Review of the experimental status of the polarization measurements in heavy ion collisions is presented.

In this review talk, I discuss recent advancements in the theoretical understanding of polarization phenomena in heavy ion collisions. I will focus on recent theoretical developments concerning vector polarization and spin alignment, including their numerical study and comparison with experiments. I will highlight the successes and the open questions in the current models, offering insights...

The anomalous axial symmetry of the Lagrangian for massless fermions is known to be ultimately responsible for a variety of macroscopic transport phenomena in rotating states, e.g. the chiral vortical effect (CVE) and chiral vortical separation effect (CVSE). Their coherent interplay gives rise to the chiral vortical wave. Traditionally, only the axial and vector degrees of freedom are...

A major difficulty in QFT comes from the fact that the traditional Pauli-Dirac spin operator of Dirac’s theory is not a conserved observable. This inconvenience can be overdrawn taking the Pauli-Lubanski operator as covariant spin operator, even though this is not related directly to an $SU(2)$ symmetry. Another possibility is to focus on the new spin and position operators proposed...

We derive a Cooper-Frye-type formula for the spin alignment of neutral vector mesons, such as $\phi$ mesons, at local thermal equilibrium. We describe the local equilibrium state with a grand canonical ensemble specified by temperature, fluid velocity, and spin potential. We develop a set of Feynman rules to evaluate the Wigner function order by order in space-time gradient.

We assume that...

Including the effects of the chiral anomaly within Chiral Perturbation Theory at finite baryon chemical potential, it has been shown that neutral pions form an inhomogeneous phase dubbed the "Chiral Soliton Lattice" (CSL) above a certain critical magnetic field. Above a second (higher) critical field, the CSL becomes unstable to fluctuations of charged pions, implying they condense. I will...

We will discuss the effect of rotation on the confining and chiral properties of QCD using the linear sigma model coupled to the Polyakov loop. Enforcing the causality constraint by the spectral boundary conditions we obtain the phase diagram at finite temperature, baryon density, and angular frequency. At nonrotating limit we observe a splitting between the chiral and confining transitions...

The observation of the vector meson's global spin alignment by the STAR Collaboration reveals that strong spin correlations may exist for quarks and antiquarks in relativistic heavy-ion collisions in the normal direction of the reaction plane. We propose a systematic method to describe such correlations in the quark matter. The correlations can be classified as local and long range types. We...

It is usually believed that physics in off-equilibrium state can be equivalently studied using equilibrium state with suitable metric perturbation. We point out it is not the case for spin polarization phenomena: the exisiting chiral kinetic theory in curved space fails to recover all the couplings between spin and hydrodynamic gradients [1]. We present a new form of chiral kinetic theory in...

Non-central heavy-ion collisions contain large orbital angular momentum ($\sim 10^{3\sim 6} \hbar$) that, at high energies, is expected to induce strong vorticity in the hot bulk fluid and generate global spin polarization of produced particles. As the collision energy $\sqrt{s}$ approaches threshold, the observed global spin polarization should reach a maximum, then drop to zero as...

In this study, we calculate the shear viscosity for rotating fermions with spin-half under conditions of high temperature and density. We employ the Kubo formalism, rooted in finite-temperature quantum field theory, to compute the field correlation functions essential for this evaluation. The one-loop diagram pertinent to shear viscosity is analyzed within the context of curved space,...

We investigate an alternative approach, to the MIS relativistic approach, developed to describe fluids without an underlying boost symmetry. This "density frame" approach has no non-hydrodynamic modes and no additional parameters compared to the Landau theory of first order hydrodynamics, at the price of not being fully boost invariant. We show that the density frame equations of motion follow...

After formulating the angular momentum conservation in a covariant form, we consider the equations of spin hydrodynamics in the background of an uncharged fluid in global equilibrium with a non-vanishing thermal vorticity.

Assuming that the spin degrees of freedom are not in equilibrium, we derive relaxation-type equations for the components of the spin potential.

