Azimuthally differential pion femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV
ALICE Collaboration

TL;DR
This paper reports the first azimuthally differential pion femtoscopy measurements in Pb-Pb collisions at 2.76 TeV, revealing oscillations in source radii and a smaller final-state eccentricity compared to initial conditions.
Contribution
It introduces the first azimuthally differential measurements of pion source sizes relative to the event plane at LHC energies, providing new insights into the collision dynamics.
Findings
$R_{side}$ and $R_{out}$ oscillate out of phase, similar to RHIC observations.
Final-state source eccentricity is smaller than initial but remains positive.
Hydrodynamic models qualitatively agree but underestimate oscillation magnitudes.
Abstract
We present the first azimuthally differential measurements of the pion source size relative to the second harmonic event plane in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon pair of TeV. The measurements have been performed in the centrality range 0-50% and for pion pair transverse momenta GeV/. We find that the and radii, which characterize the pion source size in the directions perpendicular and parallel to the pion transverse momentum, oscillate out of phase, similar to what was observed at the Relativistic Heavy Ion Collider (RHIC). The final-state source eccentricity, estimated via oscillations, is found to be significantly smaller than the initial-state source eccentricity, but remains positive; indicating that even after a stronger expansion in the in-plane…
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\PHyear2017 \PHnumber013 \PHdateJanuary
\ShortTitleAzimuthally differential pion femtoscopy in Pb–Pb collisions
\CollaborationALICE Collaboration††thanks: See Appendix A for the list of collaboration members \ShortAuthorALICE Collaboration
We present the first azimuthally differential measurements of the pion source size relative to the second harmonic event plane in Pb–Pb collisions at a center-of-mass energy per nucleon-nucleon pair of = 2.76 TeV. The measurements have been performed in the centrality range 0–50% and for pion pair transverse momenta GeV/c. We find that the and radii, which characterize the pion source size in the directions perpendicular and parallel to the pion transverse momentum, oscillate out of phase, similar to what was observed at the Relativistic Heavy Ion Collider (RHIC). The final-state source eccentricity, estimated via oscillations, is found to be significantly smaller than the initial-state source eccentricity, but remains positive – indicating that even after a stronger expansion in the in-plane direction, the pion source at the freeze-out is still elongated in the out-of-plane direction. The 3+1D hydrodynamic calculations are in qualitative agreement with observed centrality and transverse momentum oscillations, but systematically underestimate the oscillation magnitude.
It was first shown in 1960 that the distribution of pions emitted in collisions at small relative angles is affected by quantum statistical effects and is sensitive to the size of the emitting source [1]. Since then, the correlation technique with two identical particles at small relative momentum, often called intensity, or Hanbury Brown–Twiss (HBT), interferometry [2, 3, 4, 5, 6], has been used to study the space-time structure of the pion-emitting source from hadron-hadron and electron-positron to heavy-ion collisions (for a review, see [7]). The so-called HBT radii, obtained in these analyses, characterize the spatial and temporal extent of the source emitting pions of a given momentum, the extensions of the so-called homogeneity regions. Due to the position-momentum correlations in particle emission, the HBT radii become sensitive to the collective velocity fields, and as such provide information on the dynamics of the system evolution [7]. Recent measurements of the centrality dependence of the HBT radii in Pb–Pb collisions at LHC energies [8] further confirm the scaling of the effective source volume with the particle rapidity density as well as stronger radial flow at higher energies.
Pion interferometry of anisotropic sources (azimuthally differential femtoscopy) was suggested in [9, 10], and the corresponding measurements [11] appeared shortly after strong directed and in-plane elliptic flow were measured in Au–Au collisions at the Alternating Gradient Synchrotron (AGS) [12, 13]. Anisotropic flow, the response of the system to the initial geometry, is usually characterized by the Fourier decomposition of the particle azimuthal distribution and quantified by the harmonic strength and orientation of the corresponding flow plane. Azimuthally differential femtoscopic measurements can be performed relative to different harmonic flow planes, providing important complementary information on the particle source. For example, the measurements of HBT radii with respect to the first harmonic (directed) flow at the AGS [14] revealed that the source was tilted relative to the beam direction [15]. Azimuthal dependence of the HBT radii relative to the higher harmonic () flow planes can originate only from the anisotropies in collective flow gradients [16, 17] and the observation [18] of such a modulation unambiguously signals a collective expansion and anisotropy in the flow fields. In particular, measurements of HBT radii with respect to the second harmonic (elliptic) flow provide information on the evolution of the system shape, which is expected to become more spherical at freeze-out compared to the initial state due to stronger in-plane expansion. In the recent RHIC beam energy scan, it was found that the eccentricity at freeze-out decreases continuously with increasing beam energy [19], a trend consistent with predictions by hydrodynamic and hadronic transport models [20, 21]. Earlier measurements [22, 23] showed that even at the highest RHIC energies the source at freeze-out remains out-of-plane extended, albeit with eccentricities significantly lower than the initial ones. Hydrodynamical calculations [20] predicted that at the Large Hadron Collider (LHC) energies, about an order of magnitude higher than the top RHIC energy, the pion source should eventually become isotropic, or even in-plane extended.
