Anisotropic flow in Xe-Xe collisions at $\mathbf{\sqrt{s_{\rm{NN}}} = 5.44}$ TeV

The first measurements of anisotropic flow coefficients $v_{\rm{n}}$ for mid-rapidity charged particles in Xe-Xe collisions at $\sqrt{s_{\rm{NN}}} = 5.44$ TeV are presented. Comparing these measurements to those from Pb-Pb collisions at $\sqrt{s_{\rm{NN}}} = 5.02$ 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 where ϕ is the azimuthal angle of the produced particle, n is the flow harmonic, and Ψ 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 , 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 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][11][12][13][14][15][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 cancelling 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, 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 degree-of-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 A-A 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 Ψ 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 non-flow, 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 v n {2, |∆η| > 2}) are measured using 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 When constructing Eq. 3 from charged particles to determine v n {m}, particle-wise weights are placed to account for non-uniformities 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 PV 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  [41]. To quantify these differences, in the bottom panel of Fig. 1, is shown, 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 eccentrici- ties. 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 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%). Figure 2 shows comparisons of two-particle p T -integrated v n {2} coefficients from Xe-Xe and Pb-Pb collisions as a function of centrality. The differences between the two systems are typically within 10% except for v 2 {2} in central 0-5% collisions where the Xe-Xe values are ∼ 35% higher. For the V-USPHYDRO and EKRT models [20,21] shown, both sets of the used initial condition models demon-   ities above 15%. Regarding v 3 {2}, it is generally larger in Xe-Xe, which reflects the fact that the initial conditions from both models show ε 3 {2}(Xe-Xe) > ε 3 {2}(Pb-Pb) at a given centrality for the entire centrality range presented. The hydrodynamic predictions for v 3 {2} are similar for the two models, with maximum deviations of ∼ 5 % from the data. The β 3 deformation 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 [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.
Anisotropic flow in Xe-Xe collisions at √ s NN = 5.44 TeV ALICE Collaboration  Figure 4 shows comparisons of two-particle p T -differential v 2 {2, |∆η| > 2} coefficients from Xe-Xe and Pb-Pb collisions in 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 semi-central bins, it appears the differences observed in Fig. 2 are larger in the mid-p T region, and this will be investigated more quantitively. Figure 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. Figure 6 shows the p T -integrated v n {2}/ε n {2} ratios as a function of 1/S dN ch /dη in Xe-Xe and Pb-Pb collisions, where S and ε n {2} are obtained using various initial state models. The v n {2}/ε n {2} ratio provides estimates of κ n as per Eq. 2. As mentioned, when comparing v n /ε n from different systems, a violation of the scaling with 1/S dN ch /dη (which increases with centrality), maybe indicative of shortcomings in the modeling of the initial state (and its fluctuations). Regarding the model parameters used for this exercise, in the transverse plane for a single event, both the eccentricities and areas are calculated in the center of mass frame respectively according to ε n = r ′n cos(nφ ′ ) 2 + r ′n sin(nφ ′ ) 2 r ′n , which is defined such that the sources that contribute to the eccentricity and area have the property x ′ = y ′ = 0, where x ′ , y ′ and ϕ ′ , r ′ are the cartesian and the polar coordinates of the source, respectively. The quantities σ x ′ and σ y ′ represent the standard deviations of the source distributions. The event averages Anisotropic flow in Xe-Xe collisions at √ s NN = 5.44 TeV ALICE Collaboration used for Fig. 6 are ε n {2} = ε n 2 + σ 2 ε n and S . The normalization of the area is chosen such that for a Gaussian distribution the average density coincides with N part /S (N part is the number of participating nucleons), and was used in a previous ALICE publication [53]. A deformation of β 2 = 0.18 ± 0.02 for the 129 Xe nucleus is used [30,54]. The value was obtained from extrapolating measurements of β 2 from nearby isotopes ( 128 Xe and 130 Xe), and theoretical calculations [47,55,56], with the uncertainty reflecting the different values obtained from each approach. The box errors in the figure represent the corresponding uncertainties on the ratio. For the MC Glauber and KLN models, the values of ε n {2} 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 Monte Carlo (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 model parameter p = 0 is used for our scaling comparisons. This 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 for v 2 {2}/ε 2 {2}. The drop is also observed in the MC Glauber nucleon model, and appears to be present for the central Xe-Xe data. Such a drop is unexpected from hydrodynamic calculations [17,23], which show a continuous increase of v 2 /ε 2 with 1/S dN ch /dη. It may point to deficiencies in the initial state modeling of the regions in Xe-Xe and Pb-Pb collisions where initial state fluctuations play the largest role in generating second order eccentricities.
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  [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 Anisotropic flow in Xe-Xe collisions at √ s NN = 5.44 TeV ALICE Collaboration 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 √ s NN = 5.44 TeV collisions from the ALICE detector at the LHC have been presented. Hydrodynamical predictions reproduce measurements of v 2 {4}/v 2 {2} ratios from Xe-Xe collisions to within ∼ 15% (Fig. 1). In semi-central collisions, it is found that the v 2 {2} coefficient is lower in Xe-Xe collisions at √ s NN = 5.44 TeV compared with Pb-Pb collisions at √ s NN = 5.02 TeV at the same centrality. The v 3 {2} coefficient is larger, consistent with expectations from hydrodynamical models that reproduce the differences for both systems within ∼ 5% (Figs. 2 and 3). The differences for v 2 {2} are predicted to be driven largely by the hydrodynamical response of the system. For central collisions, v 2 {2} is found to be larger in Xe-Xe collisions, which 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 for v 3 {2} within uncertainties (Figs. 4 and 5). The studies of the modeling of the initial state via eccentricity scaling with transverse density (Fig. 6) have demonstrated that both the MC Glauber (constituent quarks) and the T R ENTo models provide the most satisfactory descriptions. However, the drop observed for v 2 {2}/ε 2 {2} in central Xe-Xe and Pb-Pb collisions is not expected from hydrodynamic calculations. In the case of the MC Glauber implementations, the drop is more pronounced for nucleon and constituent quark (q = 3) sources, and may require some improvements in the initial state modeling for the region in Xe-Xe and Pb-Pb collisions 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 ratio 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 centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The