Based on a generalized side-jump formalism for massless chiral fermions, which naturally takes into account the spin-orbit coupling in the scattering of two chiral fermions and the chiral vortical effect in a rotating chiral fermion matter, we have developed a covariant and total angular momentum conserved chiral transport model to study both the global and local polarizations of this matter. For a system of massless quarks of random spin orientations and finite vorticity in a box, we have demonstrated that the model can exactly conserve the total angular momentum of the system and dynamically generate the quark spin polarization expected from a thermally equilibrated quark matter. Using this model to study the spin polarization in relativistic heavy-ion collision, we have found that the local quark spin polarizations depend strongly on the reference frame where they are evaluated as a result of the nontrivial axial charge distribution caused by the chiral vortical effect. We have further shown that because of the anomalous orbital or side-jump contribution to the quark spin polarization, the local quark polarizations calculated in the medium rest frame are qualitatively consistent with the local polarizations of Lambda hyperons measured in experiments.
Predictions for the global polarization of $Λ$ hyperons in Au+Au collisions at moderately relativistic collision energies, 2.4 $\leq\sqrt{s_{NN}}\leq$ 11 GeV, are made. These are based on the thermodynamic approach to the global polarization incorporated into the model of the three-fluid dynamics. Centrality dependence of the polarization is studied. It is predicted that the polarization reaches a maximum or a plateau (depending on the equation of state and centrality) at $\sqrt{s_{NN}}\approx$ 3 GeV. It is found that the global polarization increases with increasing width of the rapidity wind…
We present a systematic study of $Λ$ hyperon's polarization observables using event-by-event (3+1)D relativistic hydrodynamics. The effects of initial hot spot size and QGP's specific shear viscosity on the polarization observables are quantified. We examine the effects of the two formulations of the thermal shear tensor on the polarization observables using the same hydrodynamic background. With event-by-event simulations, we make predictions for the Fourier coefficients of $Λ$'s longitudinal polarization $P^z$ with respect to the event planes of different orders of anisotropic flow. We propo…
The polarization of $Λ$ hyperons from relativistic flow vorticity is studied in peripheral heavy ion reactions at FAIR and NICA energies, just above the threshold of the transition to the Quark-Gluon Plasma. Previous calculations at higher energies with larger initial angular momentum, predicted significant $Λ$ polarization based on the classical vorticity term in the polarization, while relativistic modifications decreased the polarization and changed its structure in the momentum space. At the lower energies studied here, we see the same effect namely that the relativistic modifications decr…
We study the polarization change of Lambda^0's produced in ultra-relativistic heavy-ion collisions with respect to the polarization observed in proton-proton collisions as a signal for the formation of a Quark-Gluon Plasma (QGP). Assuming that, when the density of participants in the collision is larger than the critical density for QGP formation, the Lambda^0 production mechanism changes from recombination type processes to the coalescence of free valence quarks, we find that the Lambda^0 polarization depends on the relative contribution of each process to the total number of Lambda^0's produ…
In this note we discuss how angular distribution of the dileptons produced in heavy ion collisions at RHIC/LHC energies can provide an information about a degree of local equilibration of the quark-gluon plasma produced at different invariant mass regions.
We perform a systematic study of the spin polarization of hyperons in heavy-ion collisions using the MUSIC hydrodynamic model with A Multi-Phase Transport (AMPT) pre-equilibrium dynamics. Our model calculations nicely describe the measured collision-energy, centrality, rapidity, and $p_T$ dependence of $Λ$ polarization. We also study and predict the global spin polarization of $Ξ^-$ and $Ω^-$ as a function of collision energy, which provides a baseline for the studies of the magnetic moment, spin, and mass dependence of the spin polarization. For the local spin polarization, we calculate the r…
We give a short review about the hydrodynamic model and its application to the elliptic flow phenomena and the pion interferometry in relativistic heavy ion collisions.
