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.

We present the first wide-range measurement of the charged-particle pseudorapidity density distribution, for different centralities (the 0-5%, 5-10%, 10-20%, and 20-30% most central events) in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the LHC. The measurement is performed using the full coverage of the ALICE detectors, $-5.0 < \eta < 5.5$, and employing a special analysis technique based on collisions arising from LHC "satellite" bunches. We present the pseudorapidity density as a function of the number of participating nucleons as well as an extrapolation to the total number of produced charged particles ($N_{\rm ch} = 17165 \pm 772$ for the 0-5% most central collisions). From the measured ${\rm d}N_{\rm ch}/{\rm d}\eta$ distribution we derive the rapidity density distribution, ${\rm d}N_{\rm ch}/{\rm d}y$, under simple assumptions. The rapidity density distribution is found to be significantly wider than the predictions of the Landau model. We assess the validity of longitudinal scaling by comparing to lower energy results from RHIC. Finally the mechanisms of the underlying particle production are discussed based on a comparison with various theoretical models.

Data on multiplicities of charged particles produced in proton-nucleus and nucleus-nucleus collisions at 200 GeV per nucleon are presented. It is shown that the mean multiplicity of negative particles is proportional to the mean number of nucleons participating in the collision both for nucleus-nucleus and proton-nucleus collisions. The apparent consistency of pion multiplicity data with the assumption of an incoherent superposition of nucleon-nucleon collisions is critically discussed.

The production of two high-p_T jets in the interactions of quasi-real photons in e+e- collisions at sqrt{s_ee} from 189 GeV to 209 GeV is studied with data corresponding to an integrated e+e- luminosity of 550 pb^{-1}. The jets reconstructed by the k_T cluster algorithm are defined within the pseudo-rapidity range -1 < eta < 1 and with jet transverse momentum, p_T, above 3 GeV/c. The differential di-jet cross-section is measured as a function of the mean transverse momentum ptmean of the jets and is compared to perturbative QCD calculations.

We report the first measurement of charged particle elliptic flow in Pb-Pb collisions at 2.76 TeV with the ALICE detector at the CERN Large Hadron Collider. The measurement is performed in the central pseudorapidity region (|$\eta$|<0.8) and transverse momentum range 0.2< $p_{\rm T}$< 5.0 GeV/$c$. The elliptic flow signal v$_2$, measured using the 4-particle correlation method, averaged over transverse momentum and pseudorapidity is 0.087 $\pm$ 0.002 (stat) $\pm$ 0.004 (syst) in the 40-50% centrality class. The differential elliptic flow v$_2(p_{\rm T})$ reaches a maximum of 0.2 near $p_{\rm T}$ = 3 GeV/$c$. Compared to RHIC Au-Au collisions at 200 GeV, the elliptic flow increases by about 30%. Some hydrodynamic model predictions which include viscous corrections are in agreement with the observed increase.

We report measurements of Xi and Xi-bar hyperon absolute yields as a function of rapidity in 158 GeV/c Pb+Pb collisions. At midrapidity, dN/dy = 2.29 +/- 0.12 for Xi, and 0.52 +/- 0.05 for Xi-bar, leading to the ratio of Xi-bar/Xi = 0.23 +/- 0.03. Inverse slope parameters fitted to the measured transverse mass spectra are of the order of 300 MeV near mid-rapidity. The estimated total yield of Xi particles in Pb+Pb central interactions amounts to 7.4 +/- 1.0 per collision. Comparison to Xi production in properly scaled p+p reactions at the same energy reveals a dramatic enhancement (about one order of magnitude) of Xi production in Pb+Pb central collisions over elementary hadron interactions.

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Inclusive double differential multiplicities d2N/dy dpt and related quantities have been measured for protons and deuterons produced in 14.6A GeV/c Si+Al and Si+Pb collisions using the E814 forward spectrometer at the AGS at BNL. Collision ‘‘centrality’’ is determined by measuring Nc, the total charged particle multiplicity in the pseudorapidity range 0.85<η<3.8. For both systems Si + Al and Si + Pb, an increase in the proton rapidity distribution dN/dy at midrapidity and a corresponding decrease at higher rapidities are observed with increasing Nc. For Si+Pb, Boltzmann slope parameters TB increase significantly in the most central collisions. The measured distributions exhibit a centrality dependence even when σ/σgeo≲10%, where full overlap between the Si and Pb nuclei occurs in a simple geometric picture. The proton rapidity distribution dN/dy is presented for the symmetric system Si+Al over the entire rapididty interval. The total number of protons, which is the integral of this quantity over rapidity, varies with Nc. Results are compared with various model calculations, mostly using the hadronic cascade codes ARC and RQMD. No significant nuclear transparency is observed, indicating that large baryon and energy densities are produced in these collisions.

The production of π±,K±,p has been measured in p+Be and p+Au collisions for comparison with central Si+Au collisions. The inverse slope parameters T0 obtained by an exponential fit to the invariant cross sections in transverse mass are found to be, T0p,K+,ππ∼140–160 MeV in p+A collisions, whereas in central Si+Au collisions, T0p,K+∼200–220 MeV >T0ππ∼140–160 MeV at midrapidity. The π± and K+ distributions are shifted backwards in p+Au compared with p+Be. A gradual increase of (dn/dy)K+ per projectile nucleon is observed from p+Be to p+Au to central Si+Au collisions, while pions show no significant increase.

Inelastic cross sections at 60 and 200 GeV/nucleon are determined in a streamer chamber for 16 O on several nuclear targets. Charged particle multiplicity distributions for inelastic and central collisions are studied and compared with theoretical predictions. The inelastic cross section exhibit a geometrical dependence on nuclear radii. The multiplicity data are governed by the collision geometry. They are consistent with a picture of superposition of independent nucleon-nucleus interactions.