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Polarization has opened a new physics chapter in relativistic heavy-ion collisions. Since the first prediction and experimental observation of global spin polarization, a lot of progress has been made in understanding its features, both at experimental and theoretical levels. In this paper, we give an overview on the recent advances in this field. The covered topics include a review of measurements of global and local spin polarization of hyperons and the global spin alignment of vector meson’s. We account for the basic theoretical framework to describe spin polarization in a relativistic fluid such as the Quark–Gluon Plasma, including statistical quantum field theory and local thermodynamic equilibrium, spin hydrodynamics, relativistic kinetic theory with spin and coalescence models. [ABSTRACT FROM AUTHOR]

Since the first evidence of a global polarization of Λ hyperons in relativistic nuclear collisions in 2017, spin has opened a new window in the field, both at experimental and theoretical level, and an exciting perspective. The current state of the field is reviewed with regard to the theoretical understanding of the data, reporting on the most recent achievements and envisioning possible developments. The intriguing connections of spin physics in relativistic matter with fundamental questions in quantum field theory and applications in the non-relativistic domain are discussed. [ABSTRACT FROM AUTHOR]

We use a first-principle quantum-statistical method to derive the expression of the entropy production rate in relativistic spin hydrodynamics. We show that the entropy current is not uniquely defined and can be changed by means of entropy-gauge transformations, similarly as the stress-energy tensor and the spin tensor can be changed with pseudo-gauge transformations. We show that the local thermodynamic relations, which are admittedly educated guesses in relativistic spin hydrodynamics inspired by those at global thermodynamic equilibrium, do not hold in general and they are also non-invariant under entropy-gauge transformations. Notwithstanding, we show that the entropy production rate is independent of those transformations and we provide a universally applicable expression, extending that known in literature, from which the dissipative parts of the energy momentum and spin tensors can be inferred. [ABSTRACT FROM AUTHOR]

The quark–gluon plasma (QGP) produced by collisions between ultrarelativistic heavy nuclei is well described in the language of hydrodynamics. Noncentral collisions are characterized by very large angular momentum, which in a fluid system manifests as flow vorticity. This rotational structure can lead to a spin polarization of the hadrons that eventually emerge from the plasma, and thus these collisions provide experimental access to flow substructure at unprecedented detail. Recently, the first observations of Λ hyperon polarization along the direction of collisional angular momentum were reported. These measurements are in broad agreement with hydrodynamic and transport-based calculations and reveal that the QGP is the most vortical fluid ever observed. However, there remain important tensions between theory and observation that might be fundamental in nature. In the relatively mature field of heavy-ion physics, the discovery of global hyperon polarization and 3D simulations of the collision have opened an entirely new direction of research. We discuss the current status of this rapidly developing area and directions for future research. [ABSTRACT FROM AUTHOR]

We derive a sufficient condition for the existence of the entropy current of a fluid at local thermodynamic equilibrium using relativistic quantum statistical mechanics, and put forward a general method to calculate it. We also work out a specific calculation in a non-trivial case of interest, namely a system at global thermodynamic equilibrium with proper acceleration of constant magnitude along the flow lines in Minkowski space–time, whose lowest possible proper temperature is the Unruh temperature. In this case, we show that the integral of the entropy current in the right Rindler wedge is the entanglement entropy with the left Rindler wedge. [ABSTRACT FROM AUTHOR]

Abstract It is shown that the description of a relativistic fluid at local thermodynamic equilibrium depends on the particular quantum stress-energy tensor operator chosen, e.g., the canonical or symmetrized Belinfante stress-energy tensor. We argue that the Belinfante tensor is not appropriate to describe a relativistic fluid whose macroscopic polarization relaxes slowly to thermodynamic equilibrium and that a spin tensor, like the canonical spin tensor, is required. As a consequence, the description of a polarized relativistic fluid involves an extension of relativistic hydrodynamics including a new antisymmetric rank-two tensor as a dynamical field. We show that the canonical and Belinfante tensors lead to different predictions for measurable quantities such as spectrum and polarization of particles produced in relativistic heavy-ion collisions. [ABSTRACT FROM AUTHOR]

