Insights into the initial conditions and evolution of hadronic collisions with ﬂow observables.

. Studies of anisotropic ﬂow in heavy-ion collisions are one of the critical elements in understanding the production and evolution of the Quark Gluon Plasma. These proceedings review the most recent results on anisotropic ﬂow measurements at the LHC energies. In particular, recent measurements of p T -di ﬀ erential v 2 { 4 } in Pb–Pb collisions for a plethora of light-ﬂavour particles are discussed and compared to models with and without partonic coalescence. The measurements of v 2 { 2 } and v 2 { 4 } allow for the calculation of relative ﬂow ﬂuctuations, which for the ﬁrst time are also reported for (multi)strange baryons. The study is further extended to higher moments of the underlying charged-particle v 2 PDF, where a transition from non-Gaussian to Gaussian ﬂuctuations is observed. Finally, the correlation between v 2 and mean transverse momentum (cid:31) p T (cid:30) is studied in terms of the Pearson Correlation Coe ﬃ cient. This opens new venues to study nuclear deformation in ultra-central heavy-ion collisions and could provide a tool to identify processes in the pre-QGP phase.


Introduction
Studies of anisotropies in azimuthal distributions of particles produced in heavy-ion collisions have significantly contributed to the understanding of the hot and dense quark-gluon plasma (QGP).In particular, the anisotropies of energy density in the initial state give rise to large pressure gradients, which drive the expansion of the QGP.On a macroscopic level, the evolution of the QGP is described by relativistic hydrodynamics, typically studied in terms of anisotropic flow coefficients v n , which measure the momentum anisotropy of final state particles.Experimentally the hydrodynamical prescription has been observed to be dominant at low transverse momenta (p T 3 GeV/c).
One of the outcomes of the hydrodynamical evolution of the system is the (inverse) massordering of flow coefficients v n at low p T .This has been experimentally observed as, for example, v π 2 v p 2 [1] and is due to heavier particles receiving a larger boost from the flowing medium.On the other hand, at large momenta (p T 10 GeV/c) where no mass-ordering has been observed [2] the dominant source for non-zero v n is jet quenching.The transition from hydrodynamics and jet-dominated v n occurs in the intermediate p T region, 3 p T /(GeV/c) 10, where other processes such as partonic coalescence might contribute.
A common way to measure anisotropic flow coefficients in hadronic collisions is using Q-cumulants calculated from multi-particle correlations [3].The advantage of this method is that different orders of correlations exhibit different sensitivity to the moments of underlying Shaded bands show predictions from CoLBT model [8] with (left) and without (right) coalescence.Figure from [7].
v n probability density function (PDF).As a result, from the measurement of v n with 2-and 4-particle correlations (v n {2} and v n {4}, respectively) one can calculate relative flow fluctuations as prescribed in [3].On the other hand, measurements of particle correlations also receive contributions from non-flow effects such as jet fragmentation, jet quenching, and decays of resonance hadrons.To suppress the short-range correlations, one usually introduces a minimum separation in pseudorapidity, |∆η|, between the correlated particles.Alternatively, measurements of higher-order cumulants have also been shown to be less sensitive to nonflow effects [4].

