# Centrality determination of Pb-Pb collisions at $\sNN = 2.76$ TeV with ALICE

This publication describes the methods used to measure the centrality of inelastic Pb-Pb collisions at a center-of-mass energy of 2.76 TeV per colliding nucleon pair with ALICE. The centrality is a key parameter in the study of the properties of QCD matter at extreme temperature and energy density, because it is directly related to the initial overlap region of the colliding nuclei. Geometrical properties of the collision, such as the number of participating nucleons and number of binary nucleon-nucleon collisions, are deduced from a Glauber model with a sharp impact parameter selection, and shown to be consistent with those extracted from the data. The centrality determination provides a tool to compare ALICE measurements with those of other experiments and with theoretical calculations.

Figures

## Figure 1

 Compilation of total $\sigma_{\rm tot}$, elastic $\sigma_{\rm el}$, and inelastic $\sigma_{\rm inel}$ cross sections of pp and p$\bar{\mathrm {p}}$ collisions. The $\sigma_{tot}$ and $\sigma_{el}$ curves are fits performed by the COMPETE Collaboration. The pp data from ATLAS, CMS, TOTEM, and ALICE agree well with the parameterizations.

## Figure 2

 Geometric properties of Pb-Pb collisions at $\snn=2.76$ TeV obtained from a Glauber Monte Carlo calculation: Impact parameter distribution (top), sliced for percentiles of the hadronic cross section, and distributions of the number of participants (bottom) for the corresponding centrality classes.

## Figure 3

 Sensitivity of $\Npart$ (left) and $\Ncoll$ (right) to variations of parameters in the Glauber Monte Carlo model of Pb-Pb collisions at $\snn = 2.76$ TeV. The gray band represents the RMS of $\Npart$ and $\Ncoll$ respectively. It is scaled by a factor 0.1 for visibility.

## Figure 4

 Time distribution of signals in the VZERO detector on the A side. The peaks corresponding to beam-beam, beam-gas and satellite collision events are clearly visible.

## Figure 5

 Correlation between the sum and the difference of times recorded by the neutron ZDC on either side of the interaction region. The large cluster in the middle corresponds to collisions between ions in the nominal RF buckets of each beam, while the small clusters along the diagonals (spaced by 2.5ns in the time difference) correspond to collisions in which one of the ions is displaced by one or more RF buckets.

## Figure 6

 Correlation between signals in the two neutron zero-degree calorimeters, ZNA and ZNC. Single electromagnetic dissociation events produce signal in only one of the calorimeters. Mutual dissociation and hadronic interactions populate interior of the plot and can be distinguished from each other by the signal in ZEM. (Figure is from arXiv:1203.2436)

## Figure 7

 Efficiency of the three online triggers ($2$-out-of-$3$, V0AND, $3$-out-of-$3$) used for Pb-Pb collisions as a function of the VZERO amplitude calculated with HIJING and AMPT, and measured in dedicated pp runs. The efficiency in the simulation has been calculated for events with $\Npart=2$.

## Figure 8

 VZERO amplitude distribution in data (red points) and simulations with the V0AND interaction trigger. The data are compared to the sum of HIJING + QED + STARLIGHT simulations (histogram) with the same event selection.

## Figure 9

 Purity of the 3 online interaction triggers ($2$-out-of-$3$}, V0AND, $3$-out-of-$3$) and other event selections used for Pb-Pb collisions as a function of the VZERO amplitude calculated with HIJING, STARLIGHT and QED simulations. The dashed line indicates 90% of the hadronic cross section.

## Figure 10

 Distribution of the sum of amplitudes in the VZERO scintillators. The distribution is fitted with the NBD-Glauber fit (explained in the text) shown as a line. The centrality classes used in the analysis are indicated in the figure. The inset shows a zoom of the most peripheral region.

## Figure 11

 Centrality dependence of $\dNdeta$ per participant pair as a function of $\Npart$, measured in the Pb-Pb data at $\snn = 2.76$ TeV fitted with various parametrizations of $\Npart$ and $\Ncoll$, calculated with the Glauber model. The fit parameters are given in the figure.

## Figure 12

 Distribution of the VZERO amplitude zoomed in the most peripheral region. The distribution is compared to the NBD-Glauber fit and to the sum of the HIJING + STARLIGHT + QED simulations.

## Figure 13

 Spectator energy deposited in the ZDC calorimeters as a function of ZEM amplitude. The same correlation is shown for different centrality classes (5%, 10%, 20% and 30%) obtained by selecting specific VZERO amplitudes. The lines are a fit to the boundaries of the centrality classes with linear functions, where only the slope is fitted and the offset point is fixed (see text).

## Figure 14

 VZERO amplitude distribution of events of various centrality classes selected from the correlation between ZDC and ZEM amplitudes explained in the text.

## Figure 15

 Top: Correlation between SPD multiplicity and VZERO amplitude. The rapidity coverage of each detector is indicated on the figure. Bottom: VZERO amplitude distributions for the centrality classes selected by SPD. Two centrality classes (1-2% and 40-45%) are indicated and fitted with a Gaussian.

## Figure 16

 Top: Centrality resolution $\Delta_i$ for all the estimators evaluated in the analysis. Bottom: Resolution, in arbitrary units, scaled by $\sqrt{N_\mathrm{ch}}$ measured in each detector.