Heavy ion collisions generate strong fluid vorticty in the produced hot quark-gluon matter which could in turn induce measurable spin polarization of hadrons. We review recent progress on the vorticity formation and spin polarization in heavy ion collisions with transport models. We present an introduction to the fluid vorticity in non-relativistic and relativistic hydrodynamics and address various properties of the vorticity formed in heavy ion collisions. We discuss the spin polarization in a vortical fluid using the Wigner function formalism in which we derive the freeze-out formula for the…
We present a calculation of the global polarization of Lambda hyperons in relativistic Au-Au collisions at RHIC Beam Energy Scan range sqrt{s}_NN = 7.7 - 200 GeV with a 3+1 dimensional cascade + viscous hydro + cascade model, UrQMD+vHLLE. Within this model, the mean polarization of Lambda in the out-of-plane direction is predicted to decrease rapidly with collision energy from a top value of about 2% at the lowest energy examined. We explore the connection between the polarization signal and thermal vorticity and estimate the feed-down contribution to Lambda polarization due to the decay of hi…
We study the polarization of particles in relativistic heavy-ion collisions at very high energy along the beam direction within a relativistic hydrodynamic framework. We show that this component of the polarization decreases much slower with center-of-mass energy compared to the transverse component, even in the ideal longitudinal boost-invariant scenario with non-fluctuating initial state, and that it can be measured by taking advantage of its quadrupole structure in the transverse momentum plane. In the ideal longitudinal boost-invariant scenario, the polarization is proportional to the grad…
We show that the inclusion of a recently found additional term of the spin polarization vector at local equilibrium which is linear in the symmetrized gradients of the velocity field, and the assumption of hadron production at constant temperature restore the quantitative agreement between hydrodynamic model predictions and local polarization measurements in relativistic heavy ion collisions at $\sqrt{s_{\rm NN}} = 200$ GeV. The longitudinal component of the spin polarization vector turns out to be very sensitive to the temperature value, with a good fit around 155 MeV. The implications of thi…
The hot and dense matter formed in relativistic heavy-ion collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) is termed quark-gluon plasma (QGP). The evolution of the medium is characterized by non-trivial velocity and vorticity fields, resulting in the polarization of the produced particles. The spin polarization, being sensitive to the hydrothermal (flow velocity and temperature) gradients, is unique compared to conventional observables that are sensitive to the hydrothermal fields only. Hence, the recent measurements of global and local hyperon spin polariza…
We study helicity polarization through the (3+1) dimensional relativistic viscous hydrodynamic models at $\sqrt{s_{NN}}=200$GeV Au+Au collisions. Similar to the local spin polarization, we consider the helicity polarization beyond global equilibrium and investigate the contributions induced by thermal vorticity, shear viscous tensor, and the fluid acceleration. We find that the local helicity polarization induced by thermal vorticity dominates over other contributions. It also implies that in the low-energy collisions, the the fluid vorticity as part of thermal vorticity may play the crucial r…
The EM field pattern created by spectators in relativistic heavy-ion collisions plants a seed of positive (negative) magnetic helicity in the hemisphere above (below) the reaction plane. Owing to the chiral anomaly, the magnetic helicity interacts with the fermionic helicity of the collision system, and causes photons emitted in upper- and lower-hemispheres to have different preferences in the circular polarization. In this paper, we lay down a procedure to measure the variation of the circular polarization w.r.t the reaction plane in relativistic heavy-ion collisions for massless photons, as …
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 midrap…
We review the theoretical framework for the calculation of particle polarization in relativistic heavy ion collisions within the hydrodynamical model. The covariant decomposition of the mean spin vector is presented and open theoretical issues addressed.
We report on the core-corona model developed to describe the main features of hyperon global polarization in semicentral relativistic heavy-ion collisions as a function of the collision energy. We first neglect the contribution to polarization from hyperons produced in the corona. In this scenario, the global polarization turns out to be described by a delicate balance between the vorticity-to-spin transferring reactions in the core and the predominance of corona over core matter at low energies. We show how this last feature provides a key ingredient missing in our original model that helps t…
Role of polarization studies in heavy ion physics is discussed with emphasis on the search for quark-gluon plasma formation and studies of its dynamical properties.
