Flow Dominance and Factorization of Transverse Momentum Correlations in Pb-Pb Collisions at the LHC

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Flow Dominance and Factorization of Transverse Momentum Correlations in Pb-Pb Collisions at the LHC ALICE Collaboration ALICE Collaboration. (2017). Flow Dominance and Factorization of Transverse Momentum Correlations in Pb-Pb Collisions at the LHC. Physical Review Letters, 118(16), Article 162302. https://doi.org/10.1103/PhysRevLett.118.162302 2017 Flow Dominance and Factorization of Transverse Momentum Correlations in Pb-Pb Collisions at the LHC J. Adam et al.* (ALICE Collaboration) (Received 22 February 2017; published 21 April 2017) We present the first measurement of the two-particle transverse momentum differential correlation function, P2≡hΔpTΔpTi=hpTi2, in Pb-Pb collisions at ffiffiffiffiffiffiffiffi sNN p¼2.76 TeV. Results for P2are reported as a function of the relative pseudorapidity (Δη) and azimuthal angle (Δφ) between two particles for different collision centralities. The Δϕdependence is found to be largely independent of Δηfor jΔηj≥0.9. In the 5% most central Pb-Pb collisions, the two-particle transverse momentum correlation function exhibits a clear double-hump structure around Δφ¼π(i.e., on the away side), which is not observed in number correlations in the same centrality range, and thus provides an indication of the dominance of triangular flow in this collision centrality. Fourier decompositions of P2, studied as a function of the collision centrality, show that correlations at jΔηj≥0.9can be well reproduced by a flow ansatz based on the notion that measured transverse momentum correlations are strictly determined by the collective motion of the system. DOI: 10.1103/PhysRevLett.118.162302 Measurements of particle production and their correlations in heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) have provided very compelling evidence that the produced matter is characterized by extremely high temperatures and energy densities consistent with a deconfined, but strongly interacting quark-gluon plasma (sQGP). Evidence for the production of the sQGP is provided by observations of a large suppression of particle production at momenta pT≳ 3GeV=c relative to that observed in pp collisions and a strong suppression of away-side particles observed in twoparticle number correlations, as well as by anisotropic flow studies (anisotropies in particle azimuthal distributions relative to the reaction plane defined by the beam axis and a line connecting the centers of colliding nuclei) [1–11]. The comparison of measured flow coefficients, vn, with predictions from hydrodynamical models indicates that the sQGP has a vanishingly small shear viscosity over entropy density ratio [12]. Furthermore, the observation of an approximate number of constituent quark scaling of flow coefficients in the 2<p T<4GeV=c range, suggested as a signature of a deconfined medium [13], was reported by RHIC and LHC experiments [14,15]. These results imply that the two-particle number correlations observed in the region of low pT(<2GeV=c), corresponding to the bulk of particle production, are largely determined by anisotropic flow. Such flow dominance is manifested, in particular, by an approximate factorization of the measured flow coefficients, VnΔðη1;p T;1;η2;p T;2Þ¼hcosðnΔφÞi ¼ hvnðη1;p T;1Þvnðη2;p T;2Þi, observed for pairs of particles at relative pseudorapidity Δη>0.8, in different transverse momentum bins up to pT≈3–5GeV=c [16]. Two-particle transverse momentum correlations [17–21] provide additional insights into the dynamics of multiparticle production and can be used to further examine the flow dominance of two-particle correlation functions. One expects, in particular, that in the presence of anisotropic flow the differential transverse momentum correlator hΔpTΔpTishould feature azimuthal Fourier decomposition coefficients calculable with a simple formula, hereafter called the flow ansatz, in terms of the regular and pT weighted flow coefficients [17]. Such a simple relation, discussed in more detail below, is not expected for particle production arising from processes not related to the common