Particle correlations and their implication to collectivity in pPb and PbPb from CMS

The long-range two-particle correlation functions reveal the near-side ridge structures in highmultiplicity pp, pPb and PbPb collisions at the Large Hadron Collider (LHC). The model that takes into account the collective flow originated from the initial-state geometry fluctuation can successfully describe the measured long-range correlation functions of charged particles. In this review paper, the recent experimental data on the long-range correlations and the extracted elliptic and triangular flow parameters in pPb and PbPb collisions from the Compact Muon Solenoid (CMS) experiment are summarized. The flow parameters from the longrange correlation analyses are compared with those from the multiparticle cumulants and the Lee-Yang Zeros (LYZ) method. In addition, the pseudorapidity dependence of long-range two-particle correlation functions in pPb and the deduced flow parameters for identified strange hadrons (K0 S and Λ/Λ̄) in pPb and PbPb are also presented to provide more insights on the long-range correlations and flow dynamics.


Introduction
The experiments at the Relativistic Heavy Ion Collider (RHIC) found the striking near-side ridge structure in the long-range two-particle correlations and the away-side conical emission in central AuAu collisions at 200 GeV of √ s NN about a decade ago [1][2][3].Naturally, the detailed study of the long-range two-particle correlation functions became one of the most interesting and urgent topics for the LHC heavy-ion program at higher energies.Soon after the LHC beams had been available, the ALICE, AT-LAS, and CMS experiments observed near-side ridge and away-side conical emission structures by analyzing the first PbPb collision data at 2.76 TeV with much larger strengths [4][5][6].Moreover, the CMS Collaboration also found the near-side ridge structure at the low transversemomentum (p T ) region in violent pp events with the multiplicity larger than 110 [7], which has not been observed before in either hadron collisions or Monte-Carlo (MC) simulations.
The associated yield distributions for a short-range jet region (|Δη|<1) and the long-range ridge region (2< |Δη| < 4) for central 5% PbPb collisions are shown in Fig. 1 [8].As expected, Fig. 1 shows that the jet-region yield increases with p trig T as the transverse energy of jet increases.On the contrary, the ridge-region yield becomes maximum for 2 < p trig T < 6 GeV/c and decreases with p trig T and finally reaches almost zero at about 10 GeV/c.The PYTHIA8 MC simulations for pp, displayed by the solid lines in Fig. 1, are consistent with zero at all p trig T for the ridgeregion yield and cannot describe the data at all. a e-mail: bhong@korea.ac.krFor pp collisions the multiplicity (N) dependence of the associated yields for the long-range near-side ridge region (2< |Δη| < 4) at 7 TeV is displayed in Fig. 2 [8].The event sample for this analysis is selected for the momentum ranges of 2 < p trig T < 3 GeV/c and 1 < p assoc T < 2 GeV/c, where the near-side ridge effect is strongest.It is observed that the ridge effect turns on with N ∼ 50 -60 and shows a saturation around N ∼ 120.However, this statement is not yet conclusive due to large statistical and systematic uncertainties.
There have been many attempts to explain the peculiar structures in the long-range two-particle correlation functions.Among them, the most successful scenario is the higher-order hydrodynamics flow induced by the geometric fluctuation of the overlapped region in initial stage [9], and this idea was successfully applied to the PbPb data at the LHC [8].In this analysis, the one-dimensional Δφ projections of the two-particle correlation functions for relatively large pseudorapidity separation (2 < |Δη| < 4) are fitted by a Fourier series as where N assoc is the number of charged hadron pairs per trigger particle in a given (p trig T , p assoc T ) bin.Then, the extracted Fourier coefficients, V nΔ , can be factorized into the product of the single-particle harmonics, v n , by  This review paper summarizes the recent analysis results on the long-range dihadron correlations and the ex- tracted flow harmonics in PbPb and pPb from CMS.In Sec. 2, the v 2 and v 3 single-particle harmonics deduced by the long-range two-particle correlation functions are compared with the results obtained by other methods like multiparticle cumulants and the LYZ method.Section 3 presents the pseudorapidity dependence of longrange two-particle correlation functions in pPb, and Sec. 4 decribes the v 2 and v 3 single-particle harmonics for K 0 S and Λ/ Λ in pPb and PbPb.Finally, the summary in given in Sec. 5. < 260 is same for both collision systems, which corresponds to average centrality of ∼60% for PbPb.For both PbPb and pPb, pronounced near-side longrange ridge structures are seen at |Δφ| ≈ 0. The near-side ridge structure in pPb at 5.02 TeV was also observed by ALICE and ATLAS [12,13].