Relativistic calculations of the induced proton polarization in quasifree electron scattering on $^{12}C$ are presented. Good agreement with the experimental data of Woo et al. is obtained. The relativistic calculations yield a somewhat better description of the data than the non-relativistic ones. Differences between the two approaches are more pronounced at larger missing momenta suggesting further experimental work in this region.
We discuss the helicity polarization which can be locally induced from both vorticity and helicity charge in non-central heavy ion collisions. Helicity charge redistribution can be generated in viscous fluid and contributes to azimuthal asymmetry of the polarization along global angular momentum or beam momentum. We also discuss on detecting the initial net helicity charge from topological charge fluctuation or initial color longitudinal field by the helicity polarization correlation of two hyperons and the helicity alignment of vector mesons in central heavy ion collisions.
A systematic study of global spin polarizations and correlations of hadrons with different spins in relativistic heavy ion collisions
Institute of Frontier and Interdisciplinary Science, Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University（山东大学前沿交叉科学研究中心，粒子物理与粒子辐照教育部重点实验室）
Based on the result in our previous work, we calculate the polarization of quarks from parton scatterings in high energy heavy ion collisions. The result is compared with the STAR data at $\sqrt{s_{NN}}=200$ GeV.
It was proposed that the electric fields may lead to chiral separation in QGP, which is called the chiral electric separation effect. The strong electromagnetic field and the QCD vacuum can both completely be produced in the off-central nuclear-nuclear collision. We used the Wood-Saxon nucleon distribution to calculate the electric field distributions of the off-central collisions. The chiral electro field spatial distribution at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC) energy regions are systematically studied in this paper. Compared with magnetic field spatial d…
Based on the chiral kinetic equations of motion, spin polarizations of various quarks, due to the magnetic field induced by spectator protons as well as the quark-antiquark vector interaction, are studied within a partonic transport approach. Although the magnetic field in QGP enhances the splitting of the spin polarizations of partons compared to the results under the magnetic field in vacuum, the spin polarizations of $s$ and $\bar s$ quarks are also sensitive to the quark-antiquark vector interaction, challenging that the different $Λ$ and $\bar Λ$ spin polarization is a good measure of the…
The elastic proton-deuteron backward reaction is analyzed within a covariant approach based on the Bethe-Salpeter equation with realistic meson-exchange interaction. Lorentz boost and other relativistic effects in the cross section and spin correlation observables, like tensor analyzing power and polarization transfer etc., are investigated in explicit form. Results of numerical calculations for a complete set of polarization observables are presented.
Kinetic and hydrodynamic models describing early stages of relativistic heavy-ion collisions are discussed. We emphasise the role of the shear-bulk coupling for the correct determination of the time dependence of the bulk viscous pressure.
Some ideas/concepts in relativistic heavy ion collisions are discussed. To a large extent, the discussions are non-comprehensive and non-rigorous. It is intended for fresh graduate students of Homi Bhabha National Institute, Kolkata Centre, who are intending to pursue career in theoretical /experimental high energy nuclear physics. Comments and criticisms will be appreciated.
Shannon information entropy provides an effective tool to study the evolution process in relativistic heavy-ion collisions. The time evolution process of thermodynamic entropy $S_{\rm thermal}$, multiple entropy $S_{\rm mul}$, and configuration entropy $S_{\rm conf}$ at RHIC is studied using the AMPT model to generate central Au-Au collisions. By superimposing the three kinds of information entropy, we can get a more complete information entropy of the system to describe the physical information of the relativistic heavy ion collision. The results show that the four stages of the time evolutio…
We study local spin polarization in the relativistic hydrodynamic model. Generalizing the Wigner functions previously obtained from chiral kinetic theory by Y. Hidaka et al. [Phys. Rev. D 97, 016004 (2018)] to the massive case, we present the possible contributions up to the order of $\hbar$ from thermal vorticity, shear viscous tensor, other terms associated with the temperature and chemical-potential gradients, and electromagnetic fields to the local spin polarization. We then implement the (3+1)-dimensional viscous hydrodynamic model to study the spin polarizations from these sources with a…
This article summarizes our present knowledge about nuclear matter at the highest energy densities and its formation in relativistic heavy ion collisions. We review what is known about the structure and properties of the quark-gluon plasma and survey the observables that are used to glean information about it from experimental data.