In this Letter, we present the first azimuthally differential femtoscopic measurements relative to the second harmonic flow plane in Pb–Pb collisions at = 2.76 TeV from the ALICE experiment at the CERN-LHC and compare the results to previous measurements at RHIC energies and to model calculations.
The data were recorded in 2011 during the second Pb–Pb running period of the LHC. Approximately 2 million minimum bias events, 29.2 million central trigger events, and 34.1 million semi-central trigger events were used in this analysis. A detailed description of the ALICE detector can be found in [24, 25]. The Time Projection Chamber (TPC) has full azimuthal coverage and allows charged-particle track reconstruction in the pseudorapidity range , as well as particle identification via the specific ionization energy loss associated with each track. In addition to the TPC, the Time-Of-Flight (TOF) detector was used for identification of particles with transverse momentum 0.5 GeV/c.
The minimum bias, semi-central, and central triggers used in this analysis all require a signal in both V0 detectors [26]. The V0 is a small angle detector of scintillator arrays covering pseudorapidity ranges and for a collision vertex occurring at the center of the ALICE detector. The V0 detector was also used for the centrality determination [8]. The results of this analysis are reported for collision centrality classes expressed as ranges of the fraction of the inelastic Pb–Pb cross-section: 0–5%, 5–10%, 10–20%, 20–30%, 30–40%, and 40–50%. The position of the primary event vertex along the beam direction was determined for each event. Events with cm were used in this analysis to ensure a uniform pseudorapidity acceptance.
The TPC has 18 sectors covering full azimuth with 159 pad rows radially placed in each sector. Tracks with at least 80 space points in the TPC have been used in this analysis. Tracks compatible with a decay in flight (kink topology) were rejected. The track quality was determined by the of the Kalman filter fit to the reconstructed TPC clusters. The per degrees of freedom was required to be less than 4. For primary track selection, only trajectories passing within 3.2 cm from the primary vertex in the longitudinal direction and 2.4 cm in the transverse direction were used. Based on the specific ionization energy loss in the TPC gas compared with the corresponding Bethe-Bloch curve, and the time of flight in TOF, a probability for each track to be a pion, kaon, proton, or electron was determined. Particles for which the pion probability was the largest were used in this analysis. Pions were selected in the pseudorapidity range and 0.15 1.5 GeV/c.
The correlation function was calculated as
[TABLE]
where is the relative momentum of two pions, is the same-event distribution of particle pairs, and is the background distribution of uncorrelated particle pairs. Both the and distributions were measured differentially with respect to the second harmonic event-plane angle . The second harmonic event-plane angle was determined using TPC tracks. To avoid self-correlation, each event was split into two subevents ( and ). Pairs were chosen from one subevent and the second harmonic event-plane angle was determined using the other subevent particles, and vice-versa, with the event plane resolution determined from the correlations between the event planes determined in different subevents [27]. The background distribution is built by using the mixed-event technique [4] in which pairs are made out of particles from two different events with similar centrality (less than 2% difference), event-plane angle (less than 10∘ difference), and event vertex position along the beam direction (less than 4 cm difference). Requiring a minimum value in the two-track separation parameters and controls two-track reconstruction effects such as track splitting or track merging. The quantity is defined in this analysis as the azimuthal angle of the track in the laboratory frame at the radial position of 1.6 m inside the TPC. Splitting is the effect when one track is reconstructed as two tracks, and merging is the effect of two tracks being reconstructed as one. Also, to reduce the splitting effect, pairs that share more than 5% of the TPC clusters were removed from the analysis. It is observed that at large relative momentum the correlation function is a constant, and the background pair distribution is normalized such that this constant is unity. The analysis was performed for different collision centralities in several ranges of , the magnitude of the pion-pair transverse momentum , and in bins of , defined in the range (0, ) where is the pair azimuthal angle. The Bertsch-Pratt [5, 6] out–side–long coordinate system was used with the long direction pointing along the beam axis, out along the transverse pair momentum, and side being perpendicular to the other two. The three-dimensional correlation function was analyzed in the Longitudinally Co-Moving System (LCMS), in which the total longitudinal momentum of the pair is zero, .