symmetry plane, known as nonflow, such as jets or resonance decays. An agreement between the Fourier coefficients of the hΔpTΔpTicorrelator and those calculated with the flow ansatz should thus provide additional evidence of the dominance of collective flow effects. In this Letter, we present the first measurements of the differential transverse momentum correlations in Pb-Pb collisions at ffiffiffiffiffiffiffiffi sNN p¼2.76 TeV in terms of the dimensionless correlator P2defined as P2¼hΔpTΔpTiðΔη;ΔφÞ hpTi2 ¼1 hpTi2RpT;max pT;min ρ2ð~ p1;~ p2ÞΔpT;1ΔpT;2dpT;1dpT;2 RpT;max pT;min ρ2ð~ p1;~ p2ÞdpT;1dpT;2 ;ð1Þ *Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. PRL 118, 162302 (2017) PHYSICAL REVIEW LETTERS week ending 21 APRIL 2017 0031-9007=17=118(16)=162302(12) 162302-1 © 2017 CERN, for the ALICE Collaboration where ΔpT;i ¼pT;i −hpTi, with hpTi¼Rρ1pTdpT= Rρ1dpT, the inclusive average transverse momentum of particles observed in the pT;min ≤pT≤pT;max range. The quantities ρ1and ρ2represent single- and two-particle densities, respectively. For particle correlations induced strictly by anisotropic emission relative to the reaction plane, the Fourier coefficients of P2,vn½P2, should be determined by regular and the pTweighted flow coefficients defined according to the following flow ansatz [17]: vn½P2≅vpT n=hpTi−vn;ð2Þ where vnand vpT n¼Rρ1vnðpTÞpTdpT=Rρ1dpTare the regular and pTweighted coefficients, respectively [17,22]. Thus, we shall compare the Fourier coefficients of the P2 correlator to values expected from this ansatz based on coefficients vnand vpT nmeasured with traditional flow methods, e.g., the scalar product method [22]. This study is based on an analysis of a 14 ×106events subset of a sample of minimum bias trigger events recorded with the ALICE detector during the LHC run 1 in 2010. Detailed descriptions of the ALICE detector, its subsystems, and their respective performance have been reported in Refs. [23–26]. For this study, the inner tracking system and the time projection chamber (TPC) were used to reconstruct charged-particle tracks, while the V0 detector and the silicon pixel detector formed the basis of the online minimum bias trigger used to acquire the data, as described in Refs. [5,6]. The ALICE solenoidal magnet was operated with a field of 0.5 T with both positive and negative polarities. Events included in this analysis were required to have a single reconstructed primary vertex within 10 cm of the nominal interaction point along the beam axis, hereafter taken to be the zaxis. The fraction of pileup events in the analysis sample is found to be negligible after applying dedicated pileup removal criteria [26]. Correlation functions reported in this Letter are based on charged-particle tracks measured in the pseudorapidity range jηj<1.0and with full azimuthal coverage 0≤φ<2π. The analysis was limited to particles produced with 0.2<p T<2.0GeV=c corresponding largely to particles emerging from the bulk of the matter. Only tracks with a minimum of 70 reconstructed space points in the TPC, out of a maximum of 159, were included in the analysis. Contributions from photon conversions into eþe− pairs were suppressed based on an electron rejection criterion relying on the truncated average of the specific ionization energy loss hdE=dximeasured in the TPC. Tracks with hdE=dxilying within 3σdE=dx of the Bethe- Bloch parametrization of the dE=dx expectation value for electrons and at least 3σdE=dx away from the relevant parameterizations for π,K, and pwere removed. In addition, the suppression of the contamination from secondary particles originating from weak decays and from the interaction of particles with the detector material was accomplished by imposing upper limits of 3.2 and 2.4 cm (rms ∼0.36 cm) for the distance of closest approach (DCA) of a track to the reconstructed vertex in the longitudinal (DCAz) and radial (DCAxy) directions, respectively. These criteria lead to a reconstruction efficiency of about 80% for primary particles and contamination from secondaries of about 5% at pT¼1GeV=c [27]. No filters were used to suppress like-sign (LS) particle correlations resulting from Hanbury Brown–Twiss effects, which produce a