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Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV


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CERN-PH-EP-2015-324 14 December 2015


2015 CERN for the benefit of the ALICE Collaboration.

Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

Centrality dependence of the charged-particle multiplicity

density at mid-rapidity in Pb–Pb collisions at



= 5.02 TeV

ALICE Collaboration∗


The pseudorapidity density of charged particles, dNch/dη, at mid-rapidity in Pb–Pb collisions has

been measured at a center-of-mass energy per nucleon pair of√sNN= 5.02 TeV. For the 5% most

cen-tral collisions we measure a value of 1943 ± 54. The rise in dNch/dη as a function of

sNNis steeper

than that observed in proton–proton collisions and follows the trend established by measurements at lower energy. The increase of dNch/dη as a function of the average number of participant nucleons,

hNparti, calculated in a Glauber model, is compared with the previous measurement at

sNN= 2.76

TeV. A constant factor of about 1.2 describes the increase in dNch/dη from √sNN = 2.76 to 5.02

TeV for all centrality classes, within the measured range of 0–80% centrality. The results are also compared to models based on different mechanisms for particle production in nuclear collisions.

See Appendix A for the list of collaboration members


The theory describing the strong interaction, quantum chromodynamics (QCD), predicts the existence of a deconfined phase of matter, the quark-gluon plasma, at high temperature and energy density. Ultra-relativistic collisions of nuclei achieve the conditions necessary for the formation of this strongly inter-acting matter [1, 2].

The multiplicity of produced particles is an important property of the collisions related to the collision geometry, the initial parton densities and the energy density produced. Its dependence on the impact parameter is sensitive to the interplay between particle production from hard and soft processes and co-herence effects between individual nucleon–nucleon scatterings. With an increase in the collision energy, the role of hard processes i.e. parton scatterings with large momentum transfer, increases. After a two-year long shutdown, the Large Hadron Collider (LHC) restarted operation in June 2015 and produced Pb–Pb collisions at a per nucleon center-of-mass energy of√sNN= 5.02 TeV in November 2015. This is

the highest energy achieved in the laboratory to date and offers the possibility to further constrain particle production models by studying their√sNNdependence.

Collisions of extended objects such as nuclei can be classified according to their centrality, which is related to the overlap area of the nuclei. This results in different numbers of nucleons participating in the collision. The number of these participants, Npart, can be calculated by a Monte Carlo (MC) sampling

technique in the Glauber model [3].

Previous measurements of dNch/dη for nucleus–nucleus (AA) collisions were performed at the LHC by

ALICE [4], ATLAS [5] and CMS [6] at√sNN= 2.76 TeV and at lower energies, in the range

sNN= 9 to

200 GeV, with experiments at the Super Proton Synchrotron (SPS) and Relativistic Heavy Ion Collider (RHIC) [7–12]. They show that the increase of dNch/dη with energy is steeper in nucleus-nucleus

compared to proton–proton collisions. The centrality dependence ofhN2

partihdNch/dηi in Pb–Pb at

√ sNN=

2.76 TeV is very similar to that measured in√sNN= 200 GeV collisions at RHIC, pointing to a similar mechanism of particle production at the two energies.

In this Letter we present the measurement of the charged-particle pseudorapidity density averaged in the interval |η| < 0.5, hdNch/dηi, and its centrality dependence. The pseudorapidity is defined by

η ≡ − ln tan (θ /2), with θ the emission angle of the particle relative to the beam axis. The primary charged particles are defined as prompt particles produced in the collision including all decay products, except products from weak decays of light flavor hadrons and of muons.

The data were recorded with the ALICE detector in November 2015 at√sNN= 5.02 TeV. Full details on

the ALICE apparatus [13] and its operational performance [14] are given elsewhere. A brief description of the most relevant elements, along with the experimental conditions, follows. The observed interaction rate was around 300 Hz, of which about 25 Hz were from hadronic interactions, the remainder being a background from electromagnetically induced processes. A total of about 105 hadronic events are used. The interaction probability per bunch-crossing (during which bunches of ions from each beam are arranged to be co-incident at the ALICE interaction point) was sufficiently small that the chance of two hadronic interactions occurring together, so-called pileup events, was negligible.

The measurement relies on the ALICE Inner Tracking System, the innermost two layers of which form the Silicon Pixel Detector (SPD). It consists of arrays of pixels arranged with an approximate cylindrical geometry at radii of 3.9 and 7.6 cm covering intervals of |η| < 2.0 and |η| < 1.4 for the inner and outer layers, respectively. The SPD is situated in a solenoidal magnet, with its principal axis along the beam line, providing a 0.5 T magnetic field. The interaction trigger is provided by two detectors, V0A and V0C, which consist of arrays of scintillators, covering the full azimuth and more than 4 units of pseudorapidity, in the ranges 2.8 < η < 5.1 and −3.7 < η < −1.7, respectively. In all cases the η-coverage refers to collisions at the nominal interaction point. A signal must be present in both V0 detectors to trigger the recording of the interaction. The V0 detectors also provide a signal proportional to the number of charged particles striking them which is used to classify the events into centrality classes, defined in


terms of percentiles of the hadronic cross-section. In addition, an offline event selection employs the information from two Zero Degree Calorimeters (ZDC) positioned 112.5 m from the interaction point on either side. Beam background events are removed using the V0 timing information and the correlation between the sum and the difference of times measured in each of the ZDCs [14].