To isolate the Bose-Einstein contribution in the correlation function, effects due to final-state Coulomb repulsion must be taken into account. For that, the Bowler-Sinyukov fitting procedure [28, 29] was used in which the Coulomb weight is only applied to the fraction of pairs () that participate in the Bose-Einstein correlation. In this approach, the correlation function is fitted to
[TABLE]
where is the normalization factor. The function describes the Bose-Einstein correlations and is the Coulomb part of the two-pion wave function integrated over a source function corresponding to . In this analysis the Gaussian form of was used [30]:
[TABLE]
where the parameters , , and are traditionally called HBT radii in the out, side, and long directions. The cross-terms , , and describe the correlation in the out-side, side-long, and out-long directions, respectively.
The systematic errors on the extracted radii vary within 3–9% depending on and centrality. They include uncertainties related to the tracking efficiency and track quality, momentum resolution [31], different pair cuts ( and ), and correlation function fit ranges. Positive and negative pion pairs as well as data obtained with two opposite magnetic field polarities of the ALICE L3 magnet have been analyzed separately and a small difference in the results (less than 3%) has been also accounted for in the systematic error. The total systematic errors were obtained from adding the above systematic errors in quadrature.
Other than being differential in the event plane, this analysis is similar in most aspects to the analysis reported in [31], and further details can be found there. The results reported below were obtained with the second harmonic event plane [27] determined with the TPC tracks. It was checked that they are consistent with the results obtained with the event-plane angle determined with the V0 detector.
Figure 1 presents the dependence of , , , , and on the pion emission angle relative to the second harmonic event plane. The results are shown for the centrality classes 20–30% in four ranges of : 0.2–0.3, 0.3–0.4, 0.4–0.5, and 0.5–0.7 GeV/c. and exhibit clear out-of-phase oscillations. No oscillations for and are observed within the uncertainties of the measurement. The parameter shows very similar oscillations for all bins. and (not shown) are found to be consistent with zero, as expected due to symmetry, and are not further investigated in this analysis. A possible correlation between and the extracted radii was checked by fixing . No change in the radii has been observed. The curves represent the fits to the data using the functions [9, 10]:
[TABLE]
Fitting the radii’s azimuthal dependence with the functional form of Eq. Azimuthally differential pion femtoscopy in Pb–Pb collisions at = 2.76 TeV allows us to extract the average radii and the amplitudes of oscillations. The latter have to be corrected for the finite event plane resolution. There exist several methods for such a correction [7], which produce very similar results [19] well within errors of this analysis. The results shown below have been obtained with the simplest method first used by the E895 Collaboration [14], in which the amplitude of oscillation is divided by the event plane resolution factor. The correction is about 5–15%, depending on centrality.
Figure 2 shows the average radii for different values as a function of centrality. The average radii obtained in this analysis are consistent with the results reported in [31]. As expected, the radii are larger in more central collisions and at smaller values, the latter reflecting the effect of radial flow [7, 33]. The cross-term is consistent with zero, as expected due to the symmetry of the system. Figure 2 also shows the average radii calculated for charged pions in the pseudorapidity range from 3+1D hydrodynamic calculations [32], assuming freeze-out temperature = 150 MeV and a constant shear viscosity to entropy density ratio = 0.08. The 3+1D hydrodynamic calculations, while correctly describing the qualitative features of the average radii dependence on centrality and , fail to describe our results quantitatively.
Figure 3 shows the relative amplitudes of the radius oscillations , , , and . When comparing our results to the ones obtained by the STAR experiment, we observe similar relative oscillations, however STAR results [22, 23] show on average larger oscillations for . Our relative amplitudes for , , and show a clear centrality dependence, whereas the is very close to zero for all centralities, similarly to the results from RHIC [22, 19, 34].
The source eccentricity is usually defined as , where is the in-plane radius of the (assumed) elliptical source and is the out-of-plane radius. As shown in [33] the relative amplitudes of side radii oscillations are mostly determined by the spatial source anisotropy and are less affected by dynamical effects such as velocity gradients. The source eccentricity at freeze-out can be estimated from oscillations at small pion momenta with an accuracy within 20–30% as [33].
Figure 4 presents for different ranges as a function of the initial-state eccentricity for six different centralities and four bins. For the initial eccentricity we have used the nucleon participant eccentricity from the Monte Carlo Glauber model for both, Au–Au collisions at =200 GeV [18] and Pb–Pb collision at = 2.76 TeV [35]. Our results for all bins are significantly below the values of the initial eccentricity indicating a more intense expansion in the in-plane direction. Due to relatively large uncertainties of the RHIC results for narrow bins, we compare our results only to the average STAR data [22] in GeV/c and to PHENIX results [18] corresponding to GeV/c ( GeV/c). We find a smaller final-state anisotropy in the LHC regime compared to RHIC energies. This trend is qualitatively consistent with expectations from hydrodynamic and transport models [20, 21]. The final-state eccentricity remains positive also at the LHC, evidence of an out-of-plane elongated source at freeze-out. In Fig. 4, we also compare our results to the 3+1D hydrodynamic calculations [32], which were performed for similar centralities and ranges as in the experiment. This model slightly underestimates the final source eccentricity.