Abstract Polarization and chirality are direct manifestations of quantum mechanics in the Quark Gluon Plasma as a relativistic fluid. This is one of the reasons why they are intriguing phenomena, that have attracted so much attention lately. In this talk I will review what is, in my view, the current theoretical understanding and highlight the most interesting recent results. [ABSTRACT FROM AUTHOR]

Abstract STAR collaboration at RHIC has recently measured the polarization of Λ hyperons in non-central heavy ion collisions in the RHIC Beam Energy Scan (BES) program. The magnitude of the polarization was found to decrease from few percents at the lowest BES energies to ≈ 0.2% at the top RHIC energy. The polarization signal has been reproduced in different hydrodynamic calculations assuming a thermodynamic spin-vorticity coupling mechanism at the Cooper-Frye hypersurface [1]. In this work an extension of our existing calculations [2] of the Λ polarization in the RHIC BES program to the top RHIC and 2.76 TeV LHC energies is presented. The longitudinal component of the Λ polarization, which is the dominant component of the polarization at the LHC energies, is discussed. Finally we show that the global polarization of Λ originates dominantly from the relativistic analogue of the classical vorticity, whereas the quadrupole longitudinal component originates from the gradients of temperature and acceleration of the medium when the Λs are produced out of the fluid. [ABSTRACT FROM AUTHOR]

Polarization of Λ hyperons and their antiparticles is calculated in a 3 + 1 dimensional viscous hydrodynamic model with initial state from UrQMD hadron/string cascade. We find that, along with recent results from STAR, the mean polarization at fixed centrality decreases as a function of collision energy from 1.5% at s NN = 7.7 GeV to 0.2% at s NN = 200 GeV . We explore the effects which lead to such collision energy dependence, feed-down corrections and a difference between Λ and Λ ¯ . [ABSTRACT FROM AUTHOR]

We compare the reconstructed hadronization conditions in relativistic nuclear collisions in the nucleon–nucleon centre-of-mass energy range 4.7–2760 GeV in terms of temperature and baryon-chemical potential with lattice QCD calculations, by using hadronic multiplicities. We obtain hadronization temperatures and baryon chemical potentials with a fit to measured multiplicities by correcting for the effect of post-hadronization rescattering. The post-hadronization modification factors are calculated by means of a coupled hydrodynamical-transport model simulation under the same conditions of approximate isothermal and isochemical decoupling as assumed in the statistical hadronization model fits to the data. The fit quality is considerably better than without rescattering corrections, as already found in previous work. The curvature of the obtained “true” hadronization pseudo-critical line κ is found to be 0.0048 ± 0.0026 , in agreement with lattice QCD estimates; the pseudo-critical temperature at vanishing μ B is found to be 164.3 ± 1.8 MeV . [ABSTRACT FROM AUTHOR]

We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector $$\beta $$ , which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of the stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the $$\beta $$ frame and Landau frame and present an instance where they differ. [ABSTRACT FROM AUTHOR]

We briefly review recent advances in the subject of hadron production in relativistic heavy-ion collisions. We focus on the issues of chemical freeze-out, chemical equilibration and the role of post-hadronization inelastic collisions. From the observations collected in elementary and heavy-ion collisions, a picture emerges in which hadrons are born in chemical equilibrium at hadronization, thereafter undergoing inelastic and elastic collisions whose impact on the primordial distribution depends on the system size. [ABSTRACT FROM AUTHOR]

We present an analysis of hadronic multiplicities measured in Pb-Pb collisions at √SNN = 2.76 TeV as a function of the collision centrality within the statistical hadronization model. Evidence is found of a dependence of the chemical freeze-out temperature as a function of centrality, with a slow rise from central to peripheral collisions, which we interpret as an effect of posthadronization inelastic scatterings. Using correction factors calculated by means of a simulation based on the URQMD model, we are able to obtain a significant improvement in the statistical model fit quality and to reconstruct the primordial chemical equilibrium configuration. This is characterized by a nearly constant temperature of about 164 MeV, which we interpret as the actual hadronization temperature. [ABSTRACT FROM AUTHOR]