strong and narrow peak centered at Δη;Δφ¼0in LS correlation functions. Corrections for single track losses were carried out using the weight technique described in Ref. [28] with weights calculated separately for positively and negatively charged tracks, positive and negative solenoidal magnetic fields, and with 40 vertex position bins in the fiducial range jzj≤10 cm. Pair inefficiencies associated with track merging or crossing (e.g., two tracks being partly or entirely reconstructed as a single track) within the TPC were corrected for based on track charge and momentum ordering techniques [29]. The P2correla- tors were measured separately for charge pair combinations þþ,þ−, and −− and were combined with equal weights to produce the charge-independent correlation functions reported in this Letter. Systematic uncertainties were investigated by repeating the analysis for different operational and analysis conditions including two solenoidal magnetic field polarities and different event and track selection criteria, as well as different track reconstruction methods. Track selection criteria, most particularly the maximum value of the distance of closest approach to the primary vertex, dominate systematic effects. The systematic uncertainties assigned to the measurements of vncoefficients are the quadratic sums of individual contributions and range from 4% in the central 0%–10% collisions to 14% in the peripheral 70%–80% collisions. Figure 1(a) presents the correlator P2measured as a function of Δηand Δφin the 5% most central Pb-Pb collisions. The central range around Δη∼0and Δφ∼ 0ðradÞis left undercorrected by the weight correction procedure mainly due to track merging effects. It is thus not considered in this analysis. [The central range around Δη∼0and Δφ∼0ðradÞis considered, however, in a related ALICE analysis carried out with a mixed event technique [30]]. The correlator P2features a prominent near-side ridge centered at Δφ¼0, extending across the full pseudorapidity range of the measurement. It also features two distinct away-side humps at jΔφ−πj≈60° separated by a weak dip centered at Δφ¼πand also extending across the full pseudorapidity range of the acceptance. Such an away-side correlation feature, which indicates the presence of a strong third harmonic, was previously reported in ultracentral (0%–2%) Pb-Pb collisions at the LHC [16,31,32] as well as in central Au-Au PRL 118, 162302 (2017) PHYSICAL REVIEW LETTERS week ending 21 APRIL 2017 162302-2 collisions at the RHIC but for the latter case only after the subtraction of a correlated component whose shape was exclusively attributed to elliptic flow [33–35]. To further study the azimuthal angle dependence of transverse momentum correlations, projections of the measured P2correlation function are fitted with an unconstrained sixth-order Fourier decomposition in Δφaccording to FðΔφÞ¼b0þ2P6 n¼1bncosðnΔφÞ, as illustrated in Fig. 1(b). We verified that higher-order contributions, with n>6, do not significantly improve the fits for jΔηj≥0.9. Coefficients b5and b6feature large relative errors and are thus not reported in this Letter. The double hump at jΔφ−πj≈60° implies the presence of a strong third harmonic, v3, in the Fourier decompositions of the correlation functions. The large v3likely originates from fluctuations in the initial density profile of colliding nuclei [36]. The flow coefficients obtained from two-particle transverse momentum correlations, vn½P2, calculated according to vn¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bn=ðb0þ1Þ p, are plotted in Fig. 2as a function of centrality for central (0%–5%) up to peripheral collisions (70%–80%). The vn½P2coefficients exhibit a collision centrality dependence qualitatively similar to that of regular flow coefficients obtained from standard flow measurement η Δ 2−1− 012 (rad) ϕ Δ 024 )ϕΔ,ηΔ( 2 P 0 0.2 0.4 3− 10×ALICE, Pb-Pb = 2.76 TeV NN s 0-5% c < 2.0 GeV/ T p0.2 < (a) (rad)ϕΔ 024 )ϕΔ( 2 P 0 0.2 3 − 10× n=2 n=3 n=4 n=1+2+3+4+5+6 = 2.76 TeV NN sALICE, Pb-Pb c < 2.0 GeV/ T p0.2 < 0.9≥|ηΔ| 0-5% (b) FIG. 1. (a) P2ðΔη;ΔφÞin the 5% most central Pb-Pb collisions. The region jΔηj<0.15 and jΔφj<0.13 rad, where the weight technique used