The system created in non-central relativistic nucleus-nucleus collisions possesses large orbital angular momentum. Due to spin-orbit coupling, particles produced in such a system could become globally polarized along the direction of the system angular momentum. We present the results of Lambda and anti-Lambda hyperon global polarization measurements in Au+Au collisions at sqrt{s_NN}=62.4 GeV and 200 GeV performed with the STAR detector at RHIC. The observed global polarization of Lambda and anti-Lambda hyperons in the STAR acceptance is consistent with zero within the precision of the measurements. The obtained upper limit, |P_{Lambda,anti-Lambda}| <= 0.02, is compared to the theoretical values discussed recently in the literature.
Since the observation of $Λ$ global polarization at RHIC, indicating the most vortical fluid ever observed so far, many experimental and theoretical progresses have been made in understanding of vorticity and polarization phenomena in heavy-ion collisions. But there still exist open questions which are currently being studied. In these proceedings, recent experimental results on global and local polarization of hyperons in heavy-ion collisions are reviewed.
In non-central nuclear collisions, the created matter should exhibit strong vorticity, which induces spin polarization. Global polarization is a good tool to investigate the dynamics of the system. Global polarization of $Λ$ and $\barΛ$ hyperons has been measured at $\sqrt{s_{\mathrm{NN}}}$ = 2.4 GeV - 5.02 TeV in various experiments. We have measured the global polarization of $Λ$ hyperons in Au+Au collisions with fixed-target configuration at $\sqrt{s_{\mathrm{NN}}}$ = 7.2 GeV at RHIC-STAR experiment. The non-zero signal is observed and it follows the global trend of $Λ$ global polarization …
New results on global polarization of $Λ$ hyperons in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV reveal non-zero signal on the order of a few tenths of a percent. Compared with lower energy results, the current measurement shows that the polarization decreases at higher collision energy, the trend being well reproduced by theoretical calculations. The polarization is found to be larger in more peripheral collisions, as well as in the in-plane than in the out-of-plane direction. The signal seems to depend on the asymmetry between positive and negative charge in each event, which may indicate…
The recent measurements of the global polarization and vector meson spin alignment along the system orbital momentum in heavy ion collisions are briefly reviewed. A possible connection between the global polarization and the chiral anomalous effects is discussed along with possible experimental checks. Future directions, in particular those aimed on the detailed mapping of the vorticity fields, are outlined. The Blast Wave model is used for an estimate of the anisotropic flow effect on the vorticity component along the beam direction. We also point to a possibility of a circular pattern in the…
Global polarization of $Λ$ and $\barΛ$ hyperons in Au+Au collisions at collision energies $\sqrt{s_{NN}}=$ 4-40 GeV in the midrapidity region and total polarization, i.e. averaged over all rapidities, are studied within the scope of the thermodynamical approach. The relevant vorticity is simulated within the model of the three-fluid dynamics (3FD). It is found that the performed rough estimate of the global midrapidity polarization quite satisfactorily reproduces the experimental STAR data on the polarization, especially its collision-energy dependence. The total polarization increases with th…
Fluid dynamic approach is a workhorse for modelling collective dynamics in relativistic heavy-ion collisions. The approach has been successful in describing various features of the momentum distributions of hadrons produced in the heavy-ion collisions, such as $p_T$ spectra, flow coefficients $v_n$ etc. As such, the description of the phenomenon of polarization of $Λ$ hyperons in heavy-ion collisions has to be incorporated into the hydrodynamic approach. We start this chapter by introducing different definitions of vorticity in relativistic fluid dynamics. Then we present a derivation of the p…
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…
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 …
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 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…
The global polarization of the $Λ$ and $\overlineΛ$ hyperons is measured for Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 and 5.02 TeV recorded with the ALICE at the LHC. The results are reported differentially as a function of collision centrality and hyperon's transverse momentum ($p_{\rm{T}}$) for the range of centrality 5-50%, $0.5 < p_{\rm{T}} <5$ GeV/$c$, and rapidity $|y|<0.5$. The hyperon global polarization averaged for Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 and 5.02 TeV is found to be consistent with zero, $\langle P_{\rm{H}}\rangle$ (%) $\approx$ - 0.01 $\pm$ 0.05 (stat.…
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 address the issue of energy and charge dependence of global polarization of $Λ$ hyperons in peripheral $Au-Au$ collisions recently observed by the STAR collaboration at RHIC. We compare different contributions to the anomalous mechanism relating polarization to vorticity and hydrodynamic helicity in QCD matter. We stress that the suppression of the gravitational anomaly contribution in strongly correlated matter observed in lattice simulations confirms our earlier prediction of rapid decrease of polarization with increasing collision energy. Our mechanism leads to polarization of $\bar Λ$ o…
We study the structure of vorticity and hydrodynamic helicity fields in peripheral heavy-ion collisions using the kinetic Quark-Gluon String Model. The angular momentum conservation within this model holds with a good accuracy. We observe the formation of specific toroidal structures of vorticity field (vortex sheets). Their existence is mirrored in the polarization of hyperons of the percent order.