In conclusion, we have performed a measurement of two-pion azimuthally differential femtoscopy relative to the second harmonic flow plane in Pb–Pb collisions at = 2.76 TeV. The out, side, and out-side radii exhibit clear oscillations while the long radius is consistent with a constant. The relative amplitudes of oscillations only weakly depend on , with the side-radii oscillation slightly increasing with . The final-state source eccentricity, estimated via side-radius oscillations, is noticeably smaller than at lower collisions energies, but still exhibits an out-of-plane elongated source at freeze-out even after a stronger in-plane expansion. The final eccentricity is slightly larger than that predicted by existing hydrodynamic calculations.
Acknowledgements
The ALICE Collaboration would like to thank 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 centres 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; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; 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 & 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, Ministerio de Ciencia e Innovacion and Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain; Swedish Research Council (VR) and Knut & 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.
Appendix A The ALICE Collaboration
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Gianotti, P. Giubellino,, P. Giubilato, E. Gladysz-Dziadus, P. Glässel, D.M. Goméz Coral, A. Gomez Ramirez, A.S. Gonzalez, V. Gonzalez, P. González-Zamora, S. Gorbunov, L. Görlich, S. Gotovac, V. Grabski, L.K. Graczykowski, K.L. Graham, J.L. Gramling, L. Greiner, A. Grelli, C. Grigoras, V. Grigoriev, A. Grigoryan, S. Grigoryan, N. Grion, J.M. Gronefeld, F. Grosa, J.F. Grosse-Oetringhaus, R. Grosso, L. Gruber, F.R. Grull, F. Guber, R. Guernane,, B. Guerzoni, K. Gulbrandsen, T. Gunji, A. Gupta, R. Gupta, I.B. Guzman, R. Haake,, C. Hadjidakis, H. Hamagaki,, G. Hamar, J.C. Hamon, J.W. Harris, A. Harton, D. Hatzifotiadou, S. Hayashi, S.T. Heckel, E. Hellbär, H. Helstrup, A. Herghelegiu, G. Herrera Corral, F. Herrmann, B.A. Hess, K.F. Hetland, H. Hillemanns, B. Hippolyte, J. Hladky, D. Horak, R. Hosokawa, P. Hristov, C. Hughes, T.J. Humanic, N. Hussain, T. Hussain, D. Hutter, D.S. Hwang, R. Ilkaev, M. Inaba, M. Ippolitov,, M. Irfan, V. Isakov, M.S. Islam, M. Ivanov,, V. Ivanov, V. Izucheev, B. Jacak, N. Jacazio, P.M. Jacobs, M.B. Jadhav, S. Jadlovska, J. Jadlovsky, C. Jahnke, M.J. Jakubowska, M.A. Janik, P.H.S.Y. Jayarathna, C. Jena, S. Jena, M. Jercic, R.T. Jimenez Bustamante, P.G. Jones, A. Jusko, P. Kalinak, A. Kalweit, J.H. Kang, V. Kaplin, S. Kar, A. Karasu Uysal, O. Karavichev, T. Karavicheva, L. Karayan,, E. Karpechev, U. Kebschull, R. Keidel, D.L.D. Keijdener, M. Keil, B. Ketzer, M. Mohisin Khan\Arefidp3207120, P. Khan, S.A. Khan, A. Khanzadeev, Y. Kharlov, A. Khatun, A. Khuntia, M.M. Kielbowicz, B. Kileng, D.W. Kim, D.J. Kim, D. Kim, H. Kim, J.S. Kim, J. Kim, M. Kim, M. Kim, S. Kim, T. Kim, S. Kirsch, I. Kisel, S. Kiselev, A. Kisiel, G. Kiss, J.L. Klay, C. Klein, J. Klein, C. Klein-Bösing, S. Klewin, A. Kluge, M.L. Knichel, A.G. Knospe, C. Kobdaj, M. Kofarago, T. Kollegger, A. Kolojvari, V. Kondratiev, N. Kondratyeva, E. Kondratyuk, A. Konevskikh, M. Kopcik, M. Kour, C. Kouzinopoulos, O. Kovalenko, V. Kovalenko, M. Kowalski, G. Koyithatta Meethaleveedu, I. Králik, A. Kravčáková, M. Krivda,, F. Krizek, E. Kryshen, M. Krzewicki, A.M. Kubera, V. Kučera, C. Kuhn, P.G. Kuijer, A. Kumar, J. Kumar, L. Kumar, S. Kumar, S. Kundu, P. Kurashvili, A. Kurepin, A.B. Kurepin, A. Kuryakin, S. Kushpil, M.J. Kweon, Y. Kwon, S.L. La Pointe, P. La Rocca, C. Lagana Fernandes, I. Lakomov, R. Langoy, K. Lapidus, C. Lara, A. Lardeux,, A. Lattuca, E. Laudi, R. Lavicka, L. Lazaridis, R. Lea, L. Leardini, S. Lee, F. Lehas, S. Lehner, J. Lehrbach, R.C. Lemmon, V. Lenti, E. Leogrande, I. León