Anisotropy in pPb and PbPb collisions from CMS

The recent CMS results on anisotropic particle emission will be presented. Consistency between the results obtained using four-, six and eigth-particle correlation as well as the Lee-Yang zero method reveals a multi-particle nature of the long-range correlations observed in pPb collisions. By correlating an identiﬁed strange hadron ( K 0 S or Λ / ¯Λ ) with a charged particle, at large relative pseudorapidity, the magnitude of the elliptic and triangular ﬂow of strange particles from both pPb and PbPb collisions have been extracted. The results for K 0 S and Λ / ¯Λ scaled by the number of constituent quarks as a function of transverse kinetic energy per quark are in a mutual agreement (within 10) for both v 2 and v 3 over a wide range of particle transverse kinetic energy and event multiplicities. Due to the initial-state ﬂuctuations, the event-plane angle depends on both, transverse momenta ( p T ) and pseudorapidity ( η ), which consequently induce breaking of the factorization of the two-particle azimuthal anisotropy into a product of single-particle anisotropies. For p T , maximal effect of factorization breaking of about 20is observed in ultra-central PbPb collisions. For η , the effect is weakest for mid-central PbPb events and gets larger for more central or peripheral PbPb collisions as well as for high multiplicity pPb collisions. The experimental results are consistent with recent hydrodynamic predictions in which the factorization breakdown effect is incorporated. It is found that the effect is mainly sensitive to the initial-state conditions rather than the shear viscosity of the medium. Abstract. The recent CMS results on anisotropic particle emission will be pre- sented. A multi-particle nature of the long-range correlations observed in pPb collisions is revealed through consistency between the results obtained using four-, six and eight-particle correlation as well as the Lee-Yang zero method. The magnitude of the elliptic and triangular ﬂow of strange particles from both pPb and PbPb collisions have been extracted by correlating an identiﬁed strange hadron ( K 0 S or Λ/¯Λ) with a charged particle separated by a large relative pseudorapidity. The results for strange, K 0 S and Λ/¯Λ, particles scaled by the number of constituent quarks plotted as a function of transverse kinetic energy per number of constituent quarks are in a rather good mutual agreement for both v 2 and v 3 over a wide range of particle transverse kinetic energy and event multiplicities. The initial-state ﬂuctuations induce that the event-plane angle is not any more a global quantity but depends on both, transverse momenta ( p T ) and pseudorapidity ( η ), which further induces the factorization breaking of the two-particle azimuthal anisotropy into a product of single-particle anisotropies. In the p T direction, maximal eﬀect of factorization breaking of about 20% is observed in ultra-central PbPb collisions. In the η direction, the eﬀect is weakest for mid-central PbPb events and gets larger for more central or peripheral PbPb collisions as well as for high multiplicity pPb collisions. The experimental results are compared with recent hydrodynamic predictions which involve the factorization breakdown eﬀect. The eﬀect is sensitive to the initial-state conditions rather than the shear viscosity of the medium.


Introduction
The methods of the two-, four-, six-and eight-particle correlations [1] as well as the Lee-Yang Zero method (LYZ) [2,3] could be used to extract the magnitude of the azimuthal anisotropy which is characterized by Fourier coefficients, v n . The long-range (|∆η| > 2) correlation known as the ridge [4], observed in highmultiplicity pPb collisions using the two-particle correlations, gave a hint that such a structure could have a hydrodynamic origin. In order to give a strong evidence of the multi-particle nature of the observed long-range effect, the correlations among four or more charged particles from pPb collisions at √ s N N = 5.02 TeV are performed [5]. Beside charged particles, two-particle angular correlations are formed also between an identified strange hadron (K 0 S or Λ/Λ) and a charged particle [6] separated by a large relative pseudorapidity (|∆η| > 2). These correlations revealed similar ridge structures. The extracted Fourier coefficients, v 2 and v 3 , scaled to the number of constituent quarks showed that found hydrodynamic behavior happens on the partonic level. It is shown that even in the case when the hydrodynamic flow is the only source of the long-range correlations, initial-state fluctuations makes the event plane angle dependent on both, p T and η. This then leads to factorization breaking of the two-particle azimuthal anisotropy into a product of single-particle anisotropies [7][8][9]. a E-mail: Jovan.Milosevic@cern.ch 2 The CMS experiment and data used A super-conducting solenoid surrounds the tracker detector of the CMS experiment [10]. Produced magnetic field of 3.8 T enabled precise measurements of p T above 0.3 GeV/c. The data at the LHC energies of √ s N N = 2.76 TeV and 5.02 TeV in PbPb and pPb collisions with integrated luminosities of 160 µb −1 and 35 nb −1 , respectively, have been collected. The CMS detector has a wide pseudorapidity coverage (|η| < 2.5) which is excellently suited for studying the long-range correlations.

Collectivity in pPb collisions
The magnitude of the elliptic flow, v 2 , is measured using the two-, four-, sixand eight-particle correlation as well as using the LYZ method in both PbPb and pPb collisions [5]. In Fig. 1   In order to suppress jet-related non-flow effects, the elliptic flow magnitudes from two-particle correlations, v 2 {2}, are obtained applying the |∆η| > 2 cut. The obtained v 2 {2} results are consistently above the results obtained from the multi-particle correlation. Such feature appeared due to the event-by-event participant geometry fluctuations of the v 2 coefficient which affect the two-and multi-particle correlations differently. Also, the v 2 results from higher order cumulants and from LYZ method are in mutual agreement within 2% and 10% for PbPb and pPb collisions respectively. This mutual agreement between the v 2 results in high-multiplicity pPb collisions means that measured v 2 magnitude does not depend on the number of particles used in its reconstruction. This feature could be used as a strong evidence to support interpretation of the long-range correlation as a collective phenomenon not only in PbPb, but also in small systems formed in pPb collisions.