The analysis is restricted to the 80% most central events. The classification of events into centrality classes is done by using the summed amplitudes of the signals in the V0A and V0C detectors, following the method developed previously [15, 16]. The V0 amplitude is fitted with an MC implementation of the Glauber model coupled with a two-component model assuming that the effective number of particle-producing sources is given by f × Npart+ (1 − f ) × Ncoll, where Npartis the number of participating

nu-cleons, Ncoll is the number of binary nucleon–nucleon collisions and f ∼ 0.8 quantifies their relative

contributions. The number of particles produced by each source is distributed according to a Negative Binomial Distribution (NBD), parametrised with µ and k, where µ is the mean multiplicity per source and k controls the contribution at high multiplicity. In the Monte Carlo Glauber calculation, the nu-clear density for208Pb is modeled by a Woods–Saxon distribution for a spherical nucleus with a radius of 6.62 ± 0.06 fm and a skin thickness of 0.546 ± 0.010 fm, based on data from low energy electron– nucleus scattering experiments [17], and a hard-sphere exclusion distance between nucleons of 0.4 ± 0.4 fm. For√sNN= 5.02 TeV collisions, an inelastic nucleon–nucleon cross-section of 70 ± 5 mb, obtained

by interpolation [18], is used. The fit was restricted to a region where the effects of trigger inefficiency and contamination by electromagnetic processes are negligible. The NBD-Glauber fit provides a good description of the observed V0 amplitude in this region, which corresponds to the most central 90% of the cross-section. All events in the sample corresponding to 0–80% of the hadronic cross section are found to have a well-defined primary vertex, extracted by correlating hits in the two SPD layers.

The dNch/dη measurement is performed using short track segments, termed tracklets [19]. Tracklet

candidates are formed using the position of the primary vertex and a pair of hits, one in each SPD layer. For each of the hits in the pair two angles are determined with respect to the reconstructed interaction vertex and the angular differences, ∆ϕ in the bending plane and ∆θ in the polar direction, are calculated for each pair of hits. In order to reject candidates produced by the random combination of two hits, tracklets are selected by a cut on the sum of the squares, δ2 = (∆ϕ/σϕ)2+ (∆θ /σθ)2< 1.5, where

σϕ = 60 mrad and σθ = 25 sin2θ mrad. This selection effectively allows the reconstruction of charged

particles with transverse momentum (pT) above the 50 MeV/c cut-off determined by particle absorption

in the material.

The acceptance region in η depends on the position of the interaction vertex along the beamline, z. Events with |z| < 7 cm are used, corresponding to a coverage of |η| < 0.5 with an approximately constant acceptance.

A correction is needed to account for the acceptance and efficiency of a primary track to generate a tracklet, including the extrapolation to zero pT, and for the removal of combinatorial background

track-lets. This is computed using simulated data from the HIJING event generator [20] transported through a GEANT3 [21] simulation of ALICE, where the centrality definition is adjusted so that the particle density is similar to that in real data for the same centrality classes. A re-weighting of the genera-tor output is performed to reproduce the pT distributions of inclusive charged hadrons and the

rela-tive abundances of pions, protons, kaons and other strange particles as measured in Pb–Pb collisions at √sNN = 2.76 TeV [22–25]. Using results from √sNN = 2.76 TeV is justified because the relative abundances at√sNN = 2.76 TeV change very little from those at

sNN = 200 GeV. Any variation with

the increase in √sNN to 5.02 TeV will be much smaller than the differences between the default and

re-weighted HIJING simulations, which lead to differences in the results within the systematic uncer-tainties estimated below.


Centrality hdNch/dηi hNparti hNpart2 ihdNch/dηi 0–2.5% 2035 ± 52 398 ± 2 10.2 ± 0.3 2.5–5.0% 1850 ± 55 372 ± 3 9.9 ± 0.3 5.0–7.5% 1666 ± 48 346 ± 4 9.6 ± 0.3 7.5–10% 1505 ± 44 320 ± 4 9.4 ± 0.3 10–20% 1180 ± 31 263 ± 4 9.0 ± 0.3 20–30% 786 ± 20 188 ± 3 8.4 ± 0.3 30–40% 512 ± 15 131 ± 2 7.8 ± 0.3 40–50% 318 ± 12 86.3 ± 1.7 7.4 ± 0.3 50–60% 183 ± 8 53.6 ± 1.2 6.8 ± 0.3 60–70% 96.3 ± 5.8 30.4 ± 0.8 6.3 ± 0.4 70–80% 44.9 ± 3.4 15.6 ± 0.5 5.8 ± 0.5

Table 1: The hdNch/dηi and hNpart2 ihdNch/dηi values measured in |η| < 0.5 for eleven centrality classes. The

values of hNparti obtained with the Glauber model are also given. The errors are total uncertainties, the statistical

contribution being negligible.

losses due to physical processes like absorption and scattering, which may result in a charged particle not creating a tracklet. The fractions of active pixels in the inner and outer SPD layers were about 85% and 97.5%, respectively. The estimated combinatorial background amounts to about 18% in the most central (0–2.5%) and 1% in the most peripheral (70–80%) centrality classes. A correction of about 2% for contamination by secondaries from weak decays is applied based on the same simulation.