Anisotropic flow in Pb-Pb collisions at
√ s NN = 5.02 TeV Recently, the ALICE Collaboration [5,6] has reported on p T -differential measurements of v 2 for identified particles, shown in Fig. 1 [7].This is the first measurement of v 2 {4} that includes (multi) strange hyperons, although, in these proceedings, only π, K, and p are considered for brevity.At lower transverse momenta, p T 2 GeV/c v 2 {4} exhibits an inverse mass ordering, . The same holds for hyperons as reported in [7].This is expected from hydrodynamics, where heavier particles receive a larger boost in p T from the common velocity field.Around p T ≈ 2 GeV/c, we see a characteristic crossing, above which v 2 {4} is grouped between baryons and mesons.The grouping is understood in terms of coalescence, where a combination of three partons results in a larger momentum of a hadron than a combination of two partons.
The measured v 2 {4} for different particle species is also compared to predictions of CoLBT model [8].In particular, two cases are considered: one where the evolution of QGP follows hydrodynamics and fragmentation, and the other where quarks are allowed to coalesce before hadronization.At low p T we see that hydrodynamics alone underestimates the v 2 {4} for all particle species.The description of the data is significantly better once coalescence is considered.Note that even with coalescence, the model underestimates the v 2 {4} of π; this could be due to a large number of π coming from the decays of short-lived heavy resonances, where a fraction of flow builds up before the decay.
The crossing between baryons and mesons at p T ≈ 2 GeV/c is present in both models.While it comes out naturally from coalescence, in the hydro+frag model, this crossing is facilitated by a mass-dependent p T value where fragmentation starts to dominate over hydrodynamics.It therefore suggests that the observed baryon/meson crossing is not unique to quark coalescence.Nevertheless, at larger transverse momenta (p T 3 GeV/c) we find that fragmentation alone predicts a sharp decrease in v 2 {4}, a trend which is not observed in the data.On the other hand, the model including quark coalescence provides a significantly better description, although the absolute values for π and p are still underestimated.Finally, it is also worth noting that the CoLBT model does not consider jet quenching, which could further modify v 2 {4} at larger p T values.

