Evidence for collective multiparticle correlations in p − P b collisions

: The second-order azimuthal anisotropy Fourier harmonics, v2, are obtained in p − Pb and PbPb collisions over a wide pseudorapidity ( η ) range based on correlations among six or more charged particles. The p-Pb data, corresponding to an integrated luminosity of 35 nb 1 , were collected during the 2013 LHC p -Pb run at a nucleon-nucleon center-of-mass energy of 5 . 02 TeV by the CMS experiment. A sample of semiperipheral PbPb collision data at √ s NN =2.76 TeV, corresponding to an integrated luminosity of 2 . 5 µb − 1 and covering a similar range of particle multiplicities as the p − Pb data, is also analyzed for comparison. The six- and eight-particle cumulant and the Lee-Yang zeros methods are used to extract the v 2 coefficients, extending previous studies of two- and four-particle correlations. For both the p − Pb and PbPb systems, the v 2 values obtained with correlations among more than four particles are consistent with previously published four-particle results. These data support the interpretation of a collective origin for the previously observed long-range ( ∆ η ) correlations in both systems. The ratios of v 2 values corresponding to correlations including different numbers of particles are compared to theoretical predictions that assume a hydrodynamic behavior of a p-Pb system dominated by fluctuations in the positions of participant nucleons. These results provide new The second-order azimuthal anisotropy Fourier harmonics, v 2 , are obtained in p -Pb and PbPb collisions over a wide pseudorapidity ( η ) range based on correlations among six or more charged particles. The p -Pb data, corresponding to an integrated luminosity of 35 nb − 1 , were collected during the 2013 LHC p -Pb run at a nucleon-nucleon center-of-mass energy of 5 . 02 TeV by the CMS experiment. A sample of semiperipheral PbPb collision data at ﬃﬃﬃﬃﬃﬃﬃﬃ s NN p ¼ 2 . 76 TeV, corresponding to an integrated luminosity of 2 . 5 μ b − 1 and covering a similar range of particle multiplicities as the p -Pb data, is also analyzed for comparison. The six- and eight-particle cumulant and the Lee-Yang zeros methods are used to extract the v 2 coefficients, extending previous studies of two- and four-particle correlations. For both the p -Pb and PbPb systems, the v 2 values obtained with correlations among more than four particles are consistent with previously published four-particle results. These data support the interpretation of a collective origin for the previously observed long-range (large Δ η ) correlations in both systems. The ratios of v 2 values corresponding to correlations including different numbers of particles are compared to theoretical predictions that assume a hydrodynamic behavior of a p -Pb system dominated by fluctuations in the positions of participant nucleons. These results provide new insights into the multiparticle dynamics of collision systems with a very small overlapping region.

The second-order azimuthal anisotropy Fourier harmonics, v 2 , are obtained in p-Pb and PbPb collisions over a wide pseudorapidity (η) range based on correlations among six or more charged particles. The p-Pb data, corresponding to an integrated luminosity of 35 nb −1 , were collected during the 2013 LHC p-Pb run at a nucleon-nucleon center-of-mass energy of 5.02 TeV by the CMS experiment. A sample of semiperipheral PbPb collision data at ffiffiffiffiffiffiffi ffi s NN p ¼ 2.76 TeV, corresponding to an integrated luminosity of 2.5 μb −1 and covering a similar range of particle multiplicities as the p-Pb data, is also analyzed for comparison. The six-and eight-particle cumulant and the Lee-Yang zeros methods are used to extract the v 2 coefficients, extending previous studies of two-and four-particle correlations. For both the p-Pb and PbPb systems, the v 2 values obtained with correlations among more than four particles are consistent with previously published four-particle results. These data support the interpretation of a collective origin for the previously observed long-range (large Δη) correlations in both systems. The ratios of v 2 values corresponding to correlations including different numbers of particles are compared to theoretical predictions that assume a hydrodynamic behavior of a p-Pb system dominated by fluctuations in the positions of participant nucleons. These results provide new insights into the multiparticle dynamics of collision systems with a very small overlapping region. DOI: 10.1103/PhysRevLett.115.012301 PACS numbers: 25.75.Gz Measurements at the CERN LHC have led to the discovery of two-particle azimuthal correlation structures at large relative pseudorapidity (long range) in protonproton (pp) [1] and proton-lead (p-Pb) [2][3][4][5] collisions. Similar long-range structure has also been observed for ffiffiffiffiffiffiffi ffi s NN p ¼ 200 GeV deuteron-gold (d þ Au) collisions at RHIC [6,7]. The results extend previous studies of relativistic heavy-ion collisions, such as for the copper-copper [8], gold-gold [8][9][10][11][12], and lead-lead (PbPb) [13][14][15][16][17][18] systems, where similar long-range, two-particle correlations at small relative azimuthal angle jΔϕj ≈ 0 were first observed. A fundamental question is whether the observed behavior results from correlations exclusively between particle pairs, or if it is a multiparticle, collective effect. It has been suggested that the hydrodynamic collective flow of a strongly interacting and expanding medium [19][20][21] is responsible for these long-range correlations in central and midcentral heavy-ion collisions. The origin of the observed long-range correlations in collision systems with a small overlapping region, such as for pp and p-Pb collisions, is not clear since for these systems the formation of an extended hot medium is not necessarily expected. Various theoretical models have been proposed to interpret the pp [22,23] and p-Pb results, including initial-state gluon saturation without any final state interactions [24,25] and, similar to what is thought to occur in heavier systems, hydrodynamic behavior that develops in a conjectured high-density medium [26][27][28]. These models have been successful in describing different aspects of the previous experimental results.