These equations generalize...

Recent years have seen an increase in the interest to investigate the thermodynamic properties of strongly-interacting systems under rotation. Such studies are usually performed using lattice gauge techniques on the Euclidean manifold and with an imaginary angular velocity, Ω = iΩ_I . When ν = βΩ_I /2π is a rational number, the thermodynamics of free scalar fields ”fractalizes” in the large...

We describe a quantum fluid undergoing constant acceleration in the grand canonical ensemble, in thermal equilibrium at finite inverse temperature β. Writing the action of the density operator ρ as a Poincare transformation with imaginary parameters, we derive the Kubo-Martin-Schwinger (KMS) relation characterizing the two-point functions. The KMS relation sets boundary conditions for the...

A quantum fluid in thermal equilibrium can be described in the grand canonical ensemble using the density operator ρ. At finite temperature and chemical potential, the expectation values of the energy-momentum tensor and the charge current reveal the well-known thermodynamics of the Fermi-Dirac fluid. When the system is rotating or immersed in a magnetic field, deviations from the Fermi-Dirac...

The polarization of free Dirac fermions can be described by helicity, which represents the projection of the spin along the direction of motion. The helicity operator commutes with the Hamiltonian and therefore helicity is a `good'' quantum number, even in the case of massive fermions. This opens the possibility of defining a`

helicity current'', J^\mu_H, which is conserved for free...

When two relativistic heavy nuclei collide, they produce strong chromoelectric fields that lead to a rapid deceleration of the colliding nuclei. It was suggested twenty years ago that the deceleration leads to a rapid thermalization of the gluon matter through the Hawking-Unruh effect that produces a final thermal gluon state via quantum tunneling through the emerging event horizon. In the...

In this work, we study the Chiral Magnetic Effect (CME) from lattice QCD simulations in two different scenarios, particularly focusing on the leading-order coefficient of the vector current in a chiral chemical potential expansion. In the first case, we consider a system in thermal equilibrium with a non-uniform magnetic background. We show that local chiral magnetic currents appear in this...

Fermion production in an external Coulomb field on de Sitter expanding universe is studied. The amplitude and probability of pair production in an external Coulomb field are computed and the cases of large/small values of the expansion factor comparatively with the particle mass are studied. We obtain from our calculations that the modulus of the momentum is no longer a conserved quantity. We...

We investigated the Dirac eigenvalue distributions at finite chiral chemical potential and strong magnetic field. We found that the eigenvalue distributions exhibit what is called the skin effect in condensed matter physics which is typical behavior when a topological transport is expected.

We also analyzed different distribution patterns by multiplying some matrices to the Dirac operator....

The interplay between the chiral anomaly and the magnetic/vortical field created in heavy-

ion collisions can give rise to anomalous chiral effects. In this talk, the latest results of the

Chiral Magnetic Effect, Chiral Magnetic Wave, and Chiral Vortical Effect are reported in

Pb–Pb and Xe–Xe collisions recorded by the ALICE detector.

In this talk I will present the recent results of CME searches from the STAR collaboration using a novel event shape selection method and give a personal prospect on the future of the CME experimental searches. In high-energy heavy-ion collisions, the chiral magnetic effect (CME) may arise from the interplay between domains of chirality imbalanced quarks in the quark-gluon plasma and the...

The correlations of electric currents in hot non-Abelian plasma are responsible for the experimental manifestations of the chiral magnetic effect in heavy-ion collisions. We evaluate these correlations using holography, and show that they are driven by large-scale topological fluctuations. In a non-Abelian plasma with chiral fermions, local axial charge can be generated either by topological...

We study the space-time evolution of electromagnetic fields along

with the azimuthal fluctuations of these fields and their correlation

with the initial matter geometry specified by the participant plane

in the presence of finite electric $\left(\sigma\right)$ and chiral

magnetic $\left(\sigma_{\chi}\right)$ conductivities in Ru+Ru and

Zr+Zr collisions at $\sqrt{s_{NN}}=200$ GeV. We...