in this analysis does not provide a reliable efficiency correction, is excluded. (b) P2ðΔφÞfor jΔηj≥0.9. Systematic errors are shown as gray boxes. Note the statistically significant dip at Δφ∼π. ] 2 P[ n v 0 0.01 0.02 0.03 (a) 0.9≤|ηΔ |≤0.2 = 2.76 TeV NN sALICE, Pb-Pb c < 2.0 GeV/ T p0.2 < Centrality (%) 0 1020304050607080 Ratio 0.8 0.9 1 1.1 1.2 (b) (c) 1.9≤|ηΔ |≤0.9 2 v 3 v 4 v ansatz 2 v ansatz 3 v ansatz 4 v Centrality (%) 0 1020304050607080 (d) FIG. 2. vncoefficients, where n¼2, 3, 4 in the range (a) 0.2≤jΔηj≤0.9and (c) 0.9≤jΔηj≤1.9obtained from the P2correlation function. The coefficients are compared with the expectations from the flow ansatz calculated in their respective Δηranges in Pb-Pb collisions. Statistical errors are shown as vertical solid lines, whereas systematic errors are displayed as colored bands. Ratios of the vn coefficients and their corresponding flow ansatz values are shown in (b) and (d). The errors on the ratios are only statistical. PRL 118, 162302 (2017) PHYSICAL REVIEW LETTERS week ending 21 APRIL 2017 162302-3 methods [22]. In addition, they feature a hierarchy such that v2>v 3>v 4at all centralities except in the 5% most central Pb-Pb collisions, where the third is slightly larger than the second harmonic, thereby explaining the presence of the away-side double hump seen in Fig. 1. This is at variance with the dependence of the regular flow coefficients which, even in the centrality range 0%–5%, exhibit the basic hierarchy v2>v 3>v 4. The observed higher value of v3½P2relative to v2½P2implies that v3should rise faster with increasing pTthan v2, in agreement with explicit measurements of the flow coefficient dependence on pT[37]. We next consider the possible role of nonflow correlations on the correlator P2by comparing, in Fig. 2, the vn½P2coefficients obtained in the ranges 0.2≤jΔηj≤0.9 and 0.9≤jΔηj≤1.9with values predicted by the flow ansatz, introduced above. In the range 0.9≤jΔηj≤1.9 [see Fig. 2(c)], one observes that the coefficients vn½P2 are in very good agreement, at all measured collision centralities, with expectations from the flow ansatz. This agreement provides additional evidence that two-particle correlations in this relative pseudorapidity range are predominantly determined by the collective nature of particle emission at low pT, which motivates the factorization hypothesis used to derive Eq. (2). It also suggests that away-side jets, that might be associated with the near-side peak, are significantly suppressed and contribute minimally to the away-side correlated yield in that ηrange. In contrast, in the range 0.2≤jΔηj≤0.9[see Fig. 2(a)], the vn½P2 coefficients exhibit a stronger and monotonic centrality evolution. In particular, the vn½P2deviate significantly from the flow ansatz for collision centralities larger than 40%, where one expects the largest nonflow contributions associated with the presence of the correlation function near-side peak. Using the same measurement technique, we further compare features of the P2correlation function to that of the number correlation function R2, defined as R2þ1¼ZpT;max pT;min ρ2ð~ p1;~ p2ÞdpT;1dpT;2ZpT;max pT;min ρ1ð~ p1Þρ1ð~ p2ÞdpT;1dpT;2:ð3Þ Figure 3presents the Δηdependence of vn,n¼2, 3, and 4, coefficients obtained from these correlation functions for the 5% most central collisions. In this centrality interval, one finds that the hierarchies v3½P2>v 2½P2and v2½R2> v3½R2indeed hold for all measured Δη. The dominance of v3½P2across all Δηis likely a consequence of the third harmonic’s (triangular flow) stronger dependence on pT relative to that of the second harmonic (elliptic flow). The v2,v3, and v4dependencies on Δηreveal additional interesting features. In the case of the R2correlation, the coefficients v2and v3monotonically decrease over the entire Δηrange, whereas coefficients extracted from P2 exhibit a more pronounced decrease for jΔηj≤0.9. From jΔηj∼1.0to ∼2.0, the relative decrease of v2is about 5% ] 2 P[ n v 5 6 7 8 9 3− 10×(a) = 2.76 TeV NN sALICE, Pb-Pb 0-5% |ηΔ| 0.5 1 1.5 2 Ratio 0.8 0.9 1 1.1 (c) ] 2 R[ n v 0.01 0.02 0.03 n=2 n=3 n=4 (b) c < 2.0 GeV/ T p0.2 < |η Δ | 0.5 1 1.5 2 Ratio 0.8 0.9 1 1.1 (d) FIG. 3. vncoefficients, n¼2, 3, 