In these proceedings, measurements of J/psi polarization in p+p collisions at 200 and 500 GeV via the dielectron decay channel at mid-rapidity with the STAR experiment are discussed. At 200 GeV the polarization parameter, $λ_θ$, related to the polar anisotropy is obtained in the helicity frame as a function of transverse momentum, 2 < $p_{T}$ < 6 GeV/c, and compared to different model predictions. A new J/psi polarization measurement at 500 GeV extends the previous analysis to a wide transverse momentum range of 5 < $p_{T}$ < 16 GeV/c. Also, the polarization parameter related to the azimuthal …
The global polarization of the $Λ$ and $\barΛ$ hyperons ($P_{\rm H}$) has been measured in Pb--Pb collisions at $\sNN=$ 2.76 TeV and 5.02 TeV in ALICE at the Large Hadron Collider (LHC). The hyperon global polarization is found to be consistent with zero at both collision energies. The local polarization of the $Λ$ and $\barΛ$ hyperons along the beam ($z$) direction, $P_{\rm z}$, has also been measured in Pb--Pb collisions at $\sNN=5.02$ TeV. The $P_{\rm z}$, measured as a function of the hyperon emission angle relative to the second harmonic symmetry plane, exhibits a second harmonic sine mod…
We give a brief overview of recent theoretical and experimental results on the chiral magnetic effect and spin polarization effect in heavy-ion collisions. We present updated experimental results for the chiral magnetic effect and related phenomena. The time evolution of the magnetic fields in different models is discussed. The newly developed quantum kinetic theory for massive fermions is reviewed. We present theoretical and experimental results for the polarization of $Λ$ hyperons and the $ρ_{00}$ value of vector mesons.
We report on the measurement of the inclusive J/$ψ$ polarization parameters in pp collisions at a center of mass energy $\sqrt{s} = 8$ TeV with the ALICE detector at the LHC. The analysis is based on a data sample corresponding to an integrated luminosity of 1.23 pb$^{-1}$. J/$ψ$ resonances are reconstructed in their di-muon decay channel in the rapidity interval $2.5 < y < 4.0$ and over the transverse-momentum interval $2 < p_{\rm T} < 15$ GeV/$c$. The three polarization parameters ($λ_θ$, $λ_φ$, $λ_{θφ}$) are measured as a function of $p_{\rm T}$ both in the helicity and Collins-Soper refere…
Based on the three-fluid model, the global $Λ$ polarization in Au+Au collisions at 2.4 $\leq\sqrt{s_{NN}}\leq$ 7.7 GeV is calculated, including its rapidity and centrality dependence. Contributions from the thermal vorticity and meson-field term (proposed by Csernai, Kapusta and Welle) to the global polarization are considered. The results are compared with data from recent and ongoing STAR and HADES experiments. It is predicted that the polarization maximum is reached at $\sqrt{s_{NN}}\approx$ 3 GeV, if the measurements are performed with the same acceptance. The value of the polarization is …
We study inclusive $χ_{cJ}$ production with definite polarizations in polarized proton-proton collisions at $\sqrt{s}$ = 200 GeV and 500 GeV at RHIC by using non-relativistic QCD (NRQCD) color-octet mechanism. We present results of rapidity distribution of $χ_{c0}$, $χ_{c1}$ and $χ_{c2}$ production with specific polarizations in polarized p-p collisions at RHIC within the PHENIX detector acceptance range. We also present the corresponding results for the spin asymmetries.
