Azimuthal anisotropies and initial-state fluctuations from SPS to LHC energies

The v3 coefficient, obtained using the PbAu data from the CERES detector at the top SPS energy of √ sNN = 17.3 GeV, is presented. The v2 is measured over a pT range up to 100 GeV/c in PbPb collisions collected with the CMS detector. The v2{2} of charged and strange particles emitted in pp collisions shows a mass ordering effect. The v2{4} and v2{6} are comparable to the v2{2}, and thus supports the collective nature of the long-range correlations in high-multiplicity pp collisions at 13 TeV. Principle Component Analysis (PCA) of two-particle harmonics (VnΔ) is studied in PbPb and high-multiplicity pPb collisions at the LHC. The factorization breaking of the VnΔ can be attributed to the effect of initial-state fluctuations. Using a PCA, the VnΔ are characterized through the leading and sub-leading modes. The leading modes are essentially equivalent to the vn{2}. The sub-leading modes represent the largest sources of factorization breaking.


Introduction
One of main features of Quark Gluon Plasma is its hydrodynamic behavior characterized by v n coefficients extracted using methods like two-and many-particle correlations [1], the scalar product (SP) [2,3] and the Lee-Yang Zero (LYZ) [4,5].The CMS collaboration measured v 2 coefficient in PbPb collisions over a wide p T range up to 100 GeV/c [6].This measurement at high-p T is complementary to the nuclear modification factor (R AA ) measurements.The long-range (|Δη| > 2) correlation known as the ridge is observed not only in PbPb collisions [7], but also in high-multiplicity pPb collisions [8] and even in smallest system formed in high-multiplicity pp collisions [9,10] giving a hint that the ridge could have a hydrodynamic origin.To support it, the correlations among four or more charged particles are studied in pPb collisions at √ s NN = 5.02 TeV [11] and in pp collisions at √ s = 5, 7 and 13 TeV [12].The two-particle correlations between strange (K 0 S or Λ/ Λ) and charged particles [13] also revealed similar ridge structures, and the extracted v 2 , scaled to the number of constituent quarks (n q ) shows that hydrodynamic behavior happens on the partonic level.It is shown in [14,15] that even if the hydrodynamics is the only source of the long-range correlations, the initialstate fluctuations makes the event plane angle, Ψ n , dependent on both, p T and η.This leads to factorization breaking of the V nΔ into a product of single-particle anisotropies v n [16].A PCA [17,18] is applied on V nΔ coefficients constructed from 2.76 TeV PbPb collisions and 5.02 TeV high-multiplicity pPb collisions [19].Within the PCA approach, the V nΔ coefficients are characterized through leading and sub-leading mode terms.The leading modes are essentially equivalent to the v n harmonics extracted from two-particle correlations.The sub-leading modes represent the largest sources of factorization breaking.In the context of hydrodynamic models, they are a direct consequence of the initial-state fluctuations.

Experiment and data used
About 30 M of central PbAu collisions at the top SPS energy were collected.CERES detector worked in 0.5 T magnetic filed which enable precise p T measurement.The η coverage close to mid-rapidity, together with a full azimuthal (φ) coverage enables flow study.Negative pions, identified using the differential energy loss dE/dx in the Time Projection Chamber (TPC) are used in this analysis.
The CMS tracker detector is surrounded with a super-conducting solenoid producing 3.8 T magnetic field which enable precise p T measurements above 0.3 GeV/c [20].The PbPb and pPb collisions at the LHC energies of √ s NN = 2.76 TeV and 5.02 TeV with integrated luminosities of 160 μb −1 and 35 nb −1 , respectively, were collected.The data sets for pp collisions at √ s =5, 7 and 13 TeV have integrated luminosities of 1.0, 6.2 and 0.7 pb −1 respectively.A wide pseudorapidity coverage of |η| < 2.5 for the tracker and 2.9 < |η| < 5.2 for the hadronic forward (HF) calorimeters together with a full azimuthal coverage excellently suites for studying the long-range flow correlations.