EPJ Web of Conferences
Figure 5 shows the integrated near-side associated yields as a function of p trig T for the long-range ridge region (|Δη| > 2) and the short-range jet region (|Δη|<1).In order to obtain the genuine jet yields, the long-range ridge components are subtracted for both collision systems in 220 ≤ N o f f line trk < 260 [11].It is observed that the estimated jet yields increase monotonically with p trig T similarly for PbPb and pPb collisions in the same multiplicity bin.In contrast, the long-range ridge yields increase with p trig T , reaching a maximum at p trig T ≈ 2 -3 GeV/c, and gradually decrease at higher p trig T for both collisions.Moreover, the long-range ridge yields for PbPb are larger by almost a factor of two than those for pPb.
Using the method described by Eqs. 1 and 2, the single-particle second-order harmonic (v 2 ) coefficients are estimated from the long-range two-particle correlation functions for PbPb at 2.76 TeV and pPb at 5.02 TeV [14].The open circles in Fig. 6  For comparison the v 2 values obtained by multiparticle cumulant correlations [15] and the LYZ method are also displayed in Fig. 6 [16].In hydrodynamics, multiparticle correlations are arisen by anisotropic collective expansion originated from asymmetric initial geometry, and the corresponding Fourier coefficients v n can be related to the correlation functions.On the other hand, the LYZ method involves correlations among all particles and is useful for the large-order behavior of the cumulant expansion for azimuthal correlations.Figure 6 shows that the v 2 {2, |Δη| > 2} values for both systems are consistently larger than those obtained by multiparticle cumulants and the LYZ method.This difference can be understood in hydrodynamic models since the event-by-event initial geometric fluctuations affect differently to the two-particle and multiparticle cumulant correlations.As a result, the v 2 {2, |Δη| > 2} values contain the residual nonflow correlation effects, and the multiparticle cumulant method has an advantage for providing cleaner collective signals compared to the two-particle correlation method [17].The v 2 values from multiparticle cumulants and the LYZ method for PbPb increase with N o f f line trk , but those for pPb show little dependence on event multiplicity.
Figure 7 shows the single-particle third-order harmonic (v 3 ) coefficients as a function of N o f f line trk for 0.3 < p T < 3.0 GeV/c in PbPb at 2.76 TeV and pPb at 5.02 TeV obtained by the long-range two-particle correlation analysis [11].The lines in Fig. 7 6, the magnitude of v 3 {2, |Δη| > 2} is similar for PbPb and pPb in the same event multiplicity bin.This similarity of the triangular flow is non-trivial phenomenon within hydrodynamic picture because the initial-state geometry is quite different for the two collision systems.

Pseudorapidity dependence of long-range correlations in pPb
In order to gain further insights into long-range correlation in pPb, the Δη dependent analysis has been performed by limiting the trigger particles to a narrow η ranges [18].The near-side correlated ridge yields for high-multiplicity (220 < N o f f line trk < 260) pPb events are shown in Fig. 8 as a function of the pseudorapidity of the associated particle η assoc .Here, the variable η assoc is defined by the sum of Δη and η trig , the mean η value of trigger particles.The two chosen η windows for trigger particles are -2.4 < η trig < -2.0 for Pb-going-side trigger and 2.0 < η trig < 2.4 for p-goingside trigger.Figure 8 shows that the Δη dependences of the near-side ridge yields are different for Pb-going-side and p-going-side triggers.For the Pb-going-side trigger, the ridge yield is larger when the two correlated particles are closer and decreases towards higher η assoc .On the contrary, the ridge yield is almost independent of η assoc for the p-going-side trigger.
The explanation of different η assoc dependences for the two trigger conditions can be provided by hydrodynamic EPJ Web of Conferences 01005-p.4flow.In hydrodynamic scenario, the ridge yield is related to the pair density per trigger particle of the underlying event.The η dependences of the ridge yields, shown in Fig. 8, are qualitatively in accordance with the dN/dη distribution of the underlying event [19].However, they differ quantitatively as the measured ridge yield can be described by the dN/dη distribution of the underlying event multiplied by an additional linear function in Δη.The ridge yield distribution for pPb, discussed in Sec. 2, was uniform in Δη because the correlations were integrated over a wide η range of the triggered particles.But Fig. 8 demonstrates that the ridge yield in pPb indeed depends on Δη.
Figure 9 shows the self-normalized singleparticle anisotropy parameters, v 2 (η assoc )/v 2 (0) and v 3 (η assoc )/v 3 (0), obtained by Eqs. 1 and 2, as a function of η assoc for high-multiplicity pPb events with 220 < N o f f line trk < 260 at 5.02 TeV [18].The circles Fig. 9 represent the triggered data after the low-multiplicity events with N o f f line trk < 20 are subtracted for V nΔ , whereas the lines show the data without subtraction.In Fig. 9 only the long-range data points with |Δη| > 1 are displayed, and a good agreemen between the two triggered data exist in the overlapped region.Significant η dependence of v 2 is observed as a larger decrease is observed in the p-going side.For triangular flow, finite v 3 is observed, but current large statistical uncertainties unfortunately prevent any definite conclusions on the η dependence.