The STAR Collaboration is performing a wide range of measurements to determine the gluon helicity distribution in the proton. Gluon-gluon and quark-gluon scattering dominate jet production in proton-proton collisions at RHIC, so the longitudinal double-spin asymmetry, $A_{LL}$, for jet production places significant constraints on the gluon polarization in the proton. In recent years STAR has recorded large longitudinally polarized $pp$ data sets at both $\sqrt{s} = 200$ GeV and $510$ GeV. The 2009 STAR inclusive jet $A_{LL}$ measurements at $\sqrt{s} = 200$ GeV show the first experimental evid…
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 polarization of inclusive J/$ψ$ and $Υ(1{\rm S})$ produced in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=5.02$ TeV at the LHC is measured with the ALICE detector. The study is carried out by reconstructing the quarkonium through its decay to muon pairs in the rapidity region $2.5<y<4$ and measuring the polar and azimuthal angular distributions of the muons. The polarization parameters $λ_θ$, $λ_ϕ$ and $λ_{θϕ}$ are measured in the helicity and Collins-Soper reference frames, in the transverse momentum interval $2<p_{\rm T}<10$ GeV/$c$ and $p_{\rm T}<15$ GeV/$c$ for the J/$ψ$ and $Υ(1{\rm S})$,…
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 gluon polarization contribution to the proton spin is an integral part to solve the longstanding proton spin puzzle. At the Relativistic Heavy Ion Collider (RHIC), the STAR experiment has measured jets produced in mid-pseudo-rapidity, $|η| < $ 1.0, and full azimuth, $ϕ$, from longitudinally polarized $pp$ collisions to study the gluon polarization in the proton. At center of mass energies $\sqrt{s} =$ 200 and 510 GeV, jet production is dominated by hard QCD scattering processes such as gluon-gluon ($gg$) and quark-gluon ($qg$), thus making the longitudinal double-spin asymmetry ($A_{LL}$) …
We compute the Lambda and anti-Lambda global polarization in semi-central heavy-ion collisions modeling the source as consisting of a high-density core and a less dense corona. We show that when more Lambdas than anti-Lambdas are produced in the corona, and this is combined with a smaller number of Lambdas coming from the core, as compared to those coming from the corona, an amplification effect for the anti-Lambda with respect to that of Lambda polarization can occur. This amplification becomes more important for lower collision energies and quantitatively accounts for the Lambda and anti-Lam…
The hot and dense matter generated in heavy-ion collisions contains intricate vortical structure in which the local fluid vorticity can be very large. Such vorticity can polarize the spin of the produced particles. We study the event-by-event generation of the so-called thermal vorticity in Au + Au collisions at energy region $\sqrt{s}=7.7-200$ GeV and calculate its time evolution, spatial distribution, etc., in a multiphase transport (AMPT) model. We then compute the spin polarization of the $Λ$ and $\barΛ$ hyperons as a function of $\sqrt{s}$, transverse momentum $p_T$, rapidity, and azimuth…
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 $\approx0.2$% 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. In this work an extension of our existing calculations of the $Λ$ polarization in the RHIC BES program to the top RHIC an…
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 (…
We report the measurements of global spin polarization of hyperons ($P_Λ$) from FAIR, RHIC and LHC energies. The $P_Λ$ continue to follow an increasing trend at $\sqrt{s_{\mathrm NN}}$ < 7.7 GeV indicating that enormous vorticity prevail even in hadronic dominant region. New measurements of local spin polarization ($P_{z,2}$) from isobar collisions follow the same pattern observed in previous RHIC and LHC energies. An observable motivated by predicted baryonic Spin Hall Effect, the net local polarization ($P_{z,2}^{\mathrm{net}}$), shows negative value in Au+Au collisions at $\sqrt{s_{\mathrm …
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…
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 compute the $Λ$ and $\overlineΛ$ global polarizations in semi-central heavy-ion collisions using the core-corona model where the source of $Λ$'s and $\overlineΛ$'s is taken as consisting of a high-density core and a less dense corona. We show that the overall properties of the polarization excitation functions can be linked to the relative abundance of $Λ$s coming from the core versus those coming from the corona. For low collision energies, the former are more abundant whereas for higher energies the latter become more abundant. The main consequence of this reversing of the relative abunda…
