Extremely large angular orbital momentum can be produced in non-central heavy-ion collisions, leading to a strong transverse polarization of partons that scatter through the quark-gluon plasma (QGP) due to spin-orbital coupling. We develop a perturbative approach to describe the formation and spacetime evolution of quark polarization inside the QGP. Polarization from both the initial hard scatterings and interactions with the QGP have been consistently described using the quark-potential scattering approach, which has been coupled to realistic initial condition calculation and the subsequent (3+1)-dimensional viscous hydrodynamic simulation of the QGP for the first time. Within this improved approach, we have found that different spacetime-rapidity-dependent initial energy density distributions generate different time evolution profiles of the longitudinal flow velocity gradient of the QGP, which further lead to an approximately 15% difference in the final polarization of quarks collected on the hadronization hypersurface of the QGP. Therefore, in addition to the collective flow coefficients, the hyperon polarization may serve as a novel tool to help constrain the initial condition of the hot nuclear matter created in high-energy nuclear collisions.
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 investigate the muonic hydrogen 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition through a precise, non-perturbative numerical solution of the Dirac equation including the finite-size Coulomb force and finite size vacuum polarization. The results are compared with earlier perturbative calculations of (primarily) Borie, Martynenko, and Pachucki; and experimental results recently presented by Pohl et al., in which this very comparison is interpreted as requiring a modification of the proton charge radius from that obtained in electron scattering and electronic hydrogen analyses. We find no signifi…
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…
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…
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 present the quantum kinetic equation for spin polarization of massive quarks in leading log order of perturbative QCD, which describes time evolution of the spin density matrix in momentum space of a massive quark interacting with a background QCD plasma. We find that the time evolution operator of the spin density matrix, or the quantum kinetic collision terms, are universally of order $α_s^2\log(1/α_s)$ in terms of the QCD coupling constant $α_s=g^2/(4π)$. Our quantum kinetic equation is valid for an arbitrary quark mass $m\gg m_D\sim gT$, where $m_D$ is the Debye mass, and can be used to…
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…
Hydrodynamics can be formulated in terms of a perturbative series in derivatives of the temperature, chemical potential, and flow velocity around an equilibrium state. Different formulations for this series have been proposed over the years, which consequently led to the development of various hydrodynamic theories. In this work, we discuss the relativistic generalizations of the perturbative expansions put forward by Chapman and Enskog, and Hilbert, using general matching conditions in kinetic theory. This allows us to describe, in a comprehensive way, how different out-of-equilibrium definit…
In ultra-relativistic collisions of heavy ions, the strongly interacting Quark Gluon Plasma (sQGP) is created. The fluid nature of the sQGP was one of the important discoveries of high energy heavy ion physics in the last decades. Henceforth the explosion of this matter may be described by hydrodynamical models. Besides numerical simulations, it is important to study the analytic solutions of the equations of hydrodynamics, as these enable us to understand the connection of the final and initial states better. In this paper we present a perturbative, accelerating solution of relativistic hydro…
We review the basic concepts of perturbative quantum chromodynamics (QCD) and relativistic hydrodynamics, and their applications to hadron production in high energy nuclear collisions. We discuss results from the Relativistic Heavy Ion Collider (RHIC) in light of these theoretical approaches. Perturbative QCD and hydrodynamics together explain a large amount of experimental data gathered during the first decade of RHIC running, although some questions remain open. We focus primarily on practical aspects of the calculations, covering basic topics like perturbation theory, initial state nuclear …
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.
The quark gluon plasma is formed in heavy-ion collisions, and it can be described by solutions of relativistic hydrodynamics. In this paper we utilize perturbative hydrodynamics, where we study first order perturbations on top of a known solution. We investigate the perturbations on top of the Hubble flow. From this perturbative solution we can give the form of the particle emitting source and calculate observables of heavy-ion collisions. We describe the source function and the single-particle momentum spectra for a spherically symmetric solution.