Long-range correlations of K 0 S and Λ/ Λ in PbPb and pPb
To provide more insights on the particle production and expansion dynamics, long-range two-particle correlation functions have been studied for identified strange hadrons, K 0 S and Λ/ Λ, in high-multiplicity pPb collisions with 220 < N o f f line trk < 260 at 5.02 TeV [20].In this analysis the pair of two tracks are assumed to be π + π − in K 0 S reconstruction and π − p (π + p) in Λ ( Λ) reconstruction [21].Figure 10 shows the invariant-mass distributions of K 0 S and Λ/ Λ candidates with 1 < p T < 3 GeV/c for high-multiplicity pPb events (220 < N o f f line trk < 260) at 5.02 TeV [20].The peaks for K 0 S and Λ/ Λ candidates are clearly identified with small backgrounds.Each peak is fitted by a double Gaussian function with a common mean, and the background distribution is fitted by the 4th-order polynomial function.The peak region is defined as the mass window of ±2σ around the centeral value where σ is the standard deviation of the double Gaussian fit function.The amount of background in the peak region for the correlation measurement is estimated by the sideband region at least ±3σ away from the central peak value.
Figure 11 shows the two-dimensional two-particle correlation functions for K 0 S − h ± and Λ/ Λ − h ± pairs in high-multiplicity pPb events at 5.02 TeV [20].In Fig. 11 the multiplicity range is 220 ≤ N o f f line trk < 260 and the transverse-momentum range is 1 < p T < 3 GeV/c for the triggered and associated particles.The two-particle correlation functions for K 0 S − h ± and Λ/ Λ − h ± pairs show long-range ridge structures extending at least 4.8 units of |Δη| in high-multiplicity pPb events.These ridge structures diminish for low-multiplicity events for N o f f line trk < 35.The single-particle second-order harmonic (v 2 ) coefficients have been extracted for K 0 S and Λ/ Λ by using Eqs. 1 and 2. Figure 12 presents the v 2 values of K 0 S and Λ/ Λ as a function of p T at several multiplicity bins for PbPb at 2.76 TeV and pPb at 5.02 TeV [20].For comparison the v 2 data of unidentified charged particles (h ± ) are also displayed.In the low-p T region (p T 2 GeV/c) the v 2 data for K 0 S are systematically larger than those for Λ/ Λ.However, the order is reversed at higher p T region so that the v 2 data  for Λ/ Λ are larger than those of K 0 S .In the meantime, the v 2 values of unidentified charged particles, mostly consisting of pions, consistently exceeds those of K 0 S and Λ/ Λ at p T 2 GeV/c, but falls between them for the two identified strange hadron species at p T 2 GeV/c.The p T dependences of v 2 are qualitatively similar for PbPb and pPb collisions in the same multiplicity bin.These observations indicate the mass-ordering effect and crossover of v 2 at p T ∼ 2 GeV/c.Figure 13 presents the signle-particle third-order hamonic (v 3 ) coefficients for K 0 S and Λ/ Λ as a function of p T for PbPb at 2.76 TeV and pPb at 5.02 TeV [20].Due to the limited statistics the multiplicity range has been enlarged to 185 ≤ N o f f line trk < 350 for both systems.The p T dependences of v 3 are found to be similar to those of v 2 for K 0 S and Λ/ Λ.The mass-ordering effect and crossover at p T ∼ 2 GeV/c manifest also for v 3 .