To further investigate the multiparticle nature of the observed long-range correlation phenomena, in this Letter we present measurements of correlations among six or more charged particles for p-Pb collisions at a center-ofmass energy per nucleon pair of ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV. The azimuthal dependence of particle production is typically characterized by an expansion in Fourier harmonics (v n ) [29]. In hydrodynamic models, the second (v 2 ) and third (v 3 ) harmonics, called "elliptic" and "triangular" flow [30], respectively, directly reflect the response to the initial collision geometry and fluctuations [31][32][33], providing insight into the fundamental transport properties of the medium. First attempts to establish the multiparticle nature of the correlations observed in p-Pb collisions were presented in Refs. [34,35] by directly measuring fourparticle azimuthal correlations, where the elliptic flow signal was obtained using the four-particle cumulant method [36]. However, four-particle correlations can still be affected by contributions from noncollective effects such as fragmentation of back-to-back jets. By extending the studies to six-and eight-particle cumulants [36] and by also obtaining results using the Lee-Yang zeros (LYZ) method, which involves correlations among all detected particles [37,38], it is possible to further explore the collective nature of the correlations. High-statistics data obtained by the CMS experiment during the 2013 p-Pb run at the LHC are used. With a sample of very high final state multiplicity p-Pb collisions, the correlation data have been studied in a regime that is comparable to the charged particle multiplicity of the 50% most peripheral (semiperipheral) PbPb collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 2.76 TeV. The CMS detector comprises a number of subsystems [39]. The results in this Letter are mainly based on the silicon tracker information. The silicon tracker, located in the 3.8 T field of a superconducting solenoid, consists of 1440 silicon pixel and 15148 silicon strip detector modules. The silicon tracker measures charged particles within the pseudorapidity range jηj < 2.5, and it provides an impact parameter resolution of ≈15 μm and a transverse momentum (p T ) resolution better than 1.5% at p T ≈ 100 GeV=c. The electromagnetic (ECAL) and hadron (HCAL) calorimeters are also located inside the solenoid and cover the pseudorapidity range jηj < 3.0. The HCAL barrel and end caps are sampling calorimeters composed of brass and scintillator plates. The ECAL consists of lead tungstate crystals arranged in a quasiprojective geometry. Iron and quartz-fiber Čerenkov hadron forward (HF) calorimeters cover the range 2.9 < jηj < 5.2 on either side of the interaction region. These HF calorimeters are azimuthally subdivided into 20°modular wedges and further segmented to form 0.175 × 0.175 rad ðΔη × ΔϕÞ "towers." The detailed Monte Carlo (MC) simulation of the CMS detector response is based on GEANT4 [40].
