Model theory of finite and pseudofinite groups

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory

Long- and short-range correlations and their event-scale dependence in high-multiplicity pp collisions at 1as = 13 TeV

Two-particle angular correlations are measured in high-multiplicity proton-proton collisions at s = 13 TeV by the ALICE Collaboration. The yields of particle pairs at short-( 06\u3b7 3c 0) and long-range (1.6 < | 06\u3b7| < 1.8) in pseudorapidity are extracted on the near-side ( 06\u3c6 3c 0). They are reported as a function of transverse momentum (pT) in the range 1 < pT< 4 GeV/c. Furthermore, the event-scale dependence is studied for the first time by requiring the presence of high-pT leading particles or jets for varying pT thresholds. The results demonstrate that the long-range \u201cridge\u201d yield, possibly related to the collective behavior of the system, is present in events with high-pT processes as well. The magnitudes of the short- and long-range yields are found to grow with the event scale. The results are compared to EPOS LHC and PYTHIA 8 calculations, with and without string-shoving interactions. It is found that while both models describe the qualitative trends in the data, calculations from EPOS LHC show a better quantitative agreement for the pT dependency, while overestimating the event-scale dependency. [Figure not available: see fulltext.

Charged-particle multiplicity fluctuations in Pb–Pb collisions at √sNN = 2.76 TeV

Measurements of event-by-event fluctuations of charged-particle multiplicities in Pb–Pb collisions at √sNN = 2.76 TeV using the ALICE detector at the CERN Large Hadron Collider (LHC) are presented in the pseudorapidity range |η|<0.8 and transverse momentum 0.2<pT<2.0 GeV/c. The amplitude of the fluctuations is expressed in terms of the variance normalized by the mean of the multiplicity distribution. The η and pT dependences of the fluctuations and their evolution with respect to collision centrality are investigated. The multiplicity fluctuations tend to decrease from peripheral to central collisions. The results are compared to those obtained from HIJING and AMPT Monte Carlo event generators as well as to experimental data at lower collision energies. Additionally, the measured multiplicity fluctuations are discussed in the context of the isothermal compressibility of the high-density strongly-interacting system formed in central Pb–Pb collisions.publishedVersio

K0SK0S and K0SK± femtoscopy in pp collisions at √s = 5.02 and 13 TeV

Femtoscopic correlations with the particle pair combinations (KSKS0)-K-0 and (KSK +/-)-K-0 are studied in pp collisions at root s= 5.02 and 13 TeV by the ALICE experiment. At both energies, boson source parameters are extracted for both pair combinations, by fitting models based on Gaussian size distributions of the sources, to the measured two-particle correlation functions. The interaction model used for the (KSKS0)-K-0 analysis includes quantum statistics and strong final-state interactions through the f(0) (980) and a(0) (980) resonances. The model used for the (KSK +/-)-K-0 analysis includes only the final-state interaction through the a(0) resonance. Source parameters extracted in the present work are compared with published values from pp collisions at root s = 7 TeV and the different pair combinations are found to be consistent. From the observation that the strength of the (KSKS0)-K-0 correlations is significantly greater than the strength of the (KSK +/-)-K-0 correlations, the new results are compatible with the a(0) resonance being a tetraquark state of the form (q(1), (q(2)) over bar, s, (s) over bar), where q(1) and q(2) are uor d quarks. (C) 2022 European Organization for Nuclear Research, ALICE. Published by Elsevier B.V

Measurement of the production of (anti)nuclei in p–Pb collisions at sNN=8.16TeV

Measurements of (anti)proton, (anti)deuteron, and (anti)3He production in the rapidity range -1 > y > 0 as a function of the transverse momentum and event multiplicity in p–Pb collisions at a center-of-mass energy per nucleon–nucleon pair sqrt(sNN) = 8.16 TeV are presented. The coalescence parameters B2 and B3, measured as a function of the transverse momentum per nucleon and of the mean charged-particle multiplicity density, confirm a smooth evolution from low to high multiplicity across different collision systems and energies. The ratios between (anti)deuteron and (anti)3He yields and those of (anti)protons are also reported as a function of the mean charged-particle multiplicity density. A comparison with the predictions of the statistical hadronization and coalescence models for different collision systems and center-of-mass energies favors the coalescence description for the deuteron-to-proton yield ratio with respect to the canonical statistical model

