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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.

We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle, conjecturally extending previously known results to higher orders in spin at one-loop order. The extraction of the classical limit is accomplished via the on-shell leading-singularity method and using massive spinorhelicity variables. The three-point amplitude for arbitrary-spin massive particles minimally coupled to gravity is expressed in an exponential form, and in the infinite-spin limit it matches the effective stress-energy tensor of the linearized Kerr solution. A four-point gravitational Compton amplitude is obtained from an extrapolated soft theorem, equivalent to gluing two exponential three-point amplitudes, and becomes itself an exponential operator. The construction uses these amplitudes to: 1) recover the known tree-level scattering angle at all orders in spin, 2) recover the known one-loop linear-in-spin interaction, 3) match a previous conjectural expression for the one-loop scattering angle at quadratic order in spin, 4) propose new one-loop results through quartic order in spin. These connections link the computation of higher-multipole interactions to the study of deeper orders in the soft expansion. arXiv:1812.06895v3 [hep-th] 9 Sep 2019 Contents 1 Introduction 1 2 Multipole expansion of three-and four-point amplitudes 6 3 Scattering angle as Leading Singularity 17 4 Discussion 27 A Three-point amplitude with spin-1 matter 29 B Spin tensor for spin-1 matter 30 C Angular-momentum operator 32Recently, a classical version of the soft theorem up to sub-subleading order has been used by Laddha and Sen [22] to derive the spectrum of the radiated power in black-hole scattering with external soft graviton insertions. This relies on the remarkable fact that conservative and non-conservative long-range effects of interacting black holes can be computed from the scattering of massive point-like sources [23][24][25][26]. Indeed, rotating black holes can be treated via a spin-multipole expansion, the order 2s of which can be reproduced by scattering spins minimally coupled particles exchanging gravitons [27], as illustrated in figure 1a. The matching between these amplitudes with spin and a non-relativistic potential for black-hole scattering has been performed explicitly in the post-Newtonian (PN) framework [27][28][29].Here we present a complementary picture to the one of [22] by employing the soft theorem in the conservative sector (i.e. no external gravitons), focusing on rotating black holes and at the same time extending the soft factor in (1.1) to higher orders in the soft expansion. This is achieved in the following way: It was shown by one of the authors in [29] that the classical ( -independent) piece of the spin-s amplitude can be extracted from a covariant Holomorphic Classical...

The ratio of the yields of antiprotons to protons in pp collisions has been measured by the ALICE experiment at sqrt[s]=0.9 and 7 TeV during the initial running periods of the Large Hadron Collider. The measurement covers the transverse momentum interval 0.45