Anisotropy in heavy-ion collisions leads to polarization of both direct and virtual photons, the latter detected via internal conversion to dileptons pairs. Thus measurement of photon polarization probes the anisotropy at all stages of collisions. In order to characterize the polarization of virtual photons, we derive here the general structure of the photon polarization operator, rho^(mu nu), in an anisotropic medium, in terms of the four spectral functions, two transverse and one longitudinal, as usual, plus a new spectral function that reflects anisotropy in asymmetric collisions; and deriv…
Effects of the Fermi-sea polarization on the superfluidity in nuclear matter are studied in a framework of quantum hadrodynamics. The particle-hole polarization due to $σ$ and $ω$ mesons enhances the peak value of the pairing gap contrary to the previous non-relativistic studies.
Polarization-transfer components for 4He(\vec{e},e'\vec{p})3H are computed within the relativistic multiple-scattering Glauber approximation (RMSGA). The RMSGA framework adopts relativistic single-particle wave functions and electron-nucleon couplings. The predictions with free and various parametrizations for the medium-modified electromagnetic form factors are compared to the world data.
Based on the chiral kinetic approach using initial conditions from a multiphase transport model, we study the spin polarizations of quarks and antiquarks in non-central heavy ion collisions at the Relativistic Heavy Ion Collider. Because of the non-vanishing vorticity field in these collisions, quarks and antiquarks are found to acquire appreciable spin polarizations in the direction perpendicular to the reaction plane. Converting quarks and antiquarks to hadrons via the coalescence model, we further calculate the spin polarizations of Lambda and anti-Lambda hyperons and find their values comp…
Particle spin polarization is known to be linked both to rotation (angular momentum) and magnetization of a many particle system. However, in the most common formulation of relativistic kinetic theory, the spin degrees of freedom appear only as degeneracy factors multiplying phase-space distributions. Thus, it is important to develop theoretical tools that allow to make predictions regarding the spin polarization of particles, which can be directly confronted with experimental data. Herein, we discuss a link between the relativistic spin tensor and particle spin polarization, and elucidate the…
Polarization-transfer components for 4He(\vec{e},e'\vec{p})3H and 16O(\vec{e},e'\vec{p})15N are computed within the relativistic multiple-scattering Glauber approximation (RMSGA). The RMSGA framework adopts relativistic single-particle wave functions and electron-nucleon couplings. The predictions closely match those of a relativistic plane-wave model indicating the smallness of the final-state interactions for polarization-transfer components. Also short-range correlations play a modest role for the studied observables, as long as small proton missing-momenta are probed in quasi-elastic kinem…
We study the physics of the ideal relativistic rotating gas at thermodynamical equilibrium and provide analytical expressions of the momentum spectra and polarization vector for the case of massive particles with spin 1/2 and 1. We show that the finite angular momentum J entails an anisotropy in momentum spectra, with particles emitted orthogonally to J having, on average, a larger momentum than along its direction. Unlike in the non-relativistic case, the proper polarization vector turns out not to be aligned with the total angular momentum with a non-trivial momentum dependence.
An approach is developed, which essentially simplifies derivation of kinetic equation for polarization in non-relativistic scattering. This approach is applicable for collision of projectile particles with a target for any spins of colliding particles. The most detailed consideration is performed for the case of spin 1/2 projectile particle interacting with spin 1/2 particle of a target. The solution of the kinetic equation for the case of zero initial polarization is presented.