Negative magnetoresistance in topological semimetals is typically considered as a manifestation of chiral magnetic effect (CME). The relation between these two phenomena has the status of hypothesis and is based on the sequence of assumptions. In the present paper we rely on rigorous Keldysh technique of non-equilibrium theory. It allows us to investigate the accumulation of axial charge — the...

It is expected that there exists an ultra-central strong magnetic field during the early stages of heavy-ion collisions. However, due to the rapid decay, it is a weak magnetic field that along with the evolution of quark-gluon plasma (QGP)

In this work, we study the dissipative correction induced by a weak magnetic field during the QGP stage. Employing the viscous hydrodynamics simulation,...

The dynamics of relativistic leptons such as electrons and neutrinos play an important role in the evolution of core-collapse supernovae (CCSN). Nevertheless, chirality as one of the fundamental microscopic properties that could affect lepton transport through the weak interaction has been widely overlooked. In this talk, I will discuss how chiral effects such as the (effective) chiral...

Built upon the state-of-the-art model a multiphase transport (AMPT), we develop a new module of chiral anomaly transport (CAT) to trace the evolution of the initial topological charge of gauge field created through sphaleron transition at finite temperature and external magnetic field in heavy ion collisions. The eventual experimental signals of chiral magnetic effect(CME) has been measured....

We recent results of our group on quantum Hall effect, Chiral Magnetic effect, and Chiral separation effect. Using Wigner - Weyl calculus the corresponding conductivities are calculated and represented in the form of topological invariants. Effects of interactions, inhomogeneity, and deviations from equilibrium are considered.

Spin hydrodynamics can be developed from a systematic expansion in the reduced plank constant. Up to the first order in this expansion, there is no back-reaction from the spin to fluid dynamics, and, therefore, solutions to the standard hydrodynamics act as an input for the equations of motion for the spin tensor. Furthermore, one can assume a so-called ideal-spin approximation where the...

Motivated by the evidence of spin polarization of particles produced in relativistic heavy ion collisions, there is a growing interest in the so-called relativistic spin hydrodynamics. In this talk, we will present the outcomes of using a first-principle quantum-statistical method to derive the expression of the entropy current and entropy production rate in relativistic spin hydrodynamics....

Spin hydrodynamics relies on the non-unique definition of the spin tensor, representing the distribution of spin degrees of freedom, but different spin tensors lead to different physical results. In general, this pseudogauge symmetry represents a significant theoretical ambiguity in relativistic out-of-equilibrium statistical mechanics. This ambiguity may be resolved by fundamental quantum...

Using first-principle numerical simulations, we find a new spatially inhomogeneous phase in rigidly rotating gluon plasma. This mixed phase simultaneously possesses both confining and deconfining phases in thermal equilibrium. Unexpectedly, the local critical temperature of the phase transition at the rotation axis does not depend on the angular frequency within a few percent accuracy. An...

In the relativistic heavy ion collision experiment, there exist a large acceleration and rapid rotation in the non-central collision which can be considered as a system with acceleration and rotation. According to the Hawking-Unruh effect, the accelerated observer sees himself in a system with Unruh temperature $T/2\pi$. And the color glass condensate picture predicts that in heavy ion...

It is interesting to observe the effect of the pion mass beyond its physical value on the QCD phase diagram in the $T-eB$ plane. The fate of the inverse magnetic catalysis (IMC) and the behaviour of $T_{\rm CO}$ beyond the physical point are of particular interest. Lattice QCD studies hint at a possible elimination of IMC effects with increasing pion mass. We aim to understand the entire...

The observation of hyperon polarization along beam direction ($P_z$) in nucleus-nucleus collisions has opened a new way to study the complex vortical structures of the QGP. With the high-statistics data collected by the CMS experiment, we present the first $P_z$ results for $\Lambda$ and $\bar{\Lambda}$ particles in pPb collision at $\sqrt{s_{NN}}= 8.16$ TeV over a wide transverse momentum and...