Collective flow of strange particles
Detailed description of the reconstruction technique for K 0 S and Λ/Λ particles can be found in [6]. The magnitude of the single-particle flow coefficients, v 2 and v 3 , is extracted from the two-dimensional ∆φ−∆η distributions formed by correlating reconstructed strange particles candidates with charged particles. In order to remove short-range correlations such as jet fragmentation, a Fourier decomposition of the corresponding ∆φ projection is applied after averaging over |∆η| > 2 region. The v 2 results for K 0 S and Λ/Λ particles emitted from results for charged particles. Huge majority of them are pions. The v 2 results exhibit a mass ordering effect: lighter particle species have a stronger azimuthal anisotropy at the given small p T with respect to the heavier kind of particles. The effect is a bit less pronounced in PbPb collisions with respect to pPb ones. At high p T appear two branches where the baryonic flow is greater than the mesonic v 2 . In order to deeper investigate the seen effect, in the middle raw of Fig. 2 Fig. 3 is shown the v 2 magnitude divided with the number of constituent quarks, n q , and plotted as a function of transverse kinetic energy per quark, KE T /n q , with KE T = m 2 + p 2 T − m. This scaling makes that the v 2 of the shown particle species collapse onto a unique distribution. The bottom raw of Fig. 2 depicts the ratio between the data and a polynomial fit to the K 0 S data which shows that the scaling is valid to better than 10% (25%) over most of the KE T /n q range in pPb (PbPb) collisions. For p T values below 0.2 GeV/c the scaling breaks. The fact that the scaling behavior mainly holds could be related to the quark recombination model and suggests that the collective flow happens on the partonic level.

and
Beside the elliptic flow, the triangular flow, v 3 , is also measured for strange K 0 S and Λ/Λ and charged particles in both colliding systems. Their magnitudes are depicted in Fig. 4. Due to limited statistics, the triangular flow has been analyzed within a wide multiplicity range (185 ≤ N of f line trk < 350) only. As in the case of the elliptic flow, a mass ordering effect is observed also for the triangular flow in both colliding systems. The distributions of the magnitude of the triangular flow scaled to the number of the constituent quarks for K 0 S and Λ/Λ particles are in a mutual agreement better than 20% over the whole KE T /n q range. According to our knowledge, no calculations on the triangular flow scaled to the n q has been performed in parton recombination models.

Initial-state fluctuations and factorization breaking
Due to the event-by-event fluctuations in positions of nucleons which form the colliding nuclei, higher-order Fourier harmonics (n ≥ 3), measured with respect to their corresponding global event plane angles, Ψ n , appear. Recently, it was discovered [7,8] that not only magnitudes of Fourier harmonics, v n , but also Ψ n could depends on p T due to initial-state fluctuations even if the hydrodynamic flow is the only source of the correlations. It has an important consequence: the factorization of the two-particle azimuthal anisotropy, V n∆ (p (a) T ), into a product of single-particle anisotropies, v n (p (a) T ), does not hold any more precisely. A new observable, r n , is introduced. It is formed from the two-particle Fourier coefficients and it is approximately equal to cos[n(Ψ n (p (a) T ))] (more details in [8,9]). If the factorization breaks (holds), then the r n achieves value smaller (equal) than 1. If the r n has the value greater than 1 then it means that there are unremoved non-flow effects. A most pronounced effect has been found in ultra-central PbPb collisions at √ s N N = 2.76 TeV [11].  [8] with MC-Glauber and MC-KLN initial condition models, and also hydrodynamic predictions for PbPb and pPb data in Ref. [7]. Right: The η-dependent F η n parameter as defined in Eq. (12) in [9] as a function of multiplicity in PbPb collisions for n = 2, 3 and 4 and pPb collisions for n = 2. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible.
breaking effect over a wide multiplicity range. The centrality axis, drawn at the top of the figures, is applicable only to the PbPb collisions. In the case of the 2nd harmonic, the smallest effect is observed for semi-central collisions, both for p T -and η-dependencies. Going to more central or more peripheral collisions the size of the effect increases. At the same multiplicity, the size of the effect in the p T -dependence is rather similar in the two colliding systems, while in the η-dependence the effect is much stronger in pPb than in PbPb collisions. In PbPb collisions, the size of the p T -dependent 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. Oppositely to the p T -, the η-dependence of the effect for the 3rd harmonic is stronger than for the 2nd one. The p T -dependent data are qualitatively described by viscous hydrodynamic models [7,8] with fluctuating initial-state conditions, while they are mainly insensitive to the shear viscosity to entropy density ratio [9]. This promises of using the factorization data to disentangle contributions of the initial-state conditions and the mediums transport properties to the collective flow in the final state. The η-dependent factorization data show the influence of the initial-state fluctuations along the longitudinal direction. This could improve the three-dimensional modeling of the evolution of the strongly-coupled quark gluon medium.