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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 the 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.

In this paper measurements are presented of π ± , K ± , p, andp production at midrapidity (|y| < 0.5), in Pb-Pb collisions at √ s NN = 2.76 TeV as a function of centrality. The measurement covers the transverse-momentum (p T ) range from 100, 200, and 300 MeV/c up to 3, 3, and 4.6 GeV/c for π , K, and p, respectively. The measured p T distributions and yields are compared to expectations based on hydrodynamic, thermal and recombination models. The spectral shapes of central collisions show a stronger radial flow than measured at lower energies, which can be described in hydrodynamic models. In peripheral collisions, the p T distributions are not well reproduced by hydrodynamic models. Ratios of integrated particle yields are found to be nearly independent of centrality. The yield of protons normalized to pions is a factor ∼1.5 lower than the expectation from thermal models.

At su ciently high temperature and energy density, nuclear matter undergoes a transition to a phase in which quarks and gluons are not confined: the quark-gluon plasma (QGP) 1 . Such an exotic state of strongly interacting quantum chromodynamics matter is produced in the laboratory in heavy nuclei high-energy collisions, where an enhanced production of strange hadrons is observed 2-6 . Strangeness enhancement, originally proposed as a signature of QGP formation in nuclear collisions 7 , is more pronounced for multi-strange baryons. Several e ects typical of heavy-ion phenomenology have been observed in high-multiplicity proton-proton (pp) collisions 8,9 , but the enhanced production of multi-strange particles has not been reported so far. Here we present the first observation of strangeness enhancement in high-multiplicity proton-proton collisions. We find that the integrated yields of strange and multi-strange particles, relative to pions, increases significantly with the event charged-particle multiplicity. The measurements are in remarkable agreement with the p-Pb collision results 10,11 , indicating that the phenomenon is related to the final system created in the collision. In high-multiplicity events strangeness production reaches values similar to those observed in Pb-Pb collisions, where a QGP is formed.The production of strange hadrons in high-energy hadronic interactions provides a way to investigate the properties of quantum chromodynamics (QCD), the theory of strongly interacting matter. Unlike up (u) and down (d) quarks, which form ordinary matter, strange (s) quarks are not present as valence quarks in the initial state, yet they are sufficiently light to be abundantly created during the course of the collisions. In the early stages of high-energy collisions, strangeness is produced in hard (perturbative) 2 → 2 partonic scattering processes by flavour creation (gg → ss, qq → ss) and flavour excitation (gs → gs, qs → qs). Strangeness is also created