Monzón, P. Lévai, S. Li, X. Li, J. Lien, R. Lietava, S. Lindal, V. Lindenstruth, C. Lippmann, M.A. Lisa, V. Litichevskyi, H.M. Ljunggren, W.J. Llope, D.F. Lodato, V.R. Loggins, P.I. Loenne, V. Loginov, C. Loizides, P. Loncar, X. Lopez, E. López Torres, A. Lowe, P. Luettig, M. Lunardon, G. Luparello, M. Lupi, T.H. Lutz, A. Maevskaya, M. Mager, S. Mahajan, S.M. Mahmood, A. Maire, R.D. Majka, M. Malaev, I. Maldonado Cervantes, L. Malinina\Arefidp3984928, D. Mal’Kevich, P. Malzacher, A. Mamonov, V. Manko, F. Manso, V. Manzari, Y. Mao, M. Marchisone,, J. Mareš, G.V. Margagliotti, A. Margotti, J. Margutti, A. Marín, C. Markert, M. Marquard, N.A. Martin, P. Martinengo, J.A.L. Martinez, M.I. Martínez, G. Martínez García, M. Martinez Pedreira, A. Mas, S. Masciocchi, M. Masera, A. Masoni, A. Mastroserio, A.M. Mathis,, A. Matyja,, C. Mayer, J. Mazer, M. Mazzilli, M.A. Mazzoni, F. Meddi, Y. Melikyan, A. Menchaca-Rocha, E. Meninno, J. Mercado Pérez, M. Meres, S. Mhlanga, Y. Miake, M.M. Mieskolainen, D. Mihaylov, K. Mikhaylov,, L. Milano, J. Milosevic, A. Mischke, A.N. Mishra, D. Miśkowiec, J. Mitra, C.M. Mitu, N. Mohammadi, B. Mohanty, E. Montes, D.A. Moreira De Godoy, L.A.P. Moreno, S. Moretto, A. Morreale, A. Morsch, V. Muccifora, E. Mudnic, D. Mühlheim, S. Muhuri, M. Mukherjee, J.D. Mulligan, M.G. Munhoz, K. Münning, R.H. Munzer,,, H. Murakami, S. Murray, L. Musa, J. Musinsky, C.J. Myers, B. Naik, R. Nair, B.K. Nandi, R. Nania, E. Nappi, M.U. Naru, H. Natal da Luz, C. Nattrass, S.R. Navarro, K. Nayak, R. Nayak, T.K. Nayak, S. Nazarenko, A. Nedosekin, R.A. Negrao De Oliveira, L. Nellen, S.V. Nesbo, F. Ng, M. Nicassio, M. Niculescu, J. Niedziela, B.S. Nielsen, S. Nikolaev, S. Nikulin, V. Nikulin, F. Noferini,, P. Nomokonov, G. Nooren, J.C.C. Noris, J. Norman, A. Nyanin, J. Nystrand, H. Oeschler, S. Oh, A. Ohlson,, T. Okubo, L. Olah, J. Oleniacz, A.C. Oliveira Da Silva, M.H. Oliver, J. Onderwaater, C. Oppedisano, R. Orava, M. Oravec, A. Ortiz Velasquez, A. Oskarsson, J. Otwinowski, K. Oyama, M. Ozdemir, Y. Pachmayer, V. Pacik, D. Pagano, P. Pagano, G. Paić, S.K. Pal, P. Palni, J. Pan, A.K. Pandey, S. Panebianco, V. Papikyan, G.S. Pappalardo, P. Pareek, J. Park, W.J. Park, S. Parmar, A. Passfeld, S.P. Pathak, V. Paticchio, R.N. Patra, B. Paul, H. Pei, T. Peitzmann, X. Peng, L.G. Pereira, H. Pereira Da Costa, D. Peresunko,, E. Perez Lezama, V. Peskov, Y. Pestov, V. Petráček, V. Petrov, M. Petrovici, C. Petta, R.P. Pezzi, S. Piano, M. Pikna, P. Pillot, L.O.D.L. Pimentel, O. Pinazza,, L. Pinsky, D.B. Piyarathna, M. Płoskoń, M. Planinic, J. Pluta, S. Pochybova, P.L.M. Podesta-Lerma, M.G. Poghosyan, B. Polichtchouk, N. Poljak, W. Poonsawat, A. Pop, H. Poppenborg, S. Porteboeuf-Houssais, J. Porter, J. Pospisil, V. Pozdniakov, S.K. Prasad, R. Preghenella,, F. Prino, C.A. Pruneau, I. Pshenichnov, M. Puccio, G. Puddu, P. Pujahari, V. Punin, J. Putschke, H. Qvigstad, A. Rachevski, S. Raha, S. Rajput, J. Rak, A. Rakotozafindrabe, L. Ramello, F. Rami, D.B. Rana, R. Raniwala, S. Raniwala, S.S. Räsänen, B.T. Rascanu, D. Rathee, V. Ratza, I. Ravasenga, K.F. Read,, K. Redlich, A. Rehman, P. Reichelt, F. Reidt, X. Ren, R. Renfordt, A.R. Reolon, A. Reshetin, K. Reygers, V. Riabov, R.A. Ricci, T. Richert,, M. Richter, P. Riedler, W. Riegler, F. Riggi, C. Ristea, M. Rodríguez Cahuantzi, K. Røed, E. Rogochaya, D. Rohr, D. Röhrich, P.S. Rokita, F. Ronchetti,, L. Ronflette, P. Rosnet, A. Rossi, A. Rotondi, F. Roukoutakis, A. Roy, C. Roy, P. Roy, A.J. Rubio