Several sources of systematic uncertainty were investigated. The centrality determination introduces an uncertainty via the fitting of the V0 amplitude distribution to the hadronic cross-section, due to the con-tamination from electromagnetically induced reactions at small multiplicity. The fraction of the hadronic cross-section (10%) at the lowest multiplicity, where the trigger and event selection are not fully efficient and the contamination is non-negligible, was varied by an uncertainty of ±0.5%. This uncertainty was estimated by varying NBD-Glauber fitting conditions and by fitting a different centrality estimator, based on the hits in the SPD. The uncertainty from the centrality estimation results in an uncertainty of 0.5% for central 0–2.5% collisions, increasing in the more peripheral collision classes, reaching 7.5% for the 70–80% sample, where it is the largest contribution. Conversely, the uncertainty due to the subtraction of the background is largest for the central event sample, where it is about 2%, and becomes smaller as the collisions become more peripheral, amounting to only 0.2% for the 70–80% event class. This uncertainty is estimated by using an alternative method where fake hits are injected into real events.

All other sources of systematic uncertainty are independent of centrality. The uncertainty resulting from the subtraction of the contamination from weak decays of strange hadrons is estimated, from the tuned MC simulations, to amount to about 0.5% by varying the strangeness content by ±30%. The uncertainty due to the extrapolation down to zero pTis estimated to be about 0.5% by varying the number of particles

below the 50 MeV/c low-pTcut-off by ±30%. An uncertainty of 1% for variations in detector acceptance

and efficiency was evaluated by carrying out the analysis for different slices of the z-position of the interaction vertex distribution and with subsamples in azimuth.

Other effects due to particle composition, background events, pileup, material budget and tracklet selec-tion criteria were found to be negligible. The final systematic uncertainties assigned to the measurements are the quadratic sums of the individual contributions, and range from 2.6% in central 0–2.5% collisions to 7.6% in 70–80% peripheral collisions, of which 2.3% and 7.5%, respectively, are centrality dependent and 1.2% are centrality independent.

The results for hdNch/dηi are shown in Table 1. In order to compare bulk particle production at different































AA, central












pA(dA), NSD





| < 0.5







Fig. 1: Values of hN2

partihdNch/dηi for central Pb–Pb [4–7] and Au–Au [8–12] collisions (see text) as a function of

sNN. Measurements for inelastic pp and pp collisions as a function of

sare also shown [26–28] along with those from non-single diffractive p–A and d–A collisions [29, 30]. The s-dependencies of the AA and pp (pp) collision data are well described by the functions s0.155NN (solid line) and s0.103NN (dashed line), respectively. The shaded bands show the uncertainties on the extracted power-law dependencies. The central Pb–Pb measurements from CMS and ATLAS at 2.76 TeV have been shifted horizontally for clarity.

the charged-particle density is divided by the average number of participating nucleon pairs, hNparti/2.

The hNparti values are calculated with an MC-Glauber for centrality classes defined by classifying the

events according to their impact parameter and are also listed in Table 1. The systematic uncertainty on hNparti is obtained by independently varying the parameters of the Glauber model within their

es-timated uncertainties. For the most central 0–5% collisions, a density of primary charged particles at mid-rapidity hdNch/dηi = 1943 ± 54 was measured and, normalized per participant pair corresponds to


hNpartihdNch/dηi = 10.1 ± 0.3. In Figure 1 this value is compared to the existing data for central Pb–Pb

and Au–Au collisions from experiments at LHC [4–6], RHIC [8–12] and SPS [7]. The data shown are for 0–5% except for the results from PHOBOS [11] and ATLAS [5] which are for 0–6%. The dependence of hN2

partihdNch/dηi on the center-of-mass energy can be fitted with a power law of the form a · s

b. This

gives an exponent, under the assumption of uncorrelated uncertainties, of b = 0.155 ± 0.004. It is a much stronger s-dependence than for proton–proton collisions, where a value of b = 0.103 ± 0.002 is obtained from a fit to the same function [28]. The fit results are plotted with their uncertainties shown as shaded bands. The result at√sNN= 5.02 TeV confirms the trend established by lower energy data since b is not significantly different when the new point is excluded from the fit. It can also be seen in the figure that the values ofhN2

partihdNch/dηi measured by ALICE for p–Pb [18] and PHOBOS for d–Au [11] collisions






















= 5.02 TeV




= 5.02 TeV




= 2.76 TeV (x1.2)




= 2.76 TeV (x1.13)




| < 0.5



Fig. 2: ThehN2

partihdNch/dηi for Pb–Pb collisions at

sNN= 5.02 TeV in the centrality range 0–80%, as a function

of hNparti in each centrality class. The error bars indicate the point-to-point centrality-dependent uncertainties

whereas the shaded band shows the correlated contributions. Also shown is the result from non-single diffractive p–Pb collisions at the same√sNN[18]. Data from lower energy (2.76 TeV) Pb–Pb and pp collisions [4, 26], scaled

by a factor of 1.2 and 1.13 respectively, are shown for comparison. The error bars for p–Pb at√sNN= 5.02 TeV

and lower energy Pb–Pb and pp collisions indicate the total uncertainty.

the multiple collisions undergone by the participants since the proton in p–A collisions also encounters multiple nucleons.

