News on Collectivity in PbPb Collisions at CMS

The flow anisotropies with the Fourier coefficients (n = 2, 3) for the charged particles produced in PbPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV is studied with the CMS detector. In order to extract the Fourier coefficients, several methods were used, such as the scalar product method or multi-particle cumulant method. The results cover both of the low-pT region (1 < pT < 3 GeV/c) associated with hydrodynamic flow phenomena and the high-pT region where anisotropic azimuthal distributions may reflect the path-length dependence of the parton energy loss in the created medium for the seven bins of collision centrality, spanning the rang of 0-60% most-central events.


Introduction
A Quark-Gluon-Plasma (QGP) is a state of matter which quantum chromodynamic (QCD) predicts that it will occur at extremely high temperature and density.The experiments at the Relativistic Heavy Ion Collider (RHIC) have established the formation of QGP in ultra-relativistic nucleus-nucleus interactions [1][2][3][4].One of strong signatures of the existence for QGP is the suppression of high-transversemomentum (p T ) hadron yield via the nuclear modification factor, R AA , which is the ratio of the finalstate particle yields at a given p T value to that expected based on a scaling of pp collision results in the absence of the medium [1][2][3][4].The observation of dijet asymmetry in PbPb collisions at the Large Hadron Collider (LHC) furnishes further proof of jet quenching, indicating a large energy loss for partons traversing the QGP medium.
The measurement of R AA alone is not sufficient to differentiate among various parton energy-loss models.In addition, it has been shown that R AA is not sensitive to sub-nucleon spatial fluctuations [5].Additional observables, such as the azimuthal anisotropy of high p T hadrons, are needed to constrain the models [6][7][8][9][10][11][12].The anisotropy can be characterized by the coefficient of the second-order Fourier harmonic, v 2 , in the azimuthal angle φ distribution of the hadron yield relative to the reaction-plane angle Ψ RP , dN/dφ ∝ 1 + 2v 2 cos(2(φ − Ψ RP )), where Ψ RP is defined by the short-axis direction of the "almond"-shaped interaction region created in a non-central heavy-ion collision.In order to reduce the ambiguity on the measurement, scalar product or multi-particle cumulant methods can be replaced.
Furthermore, v 3 , the coefficient of the higher harmonic, is particularly sensitive to the initial-state fluctuations.Indeed, v 3 arises mainly from fluctuation in the soft sector and it remains to be seen if these fluctuations can generate triangular anisotropy at high p T .
In this paper, a study of the azimuthal anisotropy of very high p T particles (up to p T ≈ 100GeV/c) for PbPb collisions at √ s NN = 5.02 TeV at the LHC using the CMS detector is presented.The v 2 and v 3 coefficients are determined as a function of p T and collision centrality in the pseudorapidity regions of |η| < 1, where η = − ln[tan(θ/2)] and θ is the polar angle relative to the counterclockwise beam direction.The first precise measurement of the v 2 and v 3 coefficients up to very high p T region in heavy-ion collisions are represented by using scalar product method and the multi-particle cumulant analysis for several orders (4, 6 and 8) as a function of p T .

Event Selection
For this analysis, 2015 PbPb data at √ s NN = 5.02 TeV is utilized with an integrated luminosity of 404 μb −1 .Events were selected by using several trigger combinations in different p T regions and centrality bins.The minimum-bias trigger covers the low p T region (< 14 GeV/c), while the dedicated triggers on high p T tracks are used for high p T region up to 100 GeV/c.The L1 trigger seed of the triggers fired based on the highest ET Regional Calorimeter Trigger (RCT) region in the barrel of the CMS detector (|η| < 1.0).At the High Level Trigger (HLT), the leading track is passing the strict quality selection criteria describes in section 2.2.The performances of trigger for tracks used in analysis are shown in Figure 1.

Track Selection
Primary-track candidates are selected by the high-purity tracks.Additional requirements are also applied to enhance the purity of primary tracks.The significance of the separation along the beam axis (z) between the track and the best vertex, dz/σ(dz), and the significance of the impact parameter relative to the best vertex transverse to the beam, d T /σ(d T ), should be less than 3.The relative uncertainty of the transverse-momentum measurement, σ(p T )/p T , must be less than 10%.In order to reduce the fake rate of mis-reconstructed tracks and confirm high tracking efficiency, primary tracks with |η| < 1.0 and p T > 1.0 GeV/c are used in the analysis.Furthermore, tracks above 20 GeV/c in the tracker are required to match with an energy deposit in the calorimeter to further decrease the fake rate.