Montero, R. Rui, R. Russo, A. Rustamov, E. Ryabinkin, Y. Ryabov, A. Rybicki, S. Saarinen, S. Sadhu, S. Sadovsky, K. Šafařík, S.K. Saha, B. Sahlmuller, B. Sahoo, P. Sahoo, R. Sahoo, S. Sahoo, P.K. Sahu, J. Saini, S. Sakai,, M.A. Saleh, J. Salzwedel, S. Sambyal, V. Samsonov,, A. Sandoval, D. Sarkar, N. Sarkar, P. Sarma, M.H.P. Sas, E. Scapparone, F. Scarlassara, R.P. Scharenberg, H.S. Scheid, C. Schiaua, R. Schicker, C. Schmidt, H.R. Schmidt, M.O. Schmidt, M. Schmidt, J. Schukraft, Y. Schutz,,, K. Schwarz, K. Schweda, G. Scioli, E. Scomparin, R. Scott, M. Šefčík, J.E. Seger, Y. Sekiguchi, D. Sekihata, I. Selyuzhenkov,, K. Senosi, S. Senyukov,,, E. Serradilla,, P. Sett, A. Sevcenco, A. Shabanov, A. Shabetai, O. Shadura, R. Shahoyan, A. Shangaraev, A. Sharma, A. Sharma, M. Sharma, M. Sharma, N. Sharma,, A.I. Sheikh, K. Shigaki, Q. Shou, K. Shtejer,, Y. Sibiriak, S. Siddhanta, K.M. Sielewicz, T. Siemiarczuk, D. Silvermyr, C. Silvestre, G. Simatovic, G. Simonetti, R. Singaraju, R. Singh, V. Singhal, T. Sinha, B. Sitar, M. Sitta, T.B. Skaali, M. Slupecki, N. Smirnov, R.J.M. Snellings, T.W. Snellman, J. Song, M. Song, F. Soramel, S. Sorensen, F. Sozzi, E. Spiriti, I. Sputowska, B.K. Srivastava, J. Stachel, I. Stan, P. Stankus, E. Stenlund, J.H. Stiller, D. Stocco, P. Strmen, A.A.P. Suaide, T. Sugitate, C. Suire, M. Suleymanov, M. Suljic, R. Sultanov, M. Šumbera, S. Sumowidagdo, K. Suzuki, S. Swain, A. Szabo, I. Szarka, A. Szczepankiewicz, M. Szymanski, U. Tabassam, J. Takahashi, G.J. Tambave, N. Tanaka, M. Tarhini, M. Tariq, M.G. Tarzila, A. Tauro, G. Tejeda Muñoz, A. Telesca, K. Terasaki, C. Terrevoli, B. Teyssier, D. Thakur, S. Thakur, D. Thomas, R. Tieulent, A. Tikhonov, A.R. Timmins, A. Toia, S. Tripathy, S. Trogolo, G. Trombetta, V. Trubnikov, W.H. Trzaska, B.A. Trzeciak, T. Tsuji, A. Tumkin, R. Turrisi, T.S. Tveter, K. Ullaland, E.N. Umaka, A. Uras, G.L. Usai, A. Utrobicic, M. Vala,, J. Van Der Maarel, J.W. Van Hoorne, M. van Leeuwen, T. Vanat, P. Vande Vyvre, D. Varga, A. Vargas, M. Vargyas, R. Varma, M. Vasileiou, A. Vasiliev, A. Vauthier, O. Vázquez Doce,, V. Vechernin, A.M. Veen, A. Velure, E. Vercellin, S. Vergara Limón, R. Vernet, R. Vértesi, L. Vickovic, S. Vigolo, J. Viinikainen, Z. Vilakazi, O. Villalobos Baillie, A. Villatoro Tello, A. Vinogradov, L. Vinogradov, T. Virgili, V. Vislavicius, A. Vodopyanov, M.A. Völkl, K. Voloshin, S.A. Voloshin, G. Volpe, B. von Haller, I. Vorobyev,, D. Voscek, D. Vranic,, J. Vrláková, B. Wagner, J. Wagner, H. Wang, M. Wang, D. Watanabe, Y. Watanabe, M. Weber, S.G. Weber, D.F. Weiser, J.P. Wessels, U. Westerhoff, A.M. Whitehead, J. Wiechula, J. Wikne, G. Wilk, J. Wilkinson, G.A. Willems, M.C.S. Williams, B. Windelband, W.E. Witt, S. Yalcin, P. Yang, S. Yano, Z. Yin, H. Yokoyama,, I.-K. Yoo,, J.H. Yoon, V. Yurchenko, V. Zaccolo,, A. Zaman, C. Zampolli, H.J.C. Zanoli, S. Zaporozhets, N. Zardoshti, A. Zarochentsev, P. Závada, N. Zaviyalov, H. Zbroszczyk, M. Zhalov, H. Zhang,, X. Zhang,, Y. Zhang, C. Zhang, Z. Zhang, C. Zhao, N. Zhigareva, D. Zhou, Y. Zhou, Z. Zhou, H. Zhu,, J. Zhu,, X. Zhu, A. Zichichi,, A. Zimmermann, M.B. Zimmermann,, S. Zimmermann, G. Zinovjev, J. Zmeskal
Affiliation notes
{Authlist}
\Adef
0Deceased
\Adef
idp1764384Also at: Georgia State University, Atlanta, Georgia, United States
\Adef
idp3207120Also at: Also at Department of Applied Physics, Aligarh Muslim University, Aligarh, India
\Adef
idp3984928Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia
Collaboration Institutes
1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia
2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico
3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India
5Budker Institute for Nuclear Physics, Novosibirsk, Russia
6California Polytechnic State University, San Luis Obispo, California, United States
7Central China Normal University, Wuhan, China
8Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France
9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba
10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico
12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi’, Rome, Italy
13Chicago State University, Chicago, Illinois, United States
14China Institute of Atomic Energy, Beijing, China
15COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan
16Departamento de Física de Partículas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, Spain
17Department of Physics, Aligarh Muslim University, Aligarh, India