In this paper, we show that thermodynamics is sensitive to the existence of a fundamental spin tensor. In general, the thermodynamics is not invariant by a change of the stress-energy tensor of a fundamental quantum field with a divergence transformation leaving the total energy, momentum and angular momentum unchanged. Among the quantities which are changed by such a transformation, there are densities at equilibrium with rotation and nonequilibrium ones like transport coefficients and total entropy. Therefore, at least in principle, it could be possible to probe the existence of a spin tensor, with major consequences for general relativistic theories, with a thermodynamics experiment. [ABSTRACT FROM AUTHOR]

We study particle production in ultrarelativistic nuclear collisions at CERN SPS and LHC energies and the conditions of chemical freeze-out. We determine the effect of the inelastic reactions between hadrons occurring after hadronization and before chemical freeze-out employing the ultrarelativistic quantum molecular dynamics hybrid model. The differences between the initial and the final hadronic multiplicities after the rescattering stage resemble the pattern of data deviation from the statistical equilibrium calculations. By taking these differences into account in the statistical model analysis of the data, we are able to reconstruct the original hadrochemical equilibrium points in the (T, μB) plane which significantly differ from chemical freeze-out ones and closely follow the parton-hadron phase boundary recently predicted by lattice quantum chromodynamics. [ABSTRACT FROM AUTHOR]

We analyze hadrochemical freeze-out in central Pb + Pb collisions at CERN SPS energies, employing the hybrid version of the Ultrarelativistic Quantum Molecular Dynamics model, which describes the transition from a hydrodynamic stage to hadrons by the Cooper-Frye mechanism, and matches to a final hadron-resonance cascade. We fit the results both before and after the cascade stage using the statistical model to assess the effect of the cascade phase. We observe a strong effect on antibaryon yields except anti-Ω, resulting in a shift in T and µB of the freeze-out curve. We discuss indications of a similar effect in SPS and RHIC data, and propose a method to recover the bulk hadron freeze-out conditions. [ABSTRACT FROM AUTHOR]

We calculate the contribution to the polarization of Λ hyperons in relativistic nuclear collisions at high energy from the decays of Σ ∗ (1385) and Σ 0 , which are the predominant sources of Λ production besides the primary component, as a function of the Λ momentum. Particularly, we estimate the longitudinal component of the mean spin vector as a function of the azimuthal angle in the transverse plane, assuming that primary Σ ∗ and Σ 0 polarization follow the predictions of local thermodynamic equilibrium in a relativistic fluid. Provided that the rapidity dependence around midrapidity of polarization is negligible, we find that this component of the overall spin vector has a very similar pattern to the primary one. Therefore, we conclude that the secondary decays cannot account for the discrepancy in sign between experimental data and hydrodynamic model predictions of the longitudinal polarization of Λ hyperons recently measured by the STAR experiment at RHIC. [ABSTRACT FROM AUTHOR]

The system created in ultrarelativistic nuclear collisions is known to behave as an almost ideal liquid. In noncentral collisions, because of the large orbital momentum, such a system might be the fluid with the highest vorticity ever created under laboratory conditions. Particles emerging from such a highly vorticous fluid are expected to be globally polarized with their spins on average pointing along the system angular momentum. Vorticity-induced polarization is the same for particles and antiparticles, but the intense magnetic field generated in these collisions may lead to the splitting in polarization. In this paper we outline the thermal approach to the calculation of the global polarization phenomenon for particles with spin and we discuss the details of the experimental study of this phenomenon, estimating the effect of feed-down. A general formula is derived for the polarization transfer in two-body decays and, particularly, for strong and electromagnetic decays. We find that accounting for such effects is crucial when extracting vorticity and magnetic field from the experimental data. [ABSTRACT FROM AUTHOR]

A global equilibrium state of a spin polarized fluid that undergoes constant acceleration along the stream lines is described as a solution of recently introduced perfect-fluid hydrodynamic equations with spin ½. [ABSTRACT FROM AUTHOR]