Considering the finite volume of nucleons, a Lagrangian density is given. The first order self-energy of the nucleon and the equation of state of nuclear matter are calculated in the framework of relativistic mean-field approximation. Our results indicate the effects of the volume of nucleons are not negligible.
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…
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.
We show that relativistic mean fields theories with scalar, $S$, and vector, $V$, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry {\it and positive energy bound states} when $S=-V$. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.
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 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.
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…
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.
The quark-molecular-dynamics model is used to study microscopically the dynamics of the coloured quark phase and the subsequent hadron formation in relativistic S+Au collisions at the CERN-SPS. Particle spectra and hadron ratios are compared to both data and the results of hadronic transport calculations. The non-equilibrium dynamics of hadronization and the loss of correlation among quarks are studied.
We show that a quantized ideal fluid will generally exhibit a small but non-zero viscosity due to the backreaction of quantum soundwaves on the background. We use an effective field theory expansion to estimate this viscosity to first order in perturbation theory. We discuss our results, and whether this estimate can be used to obtain a more model-independent estimate of the "quantum bound" on the viscosity of physical systems
We compute the recoil polarization of the lambda-hyperon and the photon asymmetry for the quasifree photoproduction of kaons in a relativistic impulse-approximation approach. Our motivation for studying polarization observables is threefold. First, polarization observables are more effective discriminators of subtle dynamics than the unpolarized cross section. Second, earlier nonrelativistic calculations suggest an almost complete insensitivity of polarization observables to distortions effects. Finally, this insensitivity entails an enormous simplification in the theoretical treatment. Indeed…
We review studies of vortical motion and the resulting global polarization of $Λ$ and $\barΛ$ hyperons in heavy-ion collisions, in particular, within 3FD model. 3FD predictions for the global midrapidity polarization in the FAIR-NICA energy range are presented. The 3FD simulations indicate that energy dependence of the observed global polarization of hyperons in the midrapidity region is a consequence of the decrease of the vorticity in the central region with the collision energy rise because of pushing out the vorticity field into the fragmentation regions. At high collision energies this pu…
The spin polarization measurements of particles emitted in heavy-ion collisions have opened the possibility for new phenomenological investigations of spin physics in relativistic fluids. The theoretical predictions of global polarization are in agreement with the data, but consistent discrepancies stand out for the local polarization. We show that the covariant theory of relativistic quantum fluids at local equilibrium implies an additional, non-dissipative contribution to the spin polarization vector, which is proportional to the thermal shear, which has been previously overlooked. This addi…
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 argue that the enhancement in the spin polarization of anti-hyperons compared to the polarization of the hyperons in noncentral relativistic heavy-ion collisions arises as a result of an interplay between the chiral and helical vortical effects. The chiral vortical effect generates the axial current of quarks along the vorticity axis while the recently found helical vortical effect generates the helicity flow -- the projection of the quark's polarization vector onto its momentum -- along the same axis. For massless fermions, the helical charge corresponds to a difference in the contribution…
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…
A detailed analysis of 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 analyzed 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. From the results one can see the very large sensitivity of all the observa…
We analyze the pressure and density equations of state of unpolarized non-relativistic fermions at finite temperature in one spatial dimension. For attractively interacting regimes, we perform a third-order lattice perturbation theory calculation, assess its convergence properties by comparing with hybrid Monte Carlo results (there is no sign problem in this regime), and demonstrate agreement with real Langevin calculations. For repulsive interactions, we present lattice perturbation theory results as well as complex Langevin calculations, with a modified action to prevent uncontrolled excursi…
Whereas a nonrelativistic distorted wave model fails to quantitatively describe analyzing power data for exclusive proton-induced proton-knockout from the 3s_{1/2} state in Pb-208 at 202 MeV, the corresponding relativistic prediction provides a perfect description, thus suggesting that the Dirac equation is the more appropriate underlying dynamical equation. We check the consistency of this rsult by comparing predictions for both dynamical models to new high resolution data for 3s_{1/2} knockout in Pb-208 at a higher incident energy of 392 MeV.