Hypertriton Production in p-Pb Collisions at √sNN = 5.02 TeV

The study of nuclei and antinuclei production has proven to be a powerful tool to investigate the formation mechanism of loosely bound states in high-energy hadronic collisions. The first measurement of the production of ${\rm ^{3}_{\Lambda}\rm H}$ in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV is presented in this Letter. Its production yield measured in the rapidity interval -1 < y < 0 for the 40% highest multiplicity p-Pb collisions is ${\rm d} N /{\rm d} y =[\mathrm{6.3 \pm 1.8 (stat.) \pm 1.2 (syst.) ] \times 10^{-7}}$. The measurement is compared with the expectations of statistical hadronisation and coalescence models, which describe the nucleosynthesis in hadronic collisions. These two models predict very different yields of the hypertriton in small collision systems such as p-Pb and therefore the measurement of ${\rm d} N /{\rm d} y$ is crucial to distinguish between them. The precision of this measurement leads to the exclusion with a significance larger than 6$\sigma$ of some configurations of the statistical hadronisation, thus constraining the production mechanism of loosely bound states

Polarization of Λ and Λ¯ Hyperons along the Beam Direction in Pb-Pb Collisions at √sNN = 5.02 TeV

The polarization of the Lambda and (Lambda) over bar hyperons along the beam (z) direction, P-z, has been measured in Pb-Pb collisions at root s(NN) = 5.02 TeV recorded with ALICE at the Large Hadron Collider (LHC). The main contribution to P-z comes from elliptic flow-induced vorticity and can be characterized by the second Fourier sine coefficient P-z,P-s2 = &lt; P-z sin(2 phi - 2 Psi(2))&gt;, where phi is the hyperon azimuthal emission angle and Psi(2) is the elliptic flow plane angle. We report the measurement of P-z,P-s2 for different collision centralities and in the 30%-50% centrality interval as a function of the hyperon transverse momentum and rapidity. The P-z,P-s2 is positive similarly as measured by the STAR Collaboration in Au-Au collisions at root s(NN) = 200 GeV, with somewhat smaller amplitude in the semicentral collisions. This is the first experimental evidence of a nonzero hyperon P-z in Pb-Pb collisions at the LHC. The comparison of the measured P-z,P-s2 with the hydrodynamic model calculations shows sensitivity to the competing contributions from thermal and the recently found shear-induced vorticity, as well as to whether the polarization is acquired at the quark-gluon plasma or the hadronic phase

Study of very forward energy and its correlation with particle production at midrapidity in pp and p-Pb collisions at the LHC

The energy deposited at very forward rapidities (very forward energy) is a powerful tool for characterising proton fragmentation in pp and p-Pb collisions. The correlation of very forward energy with particle production at midrapidity provides direct insights into the initial stages and the subsequent evolution of the collision. Furthermore, the correlation with the production of particles with large transverse momenta at midrapidity provides information complementary to the measurements of the underlying event, which are usually interpreted in the framework of models implementing centrality-dependent multiple parton interactions. Results about very forward energy, measured by the ALICE zero degree calorimeters (ZDCs), and its dependence on the activity measured at midrapidity in pp collisions at √s = 13 TeV and in p-Pb collisions at √sNN = 8.16 TeV are discussed. The measurements performed in pp collisions are compared with the expectations of three hadronic interaction event generators: PYTHIA 6 (Perugia 2011 tune), PYTHIA 8 (Monash tune), and EPOS LHC. These results provide new constraints on the validity of models in describing the beam remnants at very forward rapidities, where perturbative QCD cannot be used

Characterizing the initial conditions of heavy-ion collisions at the LHC with mean transverse momentum and anisotropic flow correlations

Correlations between mean transverse momentum and anisotropic flow coefficients or are measured as a function of centrality in Pb–Pb and Xe–Xe collisions at sqrt(sNN) = 5.02 TeV and 5.44 TeV, respectively, with ALICE. In addition, the recently proposed higher-order correlation between [pt], v2, and v3 is measured for the first time, which shows an anticorrelation for the presented centrality ranges. These measurements are compared with hydrodynamic calculations using IP-Glasma and TRENTO initial-state shapes, the former based on the Color Glass Condensate effective theory with gluon saturation, and the latter a parameterized model with nucleons as the relevant degrees of freedom. The data are better described by the IP-Glasma rather than the TRENTO based calculations. In particular, Trajectum and JETSCAPE predictions, both based on the TRENTO initial state model but with different parameter settings, fail to describe the measurements. As the correlations between [pt] and vn are mainly driven by the correlations of the size and the shape of the system in the initial state, these new studies pave a novel way to characterize the initial state and help pin down the uncertainty of the extracted properties of the quark–gluon plasma recreated in relativistic heavy-ion collisions