The centrality dependence of hN2

partihdNch/dηi is shown in Figure 2. The point-to-point

centrality-dependent uncertaintes are indicated by error bars whereas the shaded bands show the correlated con-tributions. The statistical uncertainties are negligible. The data are plotted as a function of hNparti and

a strong dependence is observed, with hN2

partihdNch/dηi decreasing by a factor 1.8 from the most central

collisions, large hNparti, to the most peripheral, small hNparti. There appears to be a smooth trend towards

the value measured in minimum bias p–Pb collisions [18]. The Pb–Pb data measured at√sNN = 2.76 TeV [4] are also shown, scaled by a factor 1.2, which is calculated from the observed s0.155dependence of the results in the most central collisions, and which describes well the increase for all centralities. The proton–proton result at the same energy [26] is scaled by a factor 1.13 from the s0.103dependence. The ratio between the data measured at the two collision energies is consistent with being independent of Npart, within the uncertainties, which are largely uncorrelated. While in general the uncertainties related

to the tracklet measurement are correlated between the two analyses, the subtraction of the background and the centrality classification are, instead, uncorrelated, depending on the determination of the usable fraction of the hadronic cross-section and therefore on the run and detector conditions [15].





















= 5.02 TeV





= 0.28


HIJING 2.1, s

/s = 0.20





et al.


et al.


| < 0.5



Fig. 3: The hN2

partihdNch/dηi for Pb–Pb collisions at

sNN= 5.02 TeV in the centrality range 0-80%, as function a

of hNparti in each centrality class, compared to model predictions [31–39].

Figure 3 shows a comparison of the data to some of the models which were compared to the measure-ments at lower energy. The curves shown are predictions of the models, without any retuning of the parameters based on the new data presented here.

Predictions from commonly used Monte Carlo generators, HIJING [33] and EPOS LHC [39], are also shown. HIJING combines perturbative-QCD (pQCD) processes with soft interactions, and includes a strong impact parameter dependence of parton shadowing. The data at√sNN= 2.76 TeV were previously

compared to HIJING using gluon shadowing parameter, sg, values of 0.20 and 0.23 [4]. The higher value

gave a better estimate of the overall normalization, the lower one a better agreement with the shape. At √

sNN= 5.02 TeV a larger sgvalue of 0.28 is required to limit the multiplicity per participant, leading to

a centrality dependence which does not reproduce the data. EPOS is a model based on the Gribov-Regge theory at parton level which incorporates collective effects treated via a flow parametrisation in the EPOS LHC version. It provides a good description of the data.

Saturation-inspired models (rcBK-MC, with the MV initial conditions [35, 36], Kharzeev et al. [38] and Armesto et al. [37]) rely on pQCD and use an initial-state gluon density to fix an energy-dependent scale at which the quark and gluon densities saturate thereby limiting the number of produced partons and, in turn, of particles. This results in a factorization of the energy and centrality dependences of the multiplicity in the models, as observed in the experimental data. The rcBK-MC and Armesto et al. models provide a better description of the data, in particular of the shape, than the Kharzeev et al. model. The EKRT model [31, 32] combines collinearly factorized next-to-leading order pQCD mini-jet cross sections with a conjecture of gluon saturation to suppress soft parton production. Impact-parameter


de-pendent EPS09s parton distribution functions [40] are used. The space-time evolution of the system with the computed initial conditions is described with relativistic viscous hydrodynamics event-by-event. The normalization is fixed by exploiting the 0–5% most central multiplicity measurement [19]. The EKRT model can broadly describe both the shape and the overall magnitude of the dependence of multiplic-ity on centralmultiplic-ity. In general, theoretical models need some sort of mechanism to limit the growth of multiplicity in order to describe the centrality and energy evolution of the multiplicity.

In summary, we have measured the charged-particle pseudorapidity density hdNch/dηi in Pb–Pb

col-lisions at the highest available center-of-mass energy and observe a 20% increase for the most central collisions with respect to similar measurements at 2.76 TeV, in agreement with the previously estab-lished power-law dependence of this quantity. The centrality dependence of dNch/dη is very similar to

that previously measured in lower energy AA collisions, with a factor of 1.8 increase from peripheral to central collisions. Most of the models which were able to reproduce the data at√sNN= 2.76 TeV are able

to describe the data at√sNN = 5.02 TeV. Our results provide further constraints for models describing high-energy heavy-ion collisions.