Flow fluctuations
Measurements of v 2 {2} and v 2 {4} allow for the estimation of relative flow fluctuations For the first time these have been reported for identified particles in [7] and are shown for several centrality classes in Fig. 2. No apparent species dependence is observed in central collisions, where F(v 2 ) shows little evolution with p T .In more peripheral collisions starting from 30-40% centrality, a species dependence emerges and, in particular, F(v 2 ) of baryons and mesons show a non-monotonic evolution with minima at different p T .The baryon/meson grouping seen in v 2 is also present in F(v 2 ), but occurs at lower transverse momenta.The emerging species and p T -dependence of F(v 2 ) suggest that σ (v 2 ) is also sensitive to final state interactions.
Measuring the underlying PDF of v 2 allows us to probe the initial geometry of the collision.The higher moments of the v 2 PDF can be calculated from the measurements of v 2 using higher orders of particle correlations as prescribed in [10].The CMS Collaboration has reported on p T -integrated skewness (γ 1 ) and kurtosis (γ 2 ) of charged hadrons as a function of centrality in Pb-Pb collisions at √ s NN = 5.02 TeV [9].In addition, the contributions coming from the higher moments have been removed from the reported γ 1 and γ 2 , see Fig. 3.This contribution appears to be larger for γ 1 and generally results in steeper slopes of γ n with centrality.
The skewness of the v 2 PDF is negative in the whole centrality range and reduces in more peripheral collisions.The negative values of γ 1 originate from a larger tail of the v 2 distribution at lower values [11], and the data suggests that this effect is enhanced with increasing centrality.The kurtosis γ 2 is small up to 20% centrality and rises as collisions get more peripheral.Overall, the non-zero γ 1 and γ 2 suggest non-Gaussian fluctuations of v 2 .
To first order, v 2 is a linear response to the eccentricity 2 of the initial state.In practice, the hydrodynamical expansion of the QGP could also modify the underlying PDF.This is studied by the ALICE Collaboration, where γ 1 and γ 2 are measured as a function of p T , see Fig. 4. Interestingly, the negative (positive) values of γ 1 (γ 2 ) are only seen at p T 3 GeVc.The observed p T -dependence suggests that the v 2 PDF is modified in a nontrivial way and thus the exact linear response v n = κ n breaks down.At higher transverse momenta, γ 1 and γ 2 are consistent with zero and thus v 2 fluctuations become Gaussian.Finally, it is worth noting that the observed p Tdependence of skewness and kurtosis is observed in the same region where F(v 2 ) exhibits baryon/meson grouping, and it would therefore be interesting to measure these moments for identified particles.
3 Correlations between v 2 and p T Recently, the correlation between the mean transverse momentum p T and v 2 gained popularity as a tool to study the initial state of heavy-ion collisions.It is studied in terms of the Pearson Correlation Coefficient, ρ 2 ≡ ρ v 2  2 , p T , where p T is calculated on an event-byevent basis and in a limited kinematic region.The p T in the hydrodynamic regime is driven by the radial flow and thus is expected to increase as collisions become more central.At the same time, the elliptic component driving v 2 becomes less pronounced and in the most central collisions originates predominantly from local density fluctuations and the deformation of projectile nuclei.This can be used to study the nuclear deformation of heavy ions, as discussed in [12].
The measured ρ 2 in Pb-Pb and Xe-Xe collisions at √ s NN = 5.02 and 5.44 TeV, respectively, is reported by ALICE in [13] and shown in Fig. 5 together with comparisons to different models.The sharp drop in ρ 2 in the most central collisions is smeared out by choice of a wider centrality class, 0-5%, but the decreasing trend at low centralities is seen nevertheless.In semi-central collisions (10-60%) the correlation shows little evolution with centrality and is higher in Pb-Pb collisions compared to Xe-Xe.Comparing the ρ 2 in Pb-Pb to different models, we find that in the 0-15% centrality range the data is described by all the models considered.However, Trajectum [14], Jetscape [15], and v-USPhydro [16] predict a decreasing trend beyond 15% centrality, which clearly is not in agreement with the Pb-Pb data.On the other hand, the IP-Glasma [17] initial conditions, where gluon distributions are estimated from Color Glass Condensate (CGC) calculations, coupled to hydrodynamics code MUSIC [18,19] and UrQMD [20,21] provides a qualitatively correct description of the measurement in Pb-Pb collisions.A similar conclusion can be drawn for measurements in Xe-Xe, but here the Xe nucleus in the IP-Glasma prescription is modelled as a spherical (β 2 = 0) or as a deformed (β 2 = 0.16) nucleus.The deformation parameter β 2 = 0.16 for the Xe nucleus has been previously predicted in [22] and tested in [23] using measurements of anisotropic flow.While β 2 does not have any significant effect on ρ 2 in semi-central collisions, in the 0-5% centrality class where deformation effects are most pronounced, the IP-Glasma model with β 2 = 0.16 is preferred.On the other hand, ρ 2 can also be used to probe the fundamental processes leading to the formation of the QGP.From purely geometrical considerations, with decreasing multiplicity, the transverse size of the initial state reduces while the eccentricity grows.This drives ρ 2 towards lower values, ultimately changing the sign of the correlation.As proposed Figure from [13]. in [24], at sufficiently low multiplicity ρ 2 could probe initial momentum correlations.These can originate from novel processes leading to the pre-QGP phase, such as the Color Glass Condensate.In particular, for a fixed multiplicity, events with larger p T typically have smaller transverse sizes.In the CGC picture, this reduces the number of color domains, which in turn enhances the initial momentum anisotropy [25] and results in positive values of ρ 2 .The initial momentum correlations are weak and could only dominate over geometry at very low multiplicities.This would result in ρ 2 being positive at the lowest multiplicity, decreasing steeply as collisions become more central (competition between initial momentum-and geometry-dominated ρ 2 ), then changing the slope from negative to positive and following geometry-only driven ρ 2 .By now, multiple collaborations have reported on measurements of ρ 2 .The measurement by ALICE is shown in Fig. 6, where both Pb-Pb and pp collisions at 130, suggesting that the change of slope is not unique to CGC initial conditions.In both data and the models considered, the rise of ρ 2 at the lowest multiplicities could result from non-flow, but this requires further studies.