Results
In figure 1, the comparison between the hydrosolver+UrQMD [21] [23].Within the analyzed range, the CERES v 3 does not show centrality dependence [22].The CMS showed in [6] that the v 3 is consistent with zero while the positive v 2 persists up to very high-p T of nearly 100 GeV/c.To further explore the nature of the v 2 (p T ) dependence, the v 2 values are also calculated using the 4-, 6-and 8-particle cumulant analyses.The obtained results are shown in figure 2. In the low-p T regions, the results show the usual hydrodynamic shape with v 2 {SP} > v 2 {4} ≈ v 2 {6} ≈ v 2 {8}.At high-p T , results tend to converge to a unique distribution.Such observed collectivity at high-p T is likely to be related to the jet quenching phenomena and the pathlength dependence of the parton energy loss.The v 2 coefficient in pp collisions at 13 TeV is studied using the two-particle correlation method as well as cumulant of fourth and sixth order [12].The v 2 , as a function of charged particle multiplicity, are shown in the left panel of figure 3.In the high multiplicity region, the results are consistent with each other.Also, the ordering of the pp results obtained from different methods is similar to what was observed in pPb (middle panel) and PbPb (right panel) collisions [11]: the relation v 2 {2} ≥ v 2 {4} ≈ v 2 {6} in all three colliding systems is an evidence of a collective behavior.In order to further investigate possible collective behavior in pp collisions, the v 2 coefficients are also extracted from the correlations between the strange, K 0 S and Λ/ Λ, and charged hadrons.The upper panel of figure 4 shows the v 2 values of charged hadrons, K 0 S mesons and Λ/ Λ hyperons as a function of p T .At small-p T , a mass ordering in the v 2 is seen in pp collisions.In the bottom panel of figure 4 are presented v 2 values scaled to the number of constituent quarks, n q , plotted vs scaled kinetic transverse energy, KE T /n q , which shows that similarly as in the case of PbPb and pPb [13] collisions, a collective behavior on partonic level is present also in pp collisions at 13 TeV [12].
Due to the initial-state fluctuations, the factorization of the V nΔ into a product of single-particle anisotropies does not hold precisely.A new observable, r n (more details in [14][15][16]) is introduced.It is defined as which is approximately equal to the cos[n(Ψ n (p a T ) − Ψ n (p b T ))].If the r n is smaller (equal) than 1 then factorization breaks (holds).The value greater than 1 means that there are unremoved non-flow effects.In figure 5 are shown magnitudes of the factorization breaking effect over a wide centrality/multiplicity range.In the case of the 2nd harmonic, the smallest effect is observed for semi-central collisions.Going to more central or more peripheral collisions the size of S and Λ/ Λ particles as a function of KE T /n q .Bottom: Ratios of v 2 /n q to a smooth fit function of v 2 /n q for K 0 S vs KE T /n q [12].The error bars correspond to statistical, while the shaded areas to systematic uncertainties. the effect increases.At the same multiplicity, the size of the effect is rather similar in the two colliding systems.In PbPb collisions, the size of the r 3 is small and nearly independent of centrality, while in pPb collisions the r 3 approaches to 1 and then goes significantly above 1 at lower multiplicities.The p T -dependent data are qualitatively described by viscous hydrodynamic models with fluctuating initial-state conditions, while they are insensitive to the shear viscosity to entropy density ratio [16].This promises of using the factorization data to disentangle contributions of the initial-state conditions and the medium's transport properties to the collective flow, and improving modeling of the evolution of the strongly-coupled quark gluon medium.
The PCA results from 5.02 TeV high-multiplicity pPb and 2.76 TeV PbPb collisions [19] are presented in figure 6 and 7 respectively.The extracted leading flow modes are essentially equal to the results [7,24] obtained from two-particle correlations.A qualitatively new result obtained using the PCA method is the existence of the sub-leading mode, v (2)  n , which is a consequence of the initialstate fluctuations.A non-zero v (2)  2 is found both in pPb (left panel in figure 6) and in PbPb (upper   (1)  2 are compared to the v n harmonics measured by the CMS collaboration using the two-particle correlation method [7].The error bars correspond to statistical while shaded areas to systematic uncertainties.
row in figure 7) collisions.It is close to zero at small-p T and achieves few percent at p T ≈ 3 GeV/c.While the strength of the effect does not depend on multiplicity in pPb collisions, there is a centrality dependence of the v (2)  2 in PbPb collisions.The similar behavior is established in [16].The v (2)  3 is close to zero in both collision cases (right and bottom panel in figure 6 and 7) which is in an agreement with the results from [16].

Summary
In this contribution are presented results on the v 2 and v 3 measurements from the CERES at the top SPS energy, and from the CMS collaboration at the LHC energy.The CMS measured the v 2 up to 100 GeV/c.This result is complementary to the R AA measurements.For the first time, the v 2 has been measured in pp collision at 13 TeV.This, together with the established n q -scaling shows that collective behavior appears even in such small system as created in pp collision.Also, for the first time sub-leading flow modes, v (2)  n , are measured in PbPb and high-multiplicity pPb collisions.The obtained results are in a qualitative agreement with factorization-breaking results. .The v (1)  2 are compared to the v n harmonics measured by the ALICE collaboration using the two-particle correlation method [24].The error bars correspond to statistical while shaded areas to systematic uncertainties.

Figure 1 .
Figure 1.The negative pion v 3 (p T ) measured in PbAu collisions at √ s NN = 17.3 GeV compared with hydrosolver+UrQMD model predictions [22].Statistical uncertainties are represented with the error bars, while systematic ones are indicated by gray rectangles.Statistical errors of the model predictions are shown as yellow band.

Figure 2 .
Figure 2.The SP v 2 results compared to those from cumulant method as a function of p T over wide centrality range in 5.02 TeV PbPb collisions[6].The systematic uncertainties are denoted with shaded boxes.

Figure 4 .
Figure 4. Top: the v 2 (p T ) for K 0 S (blue squares), Λ/ Λ (red circles), and charged particles (black crosses) for the multiplicity range 105 ≤ N offline trk < 150 in 13 TeV pp collisions.Middle: the n q -scaled v 2 values of K 0 S and Λ/ Λ particles as a function of KE T /n q .Bottom: Ratios of v 2 /n q to a smooth fit function of v 2 /n q for K 0 S vs KE T /n q [12].The error bars correspond to statistical, while the shaded areas to systematic uncertainties.

Figure 5 .
Figure 5.The factorization ratios, r 2 and r 3 , as a function of event multiplicity in pPb and PbPb collisions[16].The curves show few theoretical predictions for PbPb and pPb collisions.The horizontal solid lines denote the r 2 (top) and r 3 (bottom) value of unity.The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible, and thus are not shown.

Figure 6 .
Figure 6.The first and the second mode of v 2 (p T ) (left) and v 3 (p T ) (right) from 5.02 TeV high-multiplicity pPb collisions [19].The v(1)  2 are compared to the v n harmonics measured by the CMS collaboration using the two-particle correlation method[7].The error bars correspond to statistical while shaded areas to systematic uncertainties.

Figure 7 .
Figure 7.The first and the second mode of v 2 (p T ) (upper row) and v 3 (p T ) (bottom raw) from 2.76 TeV PbPb collisions [19].The v(1)  2 are compared to the v n harmonics measured by the ALICE collaboration using the two-particle correlation method[24].The error bars correspond to statistical while shaded areas to systematic uncertainties.