The analysis is performed using data recorded by CMS during the LHC p-Pb run in 2013. The data set corresponds to an integrated luminosity of 35 nb −1 . The beam energies were 4 TeV for protons and 1.58 TeV per nucleon for lead nuclei, resulting in ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV. The beam directions were reversed during the run, allowing a check of one potential source of systematic uncertainties. As a result of the energy difference between the colliding beams, the nucleon-nucleon center of mass in the p-Pb collisions is not at rest with respect to the laboratory frame. Massless particles emitted at η cm ¼ 0 in the nucleon-nucleon center-of-mass frame will be detected at η ¼ −0.465 (clockwise proton beam) or 0.465 (counterclockwise proton beam) in the laboratory frame. A sample of ffiffiffiffiffiffiffi ffi s NN p ¼ 2.76 TeV PbPb data collected during the 2011 LHC heavyion run, corresponding to an integrated luminosity of 2.3 μb −1 , is also analyzed for comparison purposes. The triggers and event selection, as well as track reconstruction and selection, are summarized below and are identical to those used in Ref. [35].
Minimum bias (MB) p-Pb events were triggered by requiring at least one track with p T > 0.4 GeV=c to be found in the pixel tracker for a p-Pb bunch crossing. Only a small fraction (∼10 −3 ) of all MB triggered events were recorded (i.e., the trigger was "prescaled") because of hardware limits on the data acquisition rate. In order to select high-multiplicity p-Pb collisions, a dedicated highmultiplicity trigger was implemented using the CMS level-1 (L1) and high-level trigger (HLT) systems. At L1, three triggers requiring the total transverse energy summed over ECAL and HCAL to be greater than 20, 40, and 60 GeV were used since these cuts selected roughly the same events as the three HLT multiplicity selections discussed below. On-line track reconstruction for the HLT was based on the three layers of pixel detectors, and it required a track origin within a cylindrical region of length 30 cm along the beam and a radius 0.2 cm perpendicular to the beam around the nominal interaction point. For each event, the vertex reconstructed with the highest number of pixel tracks was selected. The number of pixel tracks (N on-line trk ) with jηj < 2.4, p T > 0.4 GeV=c, and a distance of closest approach to this vertex of 0.4 cm or less, was determined for each event. Several high-multiplicity ranges were defined with prescale factors that were progressively reduced until, for the highest multiplicity events, no prescaling was applied.
In the off-line analysis, hadronic collisions are selected by requiring a coincidence of at least one HF calorimeter tower containing more than 3 GeVof total energy in each of the HF detectors. Only towers within 3 < jηj < 5 are used to avoid the edges of the HF acceptance. Events are also required to contain at least one reconstructed primary vertex within 15 cm of the nominal interaction point along the beam axis and within 0.15 cm transverse to the beam trajectory. At least two reconstructed tracks are required to be associated with the primary vertex. The beam related background is suppressed by rejecting events for which less than 25% of all reconstructed tracks pass the track selection criteria of this analysis. The p-Pb instantaneous luminosity provided by the LHC in the 2013 run resulted in an approximately 3% probability of at least one additional interaction occurring in the same bunch crossing. Following the procedure developed in Ref.
[35] for rejecting such "pileup" events, a 99.8% purity of singleinteraction events is achieved for the p-Pb collisions belonging to the highest multiplicity class studied in this Letter. In p-Pb interactions simulated with the EPOS [41] and HIJING [42] event generators, requiring at least one primary particle with total energy E > 3 GeV in each of the η ranges −5 < η < −3 and 3 < η < 5 is found to select 97%-98% of the total inelastic hadronic cross section.
The CMS "high-quality" tracks described in Ref.
[43] are used in this analysis. Additionally, a reconstructed track is only considered as a candidate track from the primary vertex if the significance of the separation along the beam axis (z) between the track and the best vertex, d z =σðd z Þ, and the significance of the track-vertex impact parameter measured transverse to the beam, d T =σðd T Þ, are each less than 3. The relative uncertainty in the transverse momentum measurement, σðp T Þ=p T , is required to be less than week ending 3 JULY 2015 012301-2 10%. To ensure high tracking efficiency and to reduce the rate of incorrectly reconstructed tracks, only tracks within jηj < 2.4 and with 0.3 < p T < 3.0 GeV=c are used in the analysis. A different p T cutoff of 0.4 GeV=c is used in the multiplicity determination because of constraints on the online processing time for the HLT. The entire p-Pb data set is divided into classes of reconstructed track multiplicity, N off-line trk . The multiplicity classification in this analysis is identical to that used in Ref. [35], where more details are provided, including a table relating N off-line trk to the fraction of the MB triggered events. A subset of semiperipheral PbPb data collected during the 2011 LHC heavy-ion run with a MB trigger is also reanalyzed in order to directly compare the p-Pb and PbPb systems at the same track multiplicity. This PbPb sample is reprocessed using the same event selection and track reconstruction as for the present p-Pb analysis. A description of the 2011 PbPb data can be found in Ref. [44].