Scalar product method
The "scalar-product" event-plane method is used to study azimuthal correlations with long-range of pseudorapidity.The event-plane is determined event-by-event and consists of the beam direction and the azimuthal direction of maximum particle density.
Avoiding autocorrelation effects where a given particle, or its decay products is very important to determine the event plane which we want to characterize.This is usually done by requiring a large gap in pseudorapidity between the particles used to establish the event plane and those used to determine the Fourrier coefficients.
The azimuthal dependence of the particle yield can be written in terms of an harmonic expansion with [14] where φ and E are the particle's azimuthal angle and energy, respectively.If the impact-parameter direction is known, the reference angle Ψ can be decided as the azimuthal angle of the reaction plane Ψ R as defined by the beam and impact parameter directions.
To make the largest pseudorapidity gap possible, elliptic flow (n = 2) and triangular flow (n = 3) event planes are defined using calorimeter data, with the HF − n planes covering the pseudorapidity range of −5 ≤ η < −3 and HF + n planes covering the range 3 ≤ η < 5. Another event plane using tracker data with −0.75 ≤ η < 0.75 was also defined and used in the three-sub-event technique for determining the resolution corrections for the HF − n , HF + n .To consider asymmetries that arise from the detector acceptance and other effects correlated with the detector conditions, a two-step process is used where the event plane is first recentered and subsequently flattened [15].
In order to measure the actual v n coefficients, the current analysis utilizes the scalar product method introduced firstly by the STAR collaboration in a study of elliptic flow in AuAu collisions at √ s NN = 130 GeV [16].The Q-vectors are defined as where M is the number of particles in each event.Therefore, using the scalar product method, v n harmonics can be expressed as Here, the subscripts A, B, and C refer to three separate event planes reconstructed in different regions of pseudorapidity.The particles of interest are expressed by the Q n vector and are correlated with the A event plane.The event planes B and C effectively correct for the finite resolution of the A event plane that results from finite particle multiplicities and detector effects [17].

Multi-particle correlation technique with cumulants
Another way to measure v 2 is the Q-Cumulant method [18,19] from 4-, 6-and 8-particle correlations.This method supplies a fast, exact (no approximations), and unbiased (no interference between different harmonics) estimations for the cumulants.The cumulants are expressed in terms of the moments of the magnitude of the Q n flow vector.We first define the m-particle (m = 2, 4, 6 or 8) correlator as where φ i is the azimuthal angle of the i-th particle, and indicates that the average is taken over all m-particle combinations for all events.In order to remove self-correlations, it is required that the m particles be distinctive.The unbiased estimators of the reference m-particle cumulants, c n m, are defined as Correlating the m-particles within the reference phase space of |η| < 2.4 and p T range of 0.3 < p T < 3.0 GeV/c, we then obtain the reference flow v 2 {m}, with With respect to the reference flow, the differential v 2 m(p T , η) can then be expressed as where the differential cumulants d 2 {m} are estimated by replacing one of the m-particle cumulants in Eq. ( 5) with a particle from a certain particle of interest (POI) phase space in p T or η [17].

Results
The v 2 and v 3 results are shown in Figure 2.Those are measured by using the scalar product (SP) method as a function of p T (≈ 100 GeV/c) in 7 centrality ranges (0-60%) of PbPb collisions at √ s NN The significant positive v 2 values are observed in the most of centrality ranges up to p T ≈ 100 GeV/c.The v 2 value first rises and then falls off around 3 GeV/c quickly from low p T to high p T region.In the low p T region, v 2 values are first increasing from most central to mid-peripheral events (30-40%), and then decreasing in the more peripheral centrality ranges.At the higher p T region (>10 GeV/C), the v 2 values are slowly decreasing as p T increases.The v 3 results show similar tendency as that for v 2 .At low p T , the observed v 3 values don't depend on centrality.Significant positive v 3 are found to continue up to p T of 20 GeV/c for all centrality ranges.Above p T = 20 GeV/c, the v 3 values are consistent with zero within given uncertainties.These results of v 2 and v 3 cover the widest p T range ever achieved.Such a result at high p T is sensitive to the path length dependence of hard partons in the QGP and will be expected to put more constrain on the energy loss models.In order to investigate the origin of this correlation observed at very high p T further, we obtained v 2 values from multi-particle cumulant analysis (4, 6 and 8) and compared with the SP v 2 results as shown in Figure 4.At low p T (p T < 3 GeV/c), the results follow the expectation from hydrodynamic models meaning v 2 {SP} > v 2 {4} ≈ v 2 {6} ≈ v 2 {8}.At high p T (10 GeV/c), scalar product and multiparticle correlation results tend to converge to the same value.This observation suggests strong evidence that collective anisotropic particle emission in heavy ion collisions extend to very high p T region.Although the nature of collectivity at high p T is likely to be related to jet quenching phenomena, the observed anisotropies at both high and low p T are related to initial-state geometry and its event-by-event fluctuations.To find possible connection of azimuthal anisotropies between low-p T (dominated by hydrodynamics) and high p T (dominated by jet quenching) regions, the correlation between the v 2 results at low and high p T was studied.starting from the most central events on the left toward peripheral events on the right.The first four points have a centrality bin width of 5% (from 0 to 20%) while, for the others, the bin width is 10%.Full circles are the results obtained from SP method and open square are extracted from 4-particle correlation analysis.A strong correlation of v 2 values between high and low p T regions is observed over the full centrality range.While low p T correlations can be explained by the collective expansion of the medium, high p T correlations come from the path-length dependence of the hard-scattered partons undergo while traversing the medium.This indicates that the initial geometry and its fluctuations may be responsible for the correlations observed both at low and high p T .