18Department of Physics, Ohio State University, Columbus, Ohio, United States
19Department of Physics, Sejong University, Seoul, South Korea
20Department of Physics, University of Oslo, Oslo, Norway
21Department of Physics and Technology, University of Bergen, Bergen, Norway
22Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy
23Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
24Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
25Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
26Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy
27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy
28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy
29Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy
30Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
31Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy
32Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy
33Division of Experimental High Energy Physics, University of Lund, Lund, Sweden
34European Organization for Nuclear Research (CERN), Geneva, Switzerland
35Excellence Cluster Universe, Technische Universität München, Munich, Germany
36Faculty of Engineering, Bergen University College, Bergen, Norway
37Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia
38Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic
39Faculty of Science, P.J. Šafárik University, Košice, Slovakia
40Faculty of Technology, Buskerud and Vestfold University College, Tonsberg, Norway
41Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany
42Gangneung-Wonju National University, Gangneung, South Korea
43Gauhati University, Department of Physics, Guwahati, India
44Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany
45Helsinki Institute of Physics (HIP), Helsinki, Finland
46Hiroshima University, Hiroshima, Japan
47Indian Institute of Technology Bombay (IIT), Mumbai, India
48Indian Institute of Technology Indore, Indore, India
49Indonesian Institute of Sciences, Jakarta, Indonesia
50Inha University, Incheon, South Korea
51Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, CNRS-IN2P3, Orsay, France
52Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
53Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands
54Institute for Theoretical and Experimental Physics, Moscow, Russia
55Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia
56Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic
57Institute of Physics, Bhubaneswar, India
58Institute of Space Science (ISS), Bucharest, Romania
59Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany
60Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany
61Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, Münster, Germany
62Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico
63Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil
64Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico
65IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France, Saclay, France
66iThemba LABS, National Research Foundation, Somerset West, South Africa
67Joint Institute for Nuclear Research (JINR), Dubna, Russia
68Konkuk University, Seoul, South Korea
69Korea Institute of Science and Technology Information, Daejeon, South Korea
70KTO Karatay University, Konya, Turkey
71Laboratoire de Physique Corpusculaire (LPC), Clermont Université, Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France
72Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France
73Laboratori Nazionali di Frascati, INFN, Frascati, Italy
74Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy
75Lawrence Berkeley National Laboratory, Berkeley, California, United States
76Moscow Engineering Physics Institute, Moscow, Russia
77Nagasaki Institute of Applied Science, Nagasaki, Japan
78National and Kapodistrian University of Athens, Physics Department, Athens, Greece, Athens, Greece
79National Centre for Nuclear Studies, Warsaw, Poland
80National Institute for Physics and Nuclear Engineering, Bucharest, Romania