The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable con-tributions 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) collab-oration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: State Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds Kidagan, Armenia; Conselho Nacional de Desenvolvimento Cient´ıfico e Tec-nol´ogico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundac¸˜ao de Amparo `a Pesquisa do Estado de S˜ao Paulo (FAPESP); National Natural Science Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the Ministry of Science and Technology of China (MSTC); Min-istry of Education and Youth of the Czech Republic; Danish Natural Science Research Council, the Carlsberg Foundation and the Danish National Research Foundation; The European Research Council under the European Community’s Seventh Framework Programme; Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA, France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie (BMBF) and the Helmholtz Association; General Secretariat for Research and Technology, Ministry of Development, Greece; National Research, Development and Innovation Office (NKFIH), Hungary; Department of Atomic Energy and Department of Science and Technology of the Government of India; Istituto Nazionale di Fisica Nucleare (INFN) and Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Italy; Japan Society for the Promotion of Science (JSPS) KAKENHI and MEXT, Japan; Joint Institute for Nuclear Research, Dubna; National Research Foun-dation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT), Direccion General de Asuntos del Personal Academico(DGAPA), M´exico, Amerique Latine Formation academique - Euro-pean Commission (ALFA-EC) and the EPLANET Program (EuroEuro-pean Particle Physics Latin American Network); Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway (NFR); National Science Centre, Poland; Ministry of National Education/Institute for Atomic Physics and National Coun-cil of Scientific Research in Higher Education (CNCSI-UEFISCDI), Romania; Ministry of Education and Science of Russian Federation, Russian Academy of Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science and Innovations and The Russian Foundation for Basic Re-search; Ministry of Education of Slovakia; Department of Science and Technology, South Africa; Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT), E-Infrastructure shared


between Europe and Latin America (EELA), Ministerio de Econom´ıa y Competitividad (MINECO) of Spain, Xunta de Galicia (Conseller´ıa de Educaci´on), Centro de Aplicaciones Tecnolgicas y Desarrollo Nuclear (CEADEN), Cubaenerg´ıa, Cuba, and IAEA (International Atomic Energy Agency); Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW); Ukraine Ministry of Edu-cation and Science; United Kingdom Science and Technology Facilities Council (STFC); The United States Department of Energy, the United States National Science Foundation, the State of Texas, and the State of Ohio; Ministry of Science, Education and Sports of Croatia and Unity through Knowledge Fund, Croatia; Council of Scientific and Industrial Research (CSIR), New Delhi, India; Pontificia Universidad Cat´olica del Per´u.


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J. Adam40, D. Adamov´a84, M.M. Aggarwal88, G. Aglieri Rinella36, M. Agnello110, N. Agrawal48,

Z. Ahammed132, S. Ahmad19, S.U. Ahn68, S. Aiola136, A. Akindinov58, S.N. Alam132, D. Aleksandrov80,

B. Alessandro110, D. Alexandre101, R. Alfaro Molina64, A. Alici12 ,104, A. Alkin3, J.R.M. Almaraz119,

J. Alme38, T. Alt43, S. Altinpinar18, I. Altsybeev131, C. Alves Garcia Prado120, C. Andrei78, A. Andronic97, V. Anguelov94, T. Antiˇci´c98, F. Antinori107, P. Antonioli104, L. Aphecetche113, H. Appelsh¨auser53,

S. Arcelli28, R. Arnaldi110, O.W. Arnold37 ,93, I.C. Arsene22, M. Arslandok53, B. Audurier113,

A. Augustinus36, R. Averbeck97, M.D. Azmi19, A. Badal`a106, Y.W. Baek67, S. Bagnasco110, R. Bailhache53, R. Bala91, S. Balasubramanian136, A. Baldisseri15, R.C. Baral61, A.M. Barbano27, R. Barbera29, F. Barile33, G.G. Barnaf¨oldi135, L.S. Barnby101, V. Barret70, P. Bartalini7, K. Barth36, J. Bartke117, E. Bartsch53, M. Basile28, N. Bastid70, S. Basu132, B. Bathen54, G. Batigne113, A. Batista Camejo70, B. Batyunya66, P.C. Batzing22, I.G. Bearden81, H. Beck53, C. Bedda110, N.K. Behera50, I. Belikov55, F. Bellini28, H. Bello Martinez2, R. Bellwied122, R. Belmont134, E. Belmont-Moreno64, V. Belyaev75, P. Benacek84, G. Bencedi135, S. Beole27, I. Berceanu78, A. Bercuci78, Y. Berdnikov86, D. Berenyi135, R.A. Bertens57, D. Berzano36, L. Betev36, A. Bhasin91, I.R. Bhat91, A.K. Bhati88, B. Bhattacharjee45, J. Bhom128, L. Bianchi122,

N. Bianchi72, C. Bianchin134 ,57, J. Bielˇc´ık40, J. Bielˇc´ıkov´a84, A. Bilandzic81 ,37 ,93, G. Biro135, R. Biswas4, S. Biswas79, S. Bjelogrlic57, J.T. Blair118, D. Blau80, C. Blume53, F. Bock74 ,94, A. Bogdanov75, H. Bøggild81,