Particles of non-zero spin produced in non-central heavy-ion collisions are expected to be polarized along the direction perpendicular to the reaction plane due to spin-orbit coupling in the produced matter, and this has indeed been observed for many hyperons and vector mesons. Here, we show that the hypertriton ($_\Lambda^3$H), which is the lightest hypernucleus, is also polarized in these...

Recent experimental data indicate a strong phi vector meson spin alignment which can be explained as a result of a short distance correlation of fluctuating strong-force field. If such strong-force for strange quark exists in the late stage of heavy-ion collisions, it will also lead to spin-spin correlation of final state hyperons such as Lambda-(anti)Lambda. We calculate such spin-spin...

I will review the recent discussions on the phase diagram under rotation and magnetic field. The interpretation of rotation effects on the QCD phase transition is still controversial, and the coexisting of rotation and magnetic field makes the physical system even more confusing. The talk will go through results from lattice results, model calculations, perturbative QCD, as well as the latest...

A review talk on some of the new developments on the Chiral Magnetic Effect.

In this talk I will present a derivation of second order terms

of the spin polarization of fermions at local thermodynamic equilibrium

including second order derivatives and quadratic terms in thermal

vorticity and shear. While quadratic terms are expected to provide

a small correction to the predicted polarization, the importance of

second order derivatives can be verified only through...

The global spin alignment for the $\phi$ meson has been recently observed by the STAR collaboration at RHIC, implying that the spin of its consituent quark has a significant correlation with the spin of the consituent antiquark, which may arise from their strong interaction with the quark-gluon plasma. We develop a general framework for studying the spin alignment $\rho_{00}$ for flavorless...

We explore chiral symmetry breaking in a rotating system within a quark-meson model of interacting massless quarks, incorporating tensor channels. Our findings reveal that new interaction channels emerge due to the explicit breaking of rotational symmetry due to non-zero rotation. We demonstrate that chiral symmetry breaking leads to the generation of two independent condensates: the...

In this talk, I will review how the conductivities of anomalous transport phenomena can be extracted using lattice QCD, in particular focusing on the Chiral Separation Effect (CSE) and Chiral Magnetic Effect (CME). For the CSE, I will explain how the sign problem has been circumvented to study this effect in different setups, leading to the determination of its conductivity in QCD with...

In this report the influence of relativistic rotation on QCD properties will be considered. I am going to review the results which were obtained within lattice simulation of QCD. It has become commonplace to perform such studies in the reference frame rotating with the system under investigation. In this case there appears the gravitational field and the problem is reduced to study of QCD in...

In this presentation, I revisit the Dirac theory under an external magnetic field and rotation. Motivated by experimental observations of significant vorticities in heavy ion collisions, there has been active exploration into the thermodynamics of rotating QCD matter. While the pure rotational effect has received attention, the interplay between rotation and magnetic fields remains...

We consider macroscopic motion of quantum field systems. The Zubarev statistical operator allows us to describe several types of motion of such systems in thermal equilibrium. We formulate the corresponding effective theory on the language of a functional integral. The effective Lagrangian is calculated explicitly for the fermionic systems interacting with dynamical gauge fields. Possible...

Quark-gluon plasma (QGP) produced in relativistic heavy-ion collisions cools rapidly as the medium evolves. QGP with non-zero conserved charged current, higher thermal conductivity of medium advances in global thermalization. Being made of electrically charged partons, heat current leads to electromagnetic (EM) field induction in the medium, commonly known as the *thermoelectric effect*....

In the framework of Nambu--Jona-Lasinio model beyond mean field approximation, the effects of pion fluctuations on (inverse) magnetic catalysis and magnetic susceptibility are studied. The negative magnetic susceptibility at low temperature is observed when contributions from both neutral and charged pions are taken into account. In weak field approximation, it is observed that at finite...