81National Institute of Science Education and Research, Bhubaneswar, India
82National Nuclear Research Center, Baku, Azerbaijan
83National Research Centre Kurchatov Institute, Moscow, Russia
84Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
85Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands
86Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
87Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež u Prahy, Czech Republic
88Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
89Petersburg Nuclear Physics Institute, Gatchina, Russia
90Physics Department, Creighton University, Omaha, Nebraska, United States
91Physics Department, Panjab University, Chandigarh, India
92Physics Department, University of Cape Town, Cape Town, South Africa
93Physics Department, University of Jammu, Jammu, India
94Physics Department, University of Rajasthan, Jaipur, India
95Physikalisches Institut, Eberhard Karls Universität Tübingen, Tübingen, Germany
96Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
97Physik Department, Technische Universität München, Munich, Germany
98Purdue University, West Lafayette, Indiana, United States
99Pusan National University, Pusan, South Korea
100Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany
101Rudjer Bošković Institute, Zagreb, Croatia
102Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
103Saha Institute of Nuclear Physics, Kolkata, India
104School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom
105Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru
106Sezione INFN, Bari, Italy
107Sezione INFN, Bologna, Italy
108Sezione INFN, Cagliari, Italy
109Sezione INFN, Catania, Italy
110Sezione INFN, Padova, Italy
111Sezione INFN, Rome, Italy
112Sezione INFN, Trieste, Italy
113Sezione INFN, Turin, Italy
114SSC IHEP of NRC Kurchatov institute, Protvino, Russia
115Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
116SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3, Nantes, France
117Suranaree University of Technology, Nakhon Ratchasima, Thailand
118Technical University of Košice, Košice, Slovakia
119Technical University of Split FESB, Split, Croatia
120The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland
121The University of Texas at Austin, Physics Department, Austin, Texas, United States
122Universidad Autónoma de Sinaloa, Culiacán, Mexico
123Universidade de São Paulo (USP), São Paulo, Brazil
124Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
125Universidade Federal do ABC, Santo Andre, Brazil
126University of Houston, Houston, Texas, United States
127University of Jyväskylä, Jyväskylä, Finland
128University of Liverpool, Liverpool, United Kingdom
129University of Tennessee, Knoxville, Tennessee, United States
130University of the Witwatersrand, Johannesburg, South Africa
131University of Tokyo, Tokyo, Japan
132University of Tsukuba, Tsukuba, Japan
133University of Zagreb, Zagreb, Croatia
134Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, Lyon, France
135Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France
136Università degli Studi di Pavia, Pavia, Italy
137Università di Brescia, Brescia, Italy
138V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia
139Variable Energy Cyclotron Centre, Kolkata, India
140Warsaw University of Technology, Warsaw, Poland
141Wayne State University, Detroit, Michigan, United States
142Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary
143Yale University, New Haven, Connecticut, United States
144Yonsei University, Seoul, South Korea
145Zentrum für Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms, Germany
The reference list from the paper itself. Each links out to its DOI / PubMed record.
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- 8[8] ALICE Collaboration, K. Aamodt et al. , “Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at s NN = 2.76 subscript 𝑠 NN 2.76 \sqrt{s_{\rm NN}}~{}=~{}2.76 Te V,” Phys. Rev. Lett. 106 (2011) 032301 , ar Xiv:1012.1657 [nucl-ex] . · doi ↗