Summary
Since the first observation at RHIC almost a decade ago, understanding the origin of the near-side ridge structure in the long-range two-particle correlation functions has been prime interest in heavy-ion collisions at colliders.The LHC experiments measured much stronger ridge structure in PbPb collisions at 2.76 TeV.Furthermore, CMS found the near-side ridge structure at low transverse momenta even in high-multiplicity pp events, which is absent in hadron collision data as well as Monte-Carlo simulations.To provide more insights on the long-range two-particle correlations and flow harmonics, CMS analyzed the PbPb and pPb data at the LHC.
The integrated near-side associated yields for the longrange ridge region were analyzed as a function of transverse momentum in PbPb and pPb collisions for highmultipicity events.The long-range ridge yields increase with transverse momentum, reaching a maximum at 2-3 EPJ Web of Conferences 01005-p.6  GeV/c, and gradually decrease at higher transverse momentum for both systems.The single-particle secondorder Fourier coefficients (v 2 ) were extracted from the long-range two-particle correlation functions.The v 2 data exhibit a moderate increase with multiplicity in PbPb but remain relatively constant in pPb, especially at highmultiplicity bins.The magnitude of v 2 is observed to be larger in PbPb than in pPb over a wide multiplicity range.The v 2 values from multiparticle cumulant correlations and the LYZ method were compared with the present data.The v 2 in PbPb increases with multiplicity, but that in pPb show little dependence on multiplicity.On the other hand, the single-particle third-order Fourier coefficients (v 3 ) is similar each other for PbPb and pPb in the same event multiplicity bin.
The pseudorapidity dependences of the near-side ridge yield and the single-particle Fourier coefficients were investigated by limiting the trigger particles to a narrow η range.The two η triggers for Pb-going and p-going sides were chosen.The long-range near-side ridge yields for high-multiplicity pPb events showed different η dependences for the two triggers.The ridge yield is larger when the two particles are closer and decreases towards higher η assoc for the Pb-going-side trigger, but almost indepen-  dent of η assoc for the p-going-side trigger.In the hydrodynamic scenario, the ridge yield is related to the pair density per trigger particle of the underlying event.The present data are qualitatively in accordance with the dN/dη distribution of the underlying event.
Finally, the long-range two-particle correlation functions were analyzed for identified strange hadrons, K 0 S and Λ/ Λ, in PbPb and pPb.The two-dimensional two-particle correlation functions for K 0 S − h ± and Λ/ Λ − h ± pairs show long-range ridge structures extending more than 4.8 units of |Δη| in high-multiplicity pPb events.The single-particle harmonics v 2 and v 3 were extracted for K 0 S and Λ/ Λ for PbPb and pPb.The mass ordering and crossover of v 2 and v 3 at p T ∼ 2 GeV/c were observed: the v 2 and v 3 of K 0 S is systematically larger than those of Λ/ Λ in the low p T region at around 2 GeV/c, and vice versa at the higher p T region.

Figure 1 .
Figure 1.Integrated near-side associated yields as a function of p trig T for (a) the short-range jet region (|Δη|<1) and (b) the long-range ridge region (2< |Δη| < 4) [8].The event samples are chosen for the most central 5% PbPb collisions at 2.76 TeV with 2 < p assoc T < 4 GeV/c.The error bars represent the statistical uncertainties and the brackets around the symbols represent the systematic uncertainties.The solid lines are the calculations by PYTHIA8 of pp collisions at the same energy.The ridge-region yields are extracted by integrating the near-side long range Δφ correlation functions, and the jet-region yields are estimated by the difference between the short-and longrange near-side integrals.

Figure 3 .
Figure 3. Single-particle harmonics, v 2 ∼ v 5 , extracted from the long-range two-particle azimuthal correlations as a function of the number of participant nucleons (N part ) in PbPb collisions at 2.76 TeV [10].The chosen transverse-momentum ranges for the triggered and associated hadrons are 1 < p T < 1.5 GeV/c and 1 < p assoc T < 3 GeV/c, respectively.

Figure 4 .Figure 4 < 3
Figure 4. Two-dimensional two-particle correlation functions for (a) PbPb at 2.76 TeV and (b) pPb at 5.02 TeV [11].The analyzed multiplicity range of 220 ≤ N o f f line trk < 260, is same for PbPb and pPb collisions, and the transverse-momentum range of 1 < p T < 3 GeV/c is same for the triggered and associated particles.The sharp near-side peaks for jets are truncated for better illustration of the long-range ridge structure.
show the extracted v 2 values as a function of N o f f line trk for 0.3 < p T < 3.0 GeV/c.The v 2 {2, |Δη| > 2} values exhibit a moderate increase with N o f f line trk in PbPb but remain relatively constant in pPb, especially, at high multiplicity.The magnitude of v 2 {2, |Δη| > 2} is found to be larger in PbPb than in pPb over a wide multiplicity range.
represent the extracted v 3 values after the low-multiplicity data with N o f f line trk < 20 are subtracted for V nΔ to get rid of the enhanced jet correlations coming from the preferential selection of highmultiplicity events.As this subtraction procedure usually affects the high-p T region of low-multipicity events, v 2 {2, |Δη| > 2} and v 3 {2, |Δη| > 2} remain almost unchanged in the high-multiplicity region for N o f f line trk > 200.XLIV International Symposium on Multiparticle Dynamics (ISMD 2014) 01005-p.3