L. Boldizs´ar135, M. Bombara41, J. Book53, H. Borel15, A. Borissov96, M. Borri83 ,124, F. Boss´u65, E. Botta27,

C. Bourjau81, P. Braun-Munzinger97, M. Bregant120, T. Breitner52, T.A. Broker53, T.A. Browning95,

M. Broz40, E.J. Brucken46, E. Bruna110, G.E. Bruno33, D. Budnikov99, H. Buesching53, S. Bufalino36 ,27, P. Buncic36, O. Busch94 ,128, Z. Buthelezi65, J.B. Butt16, J.T. Buxton20, D. Caffarri36, X. Cai7, H. Caines136, L. Calero Diaz72, A. Caliva57, E. Calvo Villar102, P. Camerini26, F. Carena36, W. Carena36, F. Carnesecchi28, J. Castillo Castellanos15, A.J. Castro125, E.A.R. Casula25, C. Ceballos Sanchez9, P. Cerello110, J. Cerkala115, B. Chang123, S. Chapeland36, M. Chartier124, J.L. Charvet15, S. Chattopadhyay132, S. Chattopadhyay100, A. Chauvin93 ,37, V. Chelnokov3, M. Cherney87, C. Cheshkov130, B. Cheynis130, V. Chibante Barroso36, D.D. Chinellato121, S. Cho50, P. Chochula36, K. Choi96, M. Chojnacki81, S. Choudhury132, P. Christakoglou82, C.H. Christensen81, P. Christiansen34, T. Chujo128, S.U. Chung96, C. Cicalo105, L. Cifarelli12 ,28,

F. Cindolo104, J. Cleymans90, F. Colamaria33, D. Colella59 ,36, A. Collu74 ,25, M. Colocci28, G. Conesa Balbastre71, Z. Conesa del Valle51, M.E. Connors,ii,136, J.G. Contreras40, T.M. Cormier85, Y. Corrales Morales110, I. Cort´es Maldonado2, P. Cortese32, M.R. Cosentino120, F. Costa36, P. Crochet70, R. Cruz Albino11, E. Cuautle63, L. Cunqueiro54 ,36, T. Dahms93 ,37, A. Dainese107, M.C. Danisch94, A. Danu62, D. Das100, I. Das100 ,51, S. Das4, A. Dash121 ,79, S. Dash48, S. De120, A. De Caro12 ,31, G. de Cataldo103, C. de

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T.W. Snellman123, C. Søgaard34, J. Song96, M. Song137, Z. Song7, F. Soramel30, S. Sorensen125,

R.D.de Souza121, F. Sozzi97, M. Spacek40, E. Spiriti72, I. Sputowska117, M. Spyropoulou-Stassinaki89,

J. Stachel94, I. Stan62, P. Stankus85, G. Stefanek77, E. Stenlund34, G. Steyn65, J.H. Stiller94, D. Stocco113, P. Strmen39, A.A.P. Suaide120, T. Sugitate47, C. Suire51, M. Suleymanov16, M. Suljic26 ,i, R. Sultanov58, M. ˇSumbera84, A. Szabo39, A. Szanto de Toledo120 ,i, I. Szarka39, A. Szczepankiewicz36, M. Szymanski133, U. Tabassam16, J. Takahashi121, G.J. Tambave18, N. Tanaka128, M.A. Tangaro33, M. Tarhini51, M. Tariq19, M.G. Tarzila78, A. Tauro36, G. Tejeda Mu˜noz2, A. Telesca36, K. Terasaki127, C. Terrevoli30, B. Teyssier130, J. Th¨ader74, D. Thomas118, R. Tieulent130, A.R. Timmins122, A. Toia53, S. Trogolo27, G. Trombetta33, V. Trubnikov3, W.H. Trzaska123, T. Tsuji127, A. Tumkin99, R. Turrisi107, T.S. Tveter22, K. Ullaland18, A. Uras130, G.L. Usai25, A. Utrobicic129, M. Vajzer84, M. Vala59, L. Valencia Palomo70, S. Vallero27, J. Van Der Maarel57, J.W. Van Hoorne36, M. van Leeuwen57, T. Vanat84, P. Vande Vyvre36, D. Varga135, A. Vargas2, M. Vargyas123, R. Varma48, M. Vasileiou89, A. Vasiliev80, A. Vauthier71, V. Vechernin131, A.M. Veen57, M. Veldhoen57, A. Velure18, M. Venaruzzo73, E. Vercellin27, S. Vergara Lim´on2, R. Vernet8, M. Verweij134, L. Vickovic116, G. Viesti30 ,i, J. Viinikainen123, Z. Vilakazi126, O. Villalobos Baillie101, A. Villatoro Tello2, A. Vinogradov80, L. Vinogradov131, Y. Vinogradov99 ,i, T. Virgili31, V. Vislavicius34, Y.P. Viyogi132,

A. Vodopyanov66, M.A. V¨olkl94, K. Voloshin58, S.A. Voloshin134, G. Volpe33, B. von Haller36,

I. Vorobyev37 ,93, D. Vranic97 ,36, J. Vrl´akov´a41, B. Vulpescu70, B. Wagner18, J. Wagner97, H. Wang57,

M. Wang7 ,113, D. Watanabe128, Y. Watanabe127, M. Weber36 ,112, S.G. Weber97, D.F. Weiser94, J.P. Wessels54, U. Westerhoff54, A.M. Whitehead90, J. Wiechula35, J. Wikne22, G. Wilk77, J. Wilkinson94,