ALI-PREL-491854
Finally, the ATLAS Collaboration reported on sensitivity to the kinematic region where ρ 2 is measured1 [26].As shown in Fig. 7, lower p T results in systematically smaller values of ρ 2 , which is most pronounced in semi-central collisions.Reducing the η acceptance from 5 to 2 units of pseudorapidity modifies ρ 2 in a non-trivial way.Most notably, the change from decreasing to increasing trend is observed at lower centrality values for a smaller acceptance.This is possibly due to larger non-flow contamination due to a smaller |∆η| separation.At the same time, it is not obvious whether initial momentum correlations can survive longitudinal decorrelation, and thus a large |∆η| gap could also destroy them.Finally, the ρ 2 measured using two different centrality estimators by ATLAS are also compared in Fig. 7, where the ΣE T -based estimator classifies events into centrality classes based on the total energy deposited into forward calorimeters and the N ch -based classification depends on the total number of charged particles reconstructed at midrapidity.It is found that the N ch -based estimator results in a steeper slope of ρ 2 and a more rapid change of behaviour within 75%-80% centrality.This is likely due to the finite resolution of the event activity, where midrapidity-based estimators are more sensitive to event-by-event fluctuations.Similar observations were previously reported in a model-inspired study [27], albeit at significantly lower center-of-mass energies and collision systems.These findings indicate that a more thorough model study is required to understand whether the observed signal in the data is unique to new phenomena or is an artefact of more basic kinematic considerations.

Summary
Measurements of the anisotropic flow at the LHC have significantly expanded our understanding of the production and evolution of the QGP.First measurements of v 2 {4} for a plethora of identified particles show a mass ordering at low p T and baryon/meson grouping at higher momenta.The trends observed in the data are qualitatively described by hydrodynamic models that consider partonic coalescence.The baryon/meson grouping is also observed in the relative flow fluctuations, but it occurs at significantly lower p T , suggesting it is of a different origin.The higher moments of the inclusive particle v 2 distribution indicate non-Gaussian fluctuations in the same p T region where baryon/meson grouping is observed for F(v 2 ), and they become Gaussian at p T 3 GeV/c.This calls for future measurements of γ 1 and γ 2 for identified particles.Finally, measurements of v 2 − p T correlations open new venues to study nuclear deformation and processes leading to the formation of the QGP.Measurements of ρ 2 in central Pb-Pb and Xe-Xe collisions suggest the deformation parameter of Xe nucleus β 2 = 0.16, which different methods have previously confirmed.The evolution of ρ 2 with centrality shows trends that are qualitatively better described by models that utilize IP-Glasma in the initial state.In ultraperipheral heavy-ion collisions, indications of a ρ 2 slope change are observed.However, this effect cannot be uniquely attributed to initial momentum correlations, and a better understanding of biases originating from the kinematic selections is required.

Figure 4 :
Figure 4: Standard skewness and kurtosis as a function of p T in Pb-Pb collisions at √ s NN = 5.02 TeV and 30-40% centrality.

Figure 5 :
Figure 5: Pearson Correlation Coefficient of v 2 and p T as a function of centrality in Pb-Pb (top) and Xe-Xe collisions at √ s NN = 5.02 and 5.44 TeV, respectively.

Figure 6 :
Figure 6: Pearson Correlation Coefficient of v 2 and p T as a function of N ch (|η| < 1.6) in Pb-Pb and high multiplicity pp collisions at √ s NN = 5.02 and 13 TeV, respectively, in comparison to multiple model predictions.

√ s NN = 5 .
02 and 13 TeV, respectively, are compared to different MC models.The measured ρ 2 is positive in the whole multiplicity region considered and is very similar in Pb-Pb and pp collisions.The change of slope in Pb-Pb collisions is observed at significantly larger multiplicity, N ch (|η| < 0.8) ≈ 100, as compared to the CGC-inspired model where the slope changes at around N ch (|η| < 0.8) ≈ 20.Moreover, IP-Glasma + MUSIC + UrQMD predicts a rapid change of ρ 2 at low multiplicity while the evolution seen in data is less pronounced.The similarities between pp and Pb-Pb data at comparable N ch suggest that the mechanism giving rise to p T -v 2 correlations in the two systems might be the same.It is also interesting to see that AMPT predicts the decreasing trend of ρ 2 at N ch (|η| < 0.8)

Figure 7 :
Figure 7: Centrality dependence of the Pearson Correlation Coefficient of v 2 and p T in Pb-Pb collisions at √ s NN = 5.02 TeV, measured in different p T regions (left), different η regions (middle), and using different centrality estimators (right).Figure from [26].