Figure 5 .
Figure 5. Integrated near-side associated yields as a function of p trig T for (a) the long-range ridge region (|Δη| > 2) and (b) the short-range jet region (|Δη|<1).For the short-range jet components in (b), the long-range ridge components are subtracted [11].The multiplicity range of 220 ≤ N o f f line trk

Figure 6 .
Figure 6.Single-particle second-order harmonic (v 2 ) coefficients for 0.3 < p T < 3.0 GeV/c as a function of N o f f line trk in PbPb at 2.76 TeV (left) and pPb at 5.02 TeV (right), obtained by various analysis methods [14].The open circles that are extracted by the long-range two-particle correlation functions [11] are compared with the results from multiparticle cumulant correlations and the LYZ method [14].

Figure 7 .
Figure 7. Single-particle third-order harmonic (v 3 ) coefficients as a function of N o f f line trk for 0.3 < p T < 3.0 GeV/c in PbPb at 2.76 TeV (circles) and pPb at 5.02 TeV (squares) obtained from the long-range two-particle correlation analysis [11].The solid and dotted lines represent the results after the low-multiplicity data for N o f f line trk

Figure 8 .
Figure 8. Near-side ridge yields for 0.3 < p trig/assoc T < 3 GeV/c as a function of the associated particle's η, η assoc , for highmultiplicity (220 < N o f f line trk < 260) pPb events [18].The triggered η ranges are -2.4 < η trig < -2.0 for the Pb-going-side trigger data (red) and 2.0 < η trig < 2.4 for the p-going-side trigger data (blue).The statistical errors are smaller than the symbol size, and the shaded bands represent systematic uncertainties.

Figure 9 .
Figure 9. Self-normalized single-particle anisotropy parameters, v 2 (η assoc )/v 2 (0) (left) and v 3 (η assoc )/v 3 (0) (right), in 0.3 < p T < 3.0 GeV/c as a function of η assoc for high-multiplicity pPb events (220 < N o f f line trk < 260) at 5.02 TeV [18].The solid and open circles represent the Pb-going-side and the p-going-side triggers, respectively, after the low-multiplicity events (N o f f line trk < 20) are subtracted.The lines show the data without the subtraction.

Figure 10 .
Figure 10.Invariant-mass distributions of K 0 S (left) and Λ/ Λ (right) candidates for high-multiplicity pPb events at 5.02 TeV [20].The multiplicity range is 220 ≤ N o f f line trk < 260 and the transverse-momentum range is 1 < p T < 3 GeV/c for the triggered and associated particles.The solid line in each panel represents the fit function that is the sum of a double Gaussian for signal and the 4th-order polynomial for background.

Figure 11 .
Figure 11.Two-dimensional two-particle correlation functions for K 0 S − h ± (left) and Λ/ Λ − h ± (right) pairs in high-multiplicity pPb events at 5.02 TeV [20].The multiplicity range is 220 ≤ N o f f line trk < 260 and the transverse-momentum range is 1 < p T < 3 GeV/c for the triggered and associated particles.The sharp near-side peaks for jets are truncated for better illustration of the long-range ridge structures.

Figure 12 .
Figure 12.Single-particle second-order harmonic (v 2 ) coefficients extracted from the long-range correlation functions for K 0 S (squares), Λ/ Λ (circles), and unidentified charged hadrons h ± (crosses) as a function of p T at different multiplicity bins[20].The upper panels are for PbPb at 2.76 TeV and the lower panels are for pPb at 5.02 TeV.

Figure 13 .
Figure 13.Single-particle third-order harmonic (v 3 ) coefficients extracted from the long-range correlation functions for K 0 S (squares), Λ/ Λ (circles), and unidentified charged hadrons h ± (crosses) as a function of p T for PbPb at 2.76 TeV (left) and pPb at 5.02 TeV (right) [20].The multiplicity condition, 185 ≤ N o f f line trk