Extending the previous two-and four-particle azimuthal correlation measurements of Ref.
[35], six-and eightparticle azimuthal correlations [36] are evaluated in this analysis as Here ϕ i ði ¼ 1; …; 8Þ are the azimuthal angles of one unique combination of multiple particles in an event, n is the harmonic number, and ⟪ Á Á Á ⟫ represents the average over all combinations from all events within a given multiplicity range. The corresponding cumulants, c n f6g and c n f8g, are calculated as follows: To account for detector effects, such as the tracking efficiency, the Q-cumulant method was extended in Ref.
[45] to allow for particles having different weights. Each reconstructed track is weighted by a correction factor to account for the reconstruction efficiency, detector acceptance, and fraction of misreconstructed tracks. This factor is derived as a function of p T and η, as described in Refs. [13,14], based on MC simulations. The combined geometrical acceptance and efficiency for track reconstruction exceeds 60% for p T ≈ 0.3 GeV=c and jηj < 2.4. The efficiency is greater than 90% in the jηj < 1 region for p T > 0.6 GeV=c. For the entire multiplicity range (up to N off-line trk ∼350) studied in this Letter, no dependence of the tracking efficiency on multiplicity is found and the rate of misreconstructed tracks remains at the 1%-2% level. The software package provided by Ref. [45] is used to implement the weights of the individual tracks in the cumulant calculations.
The LYZ method [37,38] allows a direct study of the large-order behavior by using the asymptotic form of the cumulant expansion to relate locations of the zeros of a generating function to the azimuthal correlations. This method has been employed in previous CMS PbPb analyses [17,46]. For each multiplicity bin, the v 2 harmonic averaged over 0.3 < p T < 3.0 GeV=c is found using an integral generating function [17]. Similar to the cumulant methods, a weight for each track is implemented to account for detector-related effects. In both methods, the statistical uncertainties are evaluated from data by dividing the data set into 20 subsets with roughly equal numbers of events and evaluating the standard deviation of the resulting distributions of the cumulant or v 2 fLYZg values. In the case of a low multiplicity or small flow signal, the LYZ method may overestimate the true collective flow. This effect was studied using MC pseudoexperiments for the event multiplicities covered in this analysis, and a small correction is applied to the data. The correction is less than 3% in the lowest multiplicity bin and becomes much smaller in higher-multiplicity bins. This correction is also included in the quoted LYZ systematic uncertainties.
Systematic uncertainties are estimated by varying the track quality requirements, by comparing the results using efficiency correction tables from different MC event generators, and by exploring the sensitivity of the results to the vertex position and to the N off-line trk bin width. For the p-Pb data, potential HLT bias and pileup effects are also studied by requiring the presence of only a single reconstructed vertex. No evident N off-line trk or beam direction dependent systematic effects are observed. For p-Pb collisions, a 5% systematic uncertainty is obtained for v 2 f6g and a 6% uncertainty is found for both v 2 f8g and v 2 fLYZg. The corresponding uncertainties for PbPb collisions are 2% for v 2 f6g and v 2 f8g, and 4% for v 2 fLYZg.
In Fig. 1, the six-and eight-particle cumulants, c 2 f6g and c 2 f8g, for particle p T of 0.3-3.0 GeV=c in 2.76 TeV PbPb and 5.02 TeV p-Pb collisions are shown as a function of event multiplicity. The cumulants shown are required to be at least 2 standard deviations away from their physics boundaries (c 2 f6g=σ c 2 f6g > 2, c 2 f8g=σ c 2 f8g < −2) so that the statistical uncertainties can be propagated as Gaussian The v 2 values derived using the LYZ method involving correlations among all particles are also shown. For each multiplicity bin, the values of v 2 f4g, v 2 f6g, v 2 f8g, and v 2 fLYZg for p-Pb collisions are found to be in agreement within 10%. For part of the multiplicity range, the values for v 2 f4g are larger than the others by a statistically significant amount, although still within 10%. The corresponding PbPb values are consistently higher than for p-Pb collisions, but within the PbPb system are found to be in agreement within 2% for most multiplicity ranges and within 10% for all multiplicities. This supports the collective nature of the observed correlations, i.e., involving all particles from each system, and is inconsistent with a jetrelated origin involving correlations among only a few particles. The v 2 data from two-particle correlations are consistently above the multiparticle correlation data. This behavior can be understood in hydrodynamic models, where event-by-event participant geometry fluctuations of the v 2 coefficient are expected to affect the two-and multiparticle cumulants differently [48,49]. Note that, to minimize jet-related nonflow effects, the v 2 f2g values are obtained with an η gap of 2 units between the two particles. Possible residual nonflow effects resulting from back-toback jet correlations are estimated using very low multiplicity events in Ref. [35]. Based on this analysis, such nonflow effects are expected to make a negligible contribution to v 2 f2g in very high multiplicity events. In PbPb collisions, the v 2 values from all methods show an increase with multiplicity, while little multiplicity dependence is seen for the p-Pb data. This difference might reflect the presence of a lenticular overlap geometry in PbPb collisions-which is not expected in p-Pb collisions-that gives rise to a large (and varying) initial elliptic asymmetry in the PbPb system.
