We study the spin polarization generated by the hydrodynamic gradients. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. We obtain the explicit expression for SIP using the quantum kinetic equation and linear response theory. Based on a realistic hydrodynamic model, we compute the differential spin polarization along both the beam direction $\hat{z}$ and the out-plane direction $\hat{y}$ in non-central heavy-ion collisions at $\sqrt{s_{NN}}=200$ GeV, including both SIP and thermal vorticity effects. We find that SIP contribution always shows the same azimuthal angle dependence as experimental data and competes with thermal vorticity effects. In the scenario that $Λ$ inherits and memorizes the spin polarization of strange quark, SIP wins the competition, and the resulting azimuthal angle dependent spin polarization $P_y$ and $P_z$ agrees qualitatively with the experimental data.
Recently proposed thermal-shear and spin-Hall contributions to the particle polarization in heavy-ion collisions are discussed. Alternative definitions of the thermal-shear contribution, i.e. those of Becattini-Buzzegoli-Palermo on the one hand and Liu-Yin on the other, are very similar in the midrapidity region while quite different at forward-backward rapidities, which are measured in fixed-target experiments. It is shown that the thermal-shear contribution to the global polarization with momentum averaging extended to all momenta is very different within these alternative definitions. The s…
By including the recently introduced thermal shear term that contributes to the spin polarization vector at local equilibrium, we determine longitudinal polarization of $Λ$ hyperons emitted from a hot and rotating hadronic medium using the thermal model with single freeze-out. In our analysis, we consider the RHIC top energies and use the model parameters which were determined in the earlier analyses of particle spectra and elliptic flow. We confirm that, unlike the previous calculations done by using only the thermal vorticity, the thermal shear term alone leads to the correct sign of the qua…
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…
We study the effects of the shear and bulk viscosities in the hadronic phase on the expansion of the fireball and on the particle production in relativistic heavy ion collisions. Comparing simulation with or without viscosity in the hadronic matter we find that elliptic flow observables strongly dependent on dissipative effects in the late stage. On the other hand, interferometry radii are sensitive, through the early transverse flow, on the value of the viscosity at high temperatures. We present first calculations including the effects of bulk viscosity in the hadronic phase and in the hadron…
It has been realized that thermal shear plays a similar role as thermal vorticity in polarizing spin of particles in heavy ion collisions. We point out that shear has a fundamental difference that it leads to particle redistribution in the medium. The redistribution gives rise to an additional contribution to spin polarization through the self-energy, which is parametrically the same order as the one considered so far in the literature. The self-energy contribution is in general gauge dependent. We introduce double gauge links stretching along the Schwinger-Keldysh contour to restore gauge inv…
We study the influence of a temperature-dependent shear viscosity over entropy density ratio $η/s$, different shear relaxation times $τ_π$, as well as different initial conditions on the transverse momentum spectra of charged hadrons and identified particles. We investigate the azimuthal flow asymmetries as a function of both collision energy and centrality. The elliptic flow coefficient turns out to be dominated by the hadronic viscosity at RHIC energies. Only at higher collision energies the impact of the viscosity in the QGP phase is visible in the flow asymmetries. Nevertheless, the shear …
We propose a method for extracting the shear viscosity over entropy density ratio (eta/s) of the quark-gluon plasma from experimental data. We argue that uncertainty due to poor knowledge of the earliest stages of a heavy-ion collision is smallest for ultra-central events. The most precise value of eta/s can thus be obtained from a global fit to p_T-integrated Fourier harmonics of azimuthal correlations. We further outline a method for quantifying the overall uncertainty in the extracted value. Only after a comprehensive and systematic accounting of all sources of uncertainty can a reliable me…
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…
Initial-state control of vorticity--shear competition in longitudinal $Λ$ polarization in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.36\,\mathrm{TeV}$
School of Mathematics and Physics, China University of Geosciences (Wuhan)（中国地质大学（武汉）数学与物理学院）
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.
In recent years, there has been a significant effort to extract the temperature-dependent shear ($η/s$) and bulk ($ζ/s$) viscosity over entropy ratios of the quark-gluon plasma from a global comparison of heavy-ion data with results of hydrodynamic simulations. However, anisotropic flow, which is arguably the most sensitive probe of viscosity, is only sensitive to an {\it effective\/} viscosity over entropy ratio, which is obtained by taking a weighted average over the temperature, and summing the contributions of shear and bulk. We estimate this effective viscosity using existing first-princi…
We introduce an event-by-event perturbative-QCD + saturation + hydro ("EKRT") framework for ultrarelativistic heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order perturbative QCD using a saturation conjecture to control soft particle production, and describe the space-time evolution of the QCD matter with dissipative fluid dynamics, event by event. We perform a simultaneous comparison of the centrality dependence of hadronic multiplicities, transverse momentum spectra, and flow coefficients of the azimuth-angle asymmetries, aga…
We systematically analyze the effects of the derivatives of the hydrodynamic fields on axial Wigner function that describes the spin polarization vector in phase space. We have included all possible first-order derivative contributions that are allowed by symmetry and compute the associated transport functions at one-loop using the linear response theory. In addition to reproducing known effects due to the temperature gradient and vorticity, we have identified a number of potentially significant contributions that are overlooked previously. In particular, we find that the shear strength, the s…
The gluon polarization tensor for the quark-gluon plasma with shear viscosity is derived with the viscous chromohydrodynamics. The longitudinal and transverse dielectric functions are evaluated from the gluon polarization tensor, through which the polarization energy loss suffered by a fast quark traveling through the viscous quark-gluon plasma is investigated. The numerical analysis indicates that shear viscosity significantly reduces the polarization energy loss.