4, obtained from (a) P2and (b) R2correlators, as a function of jΔηjin the 5% most central Pb-Pb collisions. Statistical errors are shown as vertical solid lines, whereas systematic uncertainties are displayed as shaded bands. (c),(d) Ratios of the vn,n¼2, 3, 4, by the corresponding values of vnmeasured at Δη¼0.3. PRL 118, 162302 (2017) PHYSICAL REVIEW LETTERS week ending 21 APRIL 2017 162302-4 for both correlators and somewhat smaller for v3. These contrasting dependencies reflect the different shapes of the near-side peaks of the two correlation functions. The narrower shape of the near-side peak of the P2distribution suggests that the near-side peak of R2might involve two components, one of which is characterized by a vanishing hΔpTΔpTifor pairs with jΔηj≤0.9. While the origin of this behavior is not fully understood, it offers the benefit of enabling the determination of flow coefficients with smaller nonflow effects using a narrower Δηgap. In summary, we presented the first measurements of the two-particle transverse momentum differential correlation function P2from Pb-Pb collisions at ffiffiffiffiffiffiffiffi sNN p¼2.76 TeV. In the 5% most central Pb-Pb collisions, P2has a shape qualitatively different to that observed in measurements of the number density correlations, with a relatively narrow near-side peak near jΔηj;jΔφj<0.5, and a longitudinally broad and double-hump structure on the away side. The double-hump structure in the 5% most central P2correla- tion indicates that this observable is more sensitive to the presence of a triangular flow component than the number correlations R2and consequently provides an indication that triangular flow features a stronger dependence on pT than elliptic flow does. Comparison of the Fourier decompositions of the R2and P2correlators, calculated as a function of jΔηj, suggests that the v2,v3, and v4coef- ficients extracted from P2reach approximately constant values beyond jΔηj∼0.9, while coefficients v2and v3 obtained from R2decrease monotonically for increasing jΔηj. The observed agreement between the flow coefficients measured from P2correlations, at jΔηj>0.9, and the values predicted from the flow ansatz provide new and independent support to the notion that the observed longrange correlations are largely due to the initial collision geometry. These results may be used to further constrain particle production models. This agreement to the flow ansatz also provides further evidence for flow coefficient factorization in heavy-ion collisions. The ALICE Collaboration thanks all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centers and the Worldwide LHC Computing Grid (WLCG) Collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science and Technology of China (MSTC), National Natural Science Foundation of China (NSFC), and Ministry of Education of China (MOEC), China; Ministry of Science, Education and Sport and Croatian Science Foundation, Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research–Natural Sciences, the Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; Ministry of Education, Research and Religious Affairs, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE) and Council of Scientific and Industrial Research (CSIR), New Delhi, India; Indonesian Institute of Science, Indonesia; Centro Fermi—Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nationaal instituut voor subatomaire fysica (Nikhef), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education and National Science Centre, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Romanian National Agency for Science, Technology and Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation and National Research Centre Kurchatov Institute, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba, PRL 118, 162302 (2017) PHYSICAL REVIEW LETTERS week ending 21 APRIL 2017 162302-5 Ministerio de Ciencia e Innovacion and Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain; Swedish Research Council (VR) and Knut and Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; National Science and Technology Development Agency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. 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