M.C.S. Williams104, B. Windelband94, M. Winn94, H. Yang57, P. Yang7, S. Yano47, C. Yasar69, Z. Yin7, H. Yokoyama128, I.-K. Yoo96, J.H. Yoon50, V. Yurchenko3, I. Yushmanov80, A. Zaborowska133, V. Zaccolo81, A. Zaman16, C. Zampolli36 ,104, H.J.C. Zanoli120, S. Zaporozhets66, N. Zardoshti101, A. Zarochentsev131, P. Z´avada60, N. Zaviyalov99, H. Zbroszczyk133, I.S. Zgura62, M. Zhalov86, H. Zhang18, X. Zhang74, Y. Zhang7, C. Zhang57, Z. Zhang7, C. Zhao22, N. Zhigareva58, D. Zhou7, Y. Zhou81, Z. Zhou18, H. Zhu18, J. Zhu113 ,7, A. Zichichi28 ,12, A. Zimmermann94, M.B. Zimmermann54 ,36, G. Zinovjev3, M. Zyzak43

Affiliation notes


iiAlso at: Georgia State University, Atlanta, Georgia, United States

iiiAlso at: Also at Department of Applied Physics, Aligarh Muslim University, Aligarh, India ivAlso at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics,

Moscow, Russia

Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2 Benem´erita Universidad Aut´onoma de Puebla, Puebla, Mexico

3 Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

4 Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS),

Kolkata, India

5 Budker Institute for Nuclear Physics, Novosibirsk, Russia

6 California Polytechnic State University, San Luis Obispo, California, United States 7 Central China Normal University, Wuhan, China

8 Centre de Calcul de l’IN2P3, Villeurbanne, France


10 Centro de Investigaciones Energ´eticas Medioambientales y Tecnol´ogicas (CIEMAT), Madrid, Spain 11 Centro de Investigaci´on y de Estudios Avanzados (CINVESTAV), Mexico City and M´erida, Mexico 12 Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Rome, Italy 13 Chicago State University, Chicago, Illinois, USA

14 China Institute of Atomic Energy, Beijing, China

15 Commissariat `a l’Energie Atomique, IRFU, Saclay, France

16 COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

17 Departamento de F´ısica de Part´ıculas and IGFAE, Universidad de Santiago de Compostela, Santiago de

Compostela, Spain

18 Department of Physics and Technology, University of Bergen, Bergen, Norway 19 Department of Physics, Aligarh Muslim University, Aligarh, India

20 Department of Physics, Ohio State University, Columbus, Ohio, United States 21 Department of Physics, Sejong University, Seoul, South Korea

22 Department of Physics, University of Oslo, Oslo, Norway

23 Dipartimento di Elettrotecnica ed Elettronica del Politecnico, Bari, Italy

24 Dipartimento di Fisica dell’Universit`a ’La Sapienza’ and Sezione INFN Rome, Italy 25 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Cagliari, Italy

26 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Trieste, Italy 27 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Turin, Italy

28 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Bologna, Italy 29 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Catania, Italy 30 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Padova, Italy

31 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Universit`a and Gruppo Collegato INFN, Salerno, Italy 32 Dipartimento di Scienze e Innovazione Tecnologica dell’Universit`a del Piemonte Orientale and Gruppo

Collegato INFN, Alessandria, Italy

33 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 34 Division of Experimental High Energy Physics, University of Lund, Lund, Sweden 35 Eberhard Karls Universit¨at T¨ubingen, T¨ubingen, Germany

36 European Organization for Nuclear Research (CERN), Geneva, Switzerland 37 Excellence Cluster Universe, Technische Universit¨at M¨unchen, Munich, Germany 38 Faculty of Engineering, Bergen University College, Bergen, Norway

39 Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia

40 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague,

Czech Republic

41 Faculty of Science, P.J. ˇSaf´arik University, Koˇsice, Slovakia

42 Faculty of Technology, Buskerud and Vestfold University College, Vestfold, Norway

43 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt,


44 Gangneung-Wonju National University, Gangneung, South Korea 45 Gauhati University, Department of Physics, Guwahati, India 46 Helsinki Institute of Physics (HIP), Helsinki, Finland 47 Hiroshima University, Hiroshima, Japan

48 Indian Institute of Technology Bombay (IIT), Mumbai, India 49 Indian Institute of Technology Indore, Indore (IITI), India 50 Inha University, Incheon, South Korea

51 Institut de Physique Nucl´eaire d’Orsay (IPNO), Universit´e Paris-Sud, CNRS-IN2P3, Orsay, France 52 Institut f¨ur Informatik, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 53 Institut f¨ur Kernphysik, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 54 Institut f¨ur Kernphysik, Westf¨alische Wilhelms-Universit¨at M¨unster, M¨unster, Germany