We use Lagrangian effective field theory techniques to construct the equations of motion for an ideal relativistic fluid whose constituent degrees of freedom have microscopic polarization. We discuss the meaning of such a system, and argue that it is the first term in the EFT appropriate for describing polarization observables in heavy ion collisions, such as final state particle polarization and chiral magnetic and vortaic effects. We show that this system will generally require non-dissipative dynamics at higher order in gradient than second order, leading to potential stability issues known…
We present a theoretical formulation for the description of nuclear excitations within the framework of relativistic random-phase approximation whereby the vacuum polarization arising from nucleon-antinucleon fields is duly accounted for. The vacuum contribution to Lagrangian is explicitly described as extra new terms of interacting mesons by means of the derivative expansion of the effective action. It is shown that the self-consistent calculation yields zero eigenvalue for the spurious isoscalar-dipole state and also conserves the vector-current density.
The azimuthal angle dependence of quark spin polarization in the longitudinal beam direction of non-central relativistic heavy ion collisions is studied in the chiral kinetic approach. Contrary to the prediction from models based on the assumption of thermal equilibrium of spin degrees of freedom that the quark spin polarization always points along the direction of local vorticity field, we find the two can have opposite directions due to the effect from the transversal component of vorticity field, which can lead to a redistribution of axial charges in the produced matter. Our finding is cons…
We discuss some open problems in hydrodynamical approach to the relativistic heavy ion collisions. In particular, we propose a new, very simple alternative approach to the relativistic dissipative hydrodynamics of Israel and Stewart.
Based on a spin-dependent Boltzmann-Uehling-Uhlenbeck transport model with spin-dependent potentials incorporated using the lattice Hamiltonian method, we have studied the global spin polarization perpendicular to the reaction plane as well as the local spin polarization in the longitudinal direction in non-central intermediate-energy heavy-ion collisions, as an extension of similar studies in relativistic heavy-ion collisions. Both the global and the local spin polarizations are found to be mostly dominated by the time-odd component of the nuclear spin-orbit potential. Impacts of various theo…
We review some of the recent progress in our understanding of the physics of ultrarelativistic heavy ion collisions due to applications of AdS/CFT correspondence.
An introductory overview of electromagnetic probes in ultra-relativistic heavy-ion collisions is provided. Experimental evidence supporting the production of thermal photons and dileptons in heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) are reviewed. Thermal electromagnetic emission evaluated from hydrodynamical models of collisions is discussed.
The isoscalar and isovector collective multipole excitations in stable nuclei are studied in the framework of relativistic random-phase approximation with the vacuum polarization arising from the nucleon-antinucleon field. A fully self-consistent calculation which guarantees the decoupling of the spurious state and the conservation of the multipole-transition current is carried out by using the derivative-expansion method for the description of the vacuum contribution. A remarkable effect of the inclusion of the vacuum polarization is the increase of the effective mass, $m^*/m_N \sim 0.8$; for…
We study the relativistic Hartree approach with the exact treatment of the vacuum polarization in the Walecka sigma-omega model. The contribution from the vacuum polarization of nucleon-antinucleon field to the source term of the meson fields is evaluated by performing the energy integrals of the Dirac Green function along the imaginary axis. With the present method of the vacuum polarization in finite system, the total binding energies and charge radii of 16O and 40Ca can be reproduced. On the other hand, the level-splittings in the single-particle level, in particular the spin-orbit splittin…
A detailed analysis of the processes of the type NN -> Dπis presented taking into account the exchange graphs of a nucleon and a pion. A large sensitivity of polarization observables to the off-mass shell effects of nucleons inside the deuteron is shown. The influence of the inclusion of the P-wave in the Deuteron Wave Function (DWF) is studied. We have analysed the sensitivity of all the observables to the form of πNN - current taking into account the off-shellnis of the nucleon and the choice of the DWF relativistic form. One can see the very large sensitivity of all the observables, especia…
