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

The pseudorapidity density of charged particles ($\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta$) at mid-rapidity in Pb-Pb collisions has been measured at a center-of-mass energy per nucleon pair of $\sqrt{s_{\rm NN}}$ = 5.02 TeV. It increases with centrality and reaches a value of $1943 \pm 54$ in $|\eta|<0.5$ for the 5% most central collisions. A rise in $\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta$ as a function of $\sqrt{s_{\rm NN}}$ for the most central collisions is observed, steeper than that observed in proton-proton collisions and following the trend established by measurements at lower energy. The centrality dependence of $\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta$ as a function of the average number of participant nucleons, ${\langle N_\mathrm{part} \rangle}$, calculated in a Glauber model, is compared with the previous measurement at lower energy. A constant factor of about 1.2 describes the increase in $\frac{2}{\langle N_\mathrm{part} \rangle}\langle \mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta \rangle$ from $\sqrt{s_{\rm NN}}$ = 2.76 TeV to $\sqrt{s_{\rm NN}}$ = 5.02 TeV for all centrality intervals, 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.

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 particleproducing sources is given by f × N part + (1 − f ) × N coll , where N part is the number of participating nucleons, N coll 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 nuclear density for 208 Pb 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 electronnucleus scattering experiments [17], and a hard-sphere exclusion distance between nucleons of 0.4 ± 0.4 fm. For √ s NN = 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 dN ch /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, δ 2 = (∆ϕ/σ ϕ ) 2 + (∆θ /σ θ ) 2 < 1.5, where σ ϕ = 60 mrad and σ θ = 25 sin 2 θ mrad. This selection effectively allows the reconstruction of charged particles with transverse momentum (p T ) 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 p T , and for the removal of combinatorial background tracklets. 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 generator output is performed to reproduce the p T distributions of inclusive charged hadrons and the relative abundances of pions, protons, kaons and other strange particles as measured in Pb 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 uncertainties estimated below.
The correction takes into account any inactive channels present at the time of data taking as well as √ s NN = 5. 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 contamination 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 p T is estimated to be about 0.5% by varying the number of particles below the 50 MeV/c low-p T cut-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 selection 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 dN ch /dη are shown in Table 1. In order to compare bulk particle production at different energies and in different collision systems, specifically for a direct comparison to pp and pp collisions, √ s NN = 5.02 TeV ALICE Collaboration the charged-particle density is divided by the average number of participating nucleon pairs, N part /2. The N part 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 N part is obtained by independently varying the parameters of the Glauber model within their estimated uncertainties. For the most central 0-5% collisions, a density of primary charged particles at mid-rapidity dN ch /dη = 1943 ± 54 was measured and, normalized per participant pair corresponds to 2 N part dN ch /dη = 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][5][6], RHIC [8][9][10][11][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 2 N part dN ch /dη 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   The centrality dependence of 2 N part dN ch /dη is shown in Figure 2. The point-to-point centralitydependent uncertaintes are indicated by error bars whereas the shaded bands show the correlated contributions. The statistical uncertainties are negligible. The data are plotted as a function of N part and a strong dependence is observed, with 2 N part dN ch /dη decreasing by a factor 1.8 from the most central collisions, large N part , to the most peripheral, small N part . There appears to be a smooth trend towards the value measured in minimum bias p-Pb collisions [18]. The Pb-Pb data measured at √ s NN = 2.76 TeV [4] are also shown, scaled by a factor 1.2, which is calculated from the observed s 0.155 dependence 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 s 0.103 dependence. The ratio between the data measured at the two collision energies is consistent with being independent of N part , 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 [   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 √ s NN = 2.76 TeV were previously compared to HIJING using gluon shadowing parameter, s g , 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 √ s NN = 5.02 TeV a larger s g value 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-√ s NN = 5.02 TeV ALICE Collaboration 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 multiplicity on centrality. 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 dN ch /dη in Pb-Pb collisions 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 established power-law dependence of this quantity. The centrality dependence of dN ch /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 √ s NN = 2.76 TeV are able to describe the data at √ s NN = 5.02 TeV. Our results provide further constraints for models describing high-energy heavy-ion collisions.

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: State Committee of Science, World Federation of Scientists          [26] ALICE Collaboration, K. Aamodt et al., "Charged-particle multiplicities in proton-proton collisions at √ s = 0.9 to 8 TeV, with ALICE at the LHC," arXiv:1509.07541 [nucl-ex].  [31] H. Niemi, K. J. Eskola, and R. Paatelainen, "Event-by-event fluctuations in perturbative QCD + saturation + hydro model: pinning down QCD matter shear viscosity in ultrarelativistic heavy-ion collisions," arXiv:1505.02677 [hep-ph].
Centrality dependence of dN ch /dη in Pb-Pb at √ s NN = 5.02 TeV ALICE Collaboration