55 Institut Pluridisciplinaire Hubert Curien (IPHC), Universit´e de Strasbourg, CNRS-IN2P3, Strasbourg,


56 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia 57 Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands 58 Institute for Theoretical and Experimental Physics, Moscow, Russia

59 Institute of Experimental Physics, Slovak Academy of Sciences, Koˇsice, Slovakia


61 Institute of Physics, Bhubaneswar, India

62 Institute of Space Science (ISS), Bucharest, Romania

63 Instituto de Ciencias Nucleares, Universidad Nacional Aut´onoma de M´exico, Mexico City, Mexico 64 Instituto de F´ısica, Universidad Nacional Aut´onoma de M´exico, Mexico City, Mexico

65 iThemba LABS, National Research Foundation, Somerset West, South Africa 66 Joint Institute for Nuclear Research (JINR), Dubna, Russia

67 Konkuk University, Seoul, South Korea

68 Korea Institute of Science and Technology Information, Daejeon, South Korea 69 KTO Karatay University, Konya, Turkey

70 Laboratoire de Physique Corpusculaire (LPC), Clermont Universit´e, Universit´e Blaise Pascal,

CNRS–IN2P3, Clermont-Ferrand, France

71 Laboratoire de Physique Subatomique et de Cosmologie, Universit´e Grenoble-Alpes, CNRS-IN2P3,

Grenoble, France

72 Laboratori Nazionali di Frascati, INFN, Frascati, Italy 73 Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

74 Lawrence Berkeley National Laboratory, Berkeley, California, United States 75 Moscow Engineering Physics Institute, Moscow, Russia

76 Nagasaki Institute of Applied Science, Nagasaki, Japan 77 National Centre for Nuclear Studies, Warsaw, Poland

78 National Institute for Physics and Nuclear Engineering, Bucharest, Romania 79 National Institute of Science Education and Research, Bhubaneswar, India 80 National Research Centre Kurchatov Institute, Moscow, Russia

81 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 82 Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands 83 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

84 Nuclear Physics Institute, Academy of Sciences of the Czech Republic, ˇReˇz u Prahy, Czech Republic 85 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

86 Petersburg Nuclear Physics Institute, Gatchina, Russia

87 Physics Department, Creighton University, Omaha, Nebraska, United States 88 Physics Department, Panjab University, Chandigarh, India

89 Physics Department, University of Athens, Athens, Greece

90 Physics Department, University of Cape Town, Cape Town, South Africa 91 Physics Department, University of Jammu, Jammu, India

92 Physics Department, University of Rajasthan, Jaipur, India

93 Physik Department, Technische Universit¨at M¨unchen, Munich, Germany

94 Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany 95 Purdue University, West Lafayette, Indiana, United States

96 Pusan National University, Pusan, South Korea

97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum f¨ur

Schwerionenforschung, Darmstadt, Germany

98 Rudjer Boˇskovi´c Institute, Zagreb, Croatia

99 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia 100 Saha Institute of Nuclear Physics, Kolkata, India

101 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 102 Secci´on F´ısica, Departamento de Ciencias, Pontificia Universidad Cat´olica del Per´u, Lima, Peru 103 Sezione INFN, Bari, Italy

104 Sezione INFN, Bologna, Italy 105 Sezione INFN, Cagliari, Italy 106 Sezione INFN, Catania, Italy 107 Sezione INFN, Padova, Italy 108 Sezione INFN, Rome, Italy 109 Sezione INFN, Trieste, Italy 110 Sezione INFN, Turin, Italy

111 SSC IHEP of NRC Kurchatov institute, Protvino, Russia

112 Stefan Meyer Institut f¨ur Subatomare Physik (SMI), Vienna, Austria


114 Suranaree University of Technology, Nakhon Ratchasima, Thailand 115 Technical University of Koˇsice, Koˇsice, Slovakia

116 Technical University of Split FESB, Split, Croatia

117 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 118 The University of Texas at Austin, Physics Department, Austin, Texas, USA

119 Universidad Aut´onoma de Sinaloa, Culiac´an, Mexico 120 Universidade de S˜ao Paulo (USP), S˜ao Paulo, Brazil

121 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 122 University of Houston, Houston, Texas, United States

123 University of Jyv¨askyl¨a, Jyv¨askyl¨a, Finland

124 University of Liverpool, Liverpool, United Kingdom

125 University of Tennessee, Knoxville, Tennessee, United States 126 University of the Witwatersrand, Johannesburg, South Africa 127 University of Tokyo, Tokyo, Japan

128 University of Tsukuba, Tsukuba, Japan 129 University of Zagreb, Zagreb, Croatia

130 Universit´e de Lyon, Universit´e Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, France 131 V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia 132 Variable Energy Cyclotron Centre, Kolkata, India

133 Warsaw University of Technology, Warsaw, Poland 134 Wayne State University, Detroit, Michigan, United States

135 Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary 136 Yale University, New Haven, Connecticut, United States

137 Yonsei University, Seoul, South Korea

138 Zentrum f¨ur Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms,


Figure 3 shows a comparison of the data to some of the models which were compared to the measure- measure-ments at lower energy


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