When chiral charged matter is exposed to extremely strong magnetic fields, novel hydrodynamic transport effects emerge [1]. These novel effects need to be estimated and possibly taken into account, for example in the hydrodynamic codes used to analyze heavy-ion collision data or magnetars. Kubo formulae link the macroscopic transport coefficients to the microscopic retarded two-point...

Weyl semimetals, a class of topological materials, exhibit a hydrodynamic regime and offer an ideal environment for investigating chiral anomalies through table-top experiments and transport measurements. In this presentation, I will consider a $(3+1)$-dimensional fluid with a $U(1)_V \times U(1)_A$ chiral anomaly as a model of Weyl semimetals. My focus will be on longitudinal thermoelectric...

We present a method for simulating the stochastic relativistic advection-diffusion equation using the Metropolis algorithm. This approach simulates dissipative dynamics by randomly transferring charge between fluid cells, combined with ideal hydrodynamic time steps. Charge transfers are accepted or rejected based on entropy as a statistical weight in a Metropolis step. This reproduces expected...

Using the imaginary part of the self-energy function in the Landau-level representation, we derive the fermion damping rate in a hot magnetized plasma at the leading order of coupling. The results are used to investigate the longitudinal and transverse electrical conductivities. In the relativistic regime, these conductivities exhibit a scaling behavior expressed in terms of dimensionless...

Magnetic fields of a large intensity can be generated in peripheral high-energy heavy-ion collisions. Although the intensity drops down fast and, moreover, it is not clear whether the fields last long enough to induce a magnetization during the quark-gluon plasma phase, most of the models and simulations predict a significant intensity that lasts up to proper times of order 1 fm after the...

Chiral Magnetic Effect (CME) is a phenomenon in which electric charge is separated by a strong magnetic field from local domains of chirality imbalance and parity violation in quantum chromodynamics (QCD). The CME-sensitive observable, charge-dependent three-particle azimuthal correlator $\Delta\gamma$, is contaminated by a major physics background proportional to the particle elliptic...

Semiclassical expansion of the Wigner function for spin-1/2 fermions having an effective spacetime-dependent mass is used to analyze spin-polarization effects. The existing framework is reformulated to obtain a differential equation directly connecting the particle spin tensor with the effective mass. It reflects the conservation of the total angular momentum in a system. In general, we find...

It is now clear, on a theoretical level, that spin polarization can not be in perfect local equilibrium with vorticity during the quark-gluon plasma evolution. Phenomenological consequences of this are however so far not clear. In this talk we argue that spin one mesons (and higher spin particles) are ideal probes of non-equilibrium between vorticity and polarization, because their density...

We investigate the effects of the QCD critical point on spin polarization of $\Lambda$ hyperons. For this we evaluate thermal vorticity and thermal shear by solving the equations of relativistic causal hydrodynamics in (3+1) dimensions. The effects of the critical point are incorporated through the equation of state and the scaling behaviour of the transport coefficients. For the same global...

In this work, we address the problem of longitudinal spin polarization of the $\Lambda$ hyperons produced in relativistic heavy-ion collisions. We combine a relativistic kinetic-theory framework that includes spin degrees of freedom treated in a classical way with the freeze-out parametrization used in previous investigations. The use of the kinetic theory allows us to incorporate dissipative...

The $\Lambda$ polarization is a crucial probe of the gradients of velocity and temperature in the quark-gluon plasma generated in heavy-ion collisions. However, it is still not systematically used to tune hydrodynamic models. In this talk, we investigate the influence of different initial conditions and parametrization of the bulk viscosity on $\Lambda$ polarization, showing that they affect...

In non-central heavy-ion collisions, a large orbital angular momentum is produced. A part of the orbital angular momentum can polarize the quarks and anti-quarks, hence the vector mesons, inside the medium. Recently, STAR measured the global spin alignment of ϕ(1020) and K∗ (892) mesons in Au+Au collisions from the RHIC Beam Energy Scan I (BES I) program [1]. The global spin alignment,...