Chiral anomaly implies the existence of non-dissipative transport phenomena, such as the chiral magnetic effect. At second order in the derivative expansion, novel quantum transport phenomena emerge. In this paper, we focus on the anomalous transport driven by a combination of shear, vorticity and magnetic field. We find that the corresponding transport phenomena -- shear-induced chiral magnetic and chiral vortical effects (siCME and siCVE) -- induce characteristic charge correlations among the hadrons produced in heavy ion collisions. We propose the charge asymmetry of triangular flow as a si…
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…
We show how anisotropy in momentum of the gluon distribution in ultrarelativistic heavy ion collisions gives rise to polarization of direct photons produced via gluon-quark Compton scattering, as well as by quark-antiquark annihilation into a gluon-photon pair. We estimate the polarization asymmetry from the Compton process within a toy model where the polarized photons are produced from thermal gluons scattered by heavy-quark scattering centers moving with Bjorken boost-invariant flow, and find that it could be as large as 10%. We conclude that polarization measurements of directly produced p…
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…
We investigate the influence of a temperature-dependent shear viscosity over entropy density ratio eta/s on the transverse momentum spectra and elliptic flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the elliptic flow in sqrt(s_NN) = 200 GeV Au+Au collisions at RHIC is dominated by the viscosity in the hadronic phase and in the phase transition region, but largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity and insensitive to the hadronic viscosity.
Quarks produced in the early stage of non-central heavy-ion collisions could develop a global spin polarization along the opposite direction of the reaction plane due to the spin-orbital coupling via parton interaction in a medium that has finite longitudinal flow shear along the direction of the impact parameter. We study how such polarization evolves via multiple scattering in a viscous quark-gluon plasma with an initial laminar flow. The final polarization is found to be sensitive to the viscosity and the initial shear of local longitudinal flow.
We introduce an event-by-event pQCD + saturation + hydro ("EKRT") framework for high-energy heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order (NLO) perturbative QCD (pQCD) using saturation to control soft particle production, and describe the space-time evolution of the QCD matter with viscous hydrodynamics, event by event (EbyE). We compare the computed centrality dependence of hadronic multiplicities, p_T spectra and flow coefficients v_n against LHC and RHIC data. We compare also the computed EbyE probability distributions…
Using the AMPT + MUSIC+UrQMD hybrid model, we study the global and local spin polarizations of $Λ$ hyperons as functions of the freeze-out temperature of the spin degree of freedom in the hadronic phase of Au+Au collisions at $\sqrt{s_{NN}}=19.6$ GeV. Including contributions from both the thermal vorticity and thermal shear of the hadronic matter, we find that, with the spin freeze-out temperature dropping from the hadronization temperature of 160 MeV to 110 MeV at the kinetic freeze-out, both the global and local spin polarizations of $Λ$ hyperons due to the thermal vorticity decrease by a fa…
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 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 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…
In heavy-ion collisions, the quark-gluon plasma is produced far from equilibrium. This regime is currently inaccessible by quantum chromodynamics (QCD) computations. We calculate shear transport and entropy far from equilibrium in a holographic model, defining a time-dependent ratio of shear viscosity to entropy density, $η/s$. Large deviations of up to 60% from its near-equilibrium value, $1/4π$, are found for realistic situations at the Large Hadron Collider. We predict the far-from-equilibrium time-dependence of $η/s$ to substantially affect the evolution of the QCD plasma and to impact the…
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…
Equilibration of highly excited baryon-rich matter is studied within the microscopic model calculations in A+A collisions at energies of BES, FAIR and NICA. It is shown that the system evolution from the very beginning of the collision can be approximated by relativistic hydrodynamics, although the hot and dense nuclear matter is not in local equilibrium yet. During the evolution of the fireball the extracted values of energy density, net baryon and net strangeness densities are used as an input to Statistical Model (SM) in order to calculate temperature $T$, chemical potentials $μ_B$ and $μ_S…
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.
We explore the influence of a temperature-dependent shear viscosity over entropy density ratio $η/s$ on the azimuthal anisotropies v_2 and v_4 of hadrons at various rapidities. We find that in Au+Au collisions at full RHIC energy, $\sqrt{s_{NN}}=200$ GeV, the flow anisotropies are dominated by hadronic viscosity at all rapidities, whereas in Pb+Pb collisions at the LHC energy, $\sqrt{s_{NN}}=2760$ GeV, the flow coefficients are affected by the viscosity both in the plasma and hadronic phases at midrapidity, but the further away from midrapidity, the more dominant the hadronic viscosity is. We …
Time evolution of shear viscosity $η$, entropy density $s$, and their ratio $η/ s$ in the central area of central gold-gold collisions at NICA energy range is studied within the UrQMD transport model. The extracted values of energy density, net baryon density and net strangeness density are used as input to (i) statistical model of ideal hadron gas to define temperature, baryo-chemical potential and strangeness chemical potential, and to (ii) UrQMD box with periodic boundary conditions to study the relaxation process of highly excited matter. During the relaxation stage, the shear viscosity is…
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 propose to measure the linear polarization of the external electromagnetic fields of a relativistic heavy ion through azimuthal asymmetries in dilepton production in ultraperipheral collisions. The asymmetries estimated with the equivalent photon approximation are shown to be sizable.
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…
The STAR Beam Energy Scan program has found a difference in the global polarization of $Λ$s and $\barΛ$s produced in $Au+Au$ collisions. This difference is larger for lower center of mass collision energies. In this work we show that a two-component source, consisting of a high density core and a lower density corona, can describe quantitatively the $Λ$ and $\barΛ$ polarization as a function of collision energy.
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…