Summary
In summary, the azimuthal anisotropy of charged particles with respect to the event plane has been studied in PbPb collisions at √ s NN = 5.02 TeV using the CMS detector.The v 2 and v 3 values are measured over a wide p T range from 1 GeV/c to 100 GeV/c in different collision centralities using scalar product method.The results cover for the first time the very high p T region beyond 60 GeV/c.Moreover, these results provide a v 3 measurement up to a p T region that has never before been studied (up to 100 GeV/c).The observed v 2 (p T ) shows a tendency of rapid increasing to a maximum at p T of ≈ 3 GeV/c and a steep fall for all of centrality ranges.The v 3 (p T ) behavior is very similar to v 2 at low p T but its value is consistent with zero over the full centrality range for p T > 20 GeV/c.The observed trend in the centrality dependence of v 2 over a wide p T range suggests a potential connection to the initial-state geometry.To further investigate the origin of the correlation at high p T , a multi-particle correlation analysis was performed to extract v 2 from 1 GeV/c to, at maximum, 100 GeV/c.expectations and is a sign of collectivity.The same behavior is observed at high p T and reflects the collective nature of these correlations.As the last, the correlations between v 2 values at low and high p T as a function of centrality have been studied.The results shows the strong correlations.The low and high p T correlations are interpreted by the collective expansion and by the path-length dependence of hard-scattered partons in the medium, respectively.These results indicate that the initial geometry and its fluctuations are responsible for the low and high p T correlations.

Figure 1 .
Figure 1.The efficiencies of L1 trigger (left) and High level trigger (right) as a function of p T measured in |η| < 1.0.L1 trigger efficiencies are estimated for p T of 12, 16, 20, 24 and 28 GeV/c, and HLT efficiencies are done in the p T regions of 12, 18, 24 and 34 GeV/c [13].

= 5 .Figure 2 .
Figure 2. The v 2 and v 3 results from SP method as a function of p T in seven centrality ranges of PbPb collisions at √ s NN = 5.02 TeV.Shaded boxes represent systematic uncertainties [17].

Figure 3
Figure 3 shows the comparison between v 2 results at √ s NN = 5.02 TeV and v 2 results obtained with the Event Plane (EP) at √ s NN = 2.76 TeV [20] and theoretical calculations from CUJET3.0 [21, 22] at 5.02 TeV.The results from SP and EP are similar up to very high p T .The difference do not exceed 5%.The model (CUJET3.0)calculations are compatible with the results at high p T (> 40 GeV/c) within systematic uncertainties in all over centrality ranges except for the most peripheral one where the model doesn't reproduce the data.

Figure 3 .Figure 4 .
Figure 3.The v 2 results from SP and EP method as a function of p T in seven centrality ranges of PbPb collisions at √ s NN = 5.02 TeV and 2.76 TeV respectively.Shaded boxes represent systematic uncertainties [17] and dashed lines are predictions from CUJET3.0 model [21, 22].

Figure 5
shows v 2 from 12 < p T < 14 GeV/c, 20 < p T < 26 GeV/c and 26 < p T < 35 GeV/c as a function of v 2 from 1.0 < p T < 1.25 GeV/c extracted from each centrality range of PbPb collisions at √ s NN = 5.02 TeV.Each point represents a different centrality range At low p T , v 2 {4}, v 2 {6} and v 2 {8} have similar values and smaller than v 2 {SP}.This follows hydrodynamic