The effect of fluctuation-driven initial-state eccentricities on multiparticle cumulants has recently been explored in the context of hydrodynamic behavior of the resulting medium [50,51]. For fluctuation-driven initial-state conditions, ratios of v 2 values derived from various orders of multiparticle cumulants are predicted to follow a universal behavior [50]. In Fig. 3, ratios of v 2 f6g=v 2 f4g (top panel) and v 2 f8g=v 2 f6g (bottom panel) are calculated and plotted against v 2 f4g=v 2 f2g in p-Pb collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV. The v 2 f2g and v 2 f4g data are taken from previously published CMS results [35]. The solid curves correspond to theoretical predictions for both large and small systems based on hydrodynamics and the assumption that the initial-state geometry is purely driven Open data points are the published two-and four-particle v 2 results [35]. Solid data points are v 2 results obtained from sixand eight-particle cumulants, and LYZ methods, averaged over the particle p T range of 0. by fluctuations [50]. The ratios from PbPb collisions are also shown for comparison. Note that the geometry of very central PbPb collisions might be dominated by fluctuations, but for these semiperipheral PbPb collisions the lenticular shape of the overlap region should also strongly contribute to the v 2 values. The CMS p-Pb data are consistent with the predictions, within statistical and systematic uncertainties. The systematic uncertainties in the ratios presented in Fig. 3 are estimated to be 2.4% for v 2 f4g=v 2 f2g for both the p-Pb and the PbPb collisions, 1% for v 2 f6g=v 2 f4g in the p-Pb and PbPb collisions, and 3.6% and 1% for v 2 f8g=v 2 f6g in the p-Pb and the PbPb collisions, respectively. Since they are all derived from the same data, the systematic uncertainties for the different cumulant orders are highly correlated and therefore partially cancel in the ratios.
Recently, other theoretical models based on quantum chromodynamics, and not involving hydrodynamics, have also been suggested to explain the observed multiparticle correlations in p-Pb collisions [52,53]. Unlike the descriptions based on hydrodynamic behavior, these models do not require significant final state interactions among quarks and gluons. They suggest similar values for v 2 f4g, v 2 f6g, v 2 f8g, and v 2 fLYZg-without yet, however, providing quantitative predictions.
In summary, multiparticle azimuthal correlations among six, eight, and all particles have been measured in p-Pb collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV by the CMS experiment. The new measurements extend previous CMS two-and four-particle correlation analyses of p-Pb collisions and strongly constrain possible explanations for the observed correlations. A direct comparison of the correlation data for p-Pb and PbPb collisions is presented as a function of particle multiplicity. Averaging over the particle p T range of 0.3-3.0 GeV=c, multiparticle correlation signals are observed in both p-Pb and PbPb collisions. The secondorder azimuthal anisotropy Fourier harmonic, v 2 , is extracted using six-and eight-particle cumulants and using the LYZ method which involves all particles. The v 2 values obtained using correlation methods including four or more particles are consistent within AE2% for the PbPb system, and within AE10% for the p-Pb system. This measurement supports the collective nature of the observed correlations. The ratios of v 2 values obtained using different numbers of particles are found to be consistent with hydrodynamic model calculations for p-Pb collisions.
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and the operation of the LHC and the CMS detector [1] CMS Collaboration, Observation of long-range near-side angular correlations in proton-proton collisions at the LHC, J. High Energy Phys. 09 (2010)