauber calculations, which use quarks contained in nucleons as the sources which contribute to the eccentricity [50]. The parameter q refers to the number of constituent quarks per nucleon. All implementations of quark sources (3, 5, or 7) appear to give a reasonable scaling for v 2 and v 3 , however some deviations are observed in central Xe-Xe and Pb-Pb collisions. The value q = 5 was found to describe the charged particle yields better than q = 3 at LHC energies (assuming the yields should scale with the total number of quarks) [50], and there are hints of a slightly better scaling with q = 5 for v 2 {2} in central Xe-Xe collisions compared to q = 3. These model implementations again show a drop for central Pb-Pb collisions, which is least pronounced for q = 7. This suggests initial state models need a higher number of sources per nucleon in order to achieve a continuous increase of v 2 {2}/ε 2 {2} for more central Pb-Pb collisions, and a transverse density scaling when comparing Xe-Xe to Pb-Pb.
Finally, in Fig. 7, an investigation of whether the transverse density scaling holds as a function of p T is shown. Two Xe-Xe and Pb-Pb centrality bins with similar transverse densities (1/S dN ch /dη ∼ 10 fm −2 ) are selected, and the p T -differential values of  The influence of radial flow should be very similar as p T = 0.710 ± 0.004 GeV/c (Xe-Xe) and p T = 0.716 ± 0.004 GeV/c (Pb-Pb) for charged hadrons [64]. The ratio is close to 1 and shows no significant p T dependence. This indicates when such a scaling holds, it does so over the p T range presented. This may show the p T -differential medium response (κ 2 (p T )) is controlled by the transverse density and size, independent of the collision system. A comparison of the scaled p T -differential coefficients for the same 30-40% centrality bin from Xe-Xe and Pb-Pb collisions is also shown. In this case, the eccentricities are similar (the differences are within 1%), however the transverse size and density of the Xe-Xe system is smaller. The ratio appears to mildly decrease with increasing p T . Whether this is the result of viscous effects related to the transverse size of the system influencing the mid-p T region more, or a smaller radial flow in Xe-Xe, remains an open question.

Summary
The first measurements of anisotropic flow coefficients v n in Xe-Xe collisions at agrees with predictions from hydrodynamic models, but the deviations tend to be larger than ∼5% with respect to these models. The differences between two-particle p T -differential v 2 {2} coefficients from Xe-Xe compared to Pb-Pb are found to be larger at mid-p T compared to low-p T , whereas no such trend is observed where ε 2 {2} has the largest contribution from initial state fluctuations. Finally, for two Xe-Xe and Pb-Pb centrality bins with a similar transverse density and size, it is found that the double ra- is largely independent of p T (Fig. 7). This may indicate the p T -differential medium response is controlled by the transverse density and size, independent of the collision system.

Acknowledgements
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centers and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the