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Magnetic field plays a crucial role in various novel phenomena in heavy-ion collisions. We solve the Maxwell equations numerically in a medium with time-dependent electric conductivity by using the Finite-Difference Time-Domain (FDTD) algorithm. We investigate the time evolution of magnetic fields in two scenarios with different electric conductivities at collision energies ranging from $\sqrt{s_\text{NN}}=$ 7.7 to 200 GeV. Our results suggest that the magnetic field may not persist long enough to induce a significant splitting between the global spin polarizations of $\Lambda$ and $\bar{\Lambda}$ at freeze-out stage. However, our results do not rule out the possibility of the magnetic field influencing the spin (anti-)alignment of vector mesons., Comment: Revtex4-2, 7 pages, 2 figures

We give a criterion for the Chandrasekhar-Kendall-Woltjer-Taylor (CKWT) state in a resistive plasma. We find that the lowest momentum (longest wavelength) of the initial helicity amplitudes of magnetic fields are the key to the CKWT state which can be reached if one helicity is favored over the other. This indicates that the imbalance between two helicities at the lowest momentum or longest wavelength in the initial conditions is essential to the CKWT state. A few examples of initial conditions for helicity amplitudes are taken to support the above statement both analytically and numerically., Comment: RevTex 4.1, 19 pages, 3 figures

We study the global polarizations of $\Lambda$, $\Xi^-$, and $\Omega^-$ hyperons in noncentral Au+Au collisions at $\sqrt{s_\mathrm{NN}}=$ 7.7-200 GeV. We highlight the importance of effect of decay feeddown to the measured global polarization. With the decay contributions taken into account, the global polarization ordering $P_{\Omega^-} > P_{\Xi^-} > P_\Lambda$ can be naturally explained, which is consistent with the observation recently reported from the STAR experiment from Au+Au collisions at 200 GeV. We also extend our calculations to predict expectations from the RHIC-BES II data., Comment: 4 pages, 2 figures, contribution to 19th International Conference on Strangeness in Quark Matter (SQM2021)

Global spin polarization of hyperons is an important observable to probe the vorticity of the quark-gluon plasma produced in heavy-ion collisions. We calculate the global polarizations of $\Lambda$, $\Xi^-$, and $\Omega^-$ in Au+Au collisions at energies $\sqrt{s_\text{NN}}=$ 7.7--200 GeV based on a multiphase transport model. Our calculations suggest that their primary global polarizations fulfill $P_{\Omega^-}\simeq 5/3P_{\Xi^-}\simeq 5/3P_\Lambda$. We also estimate the feed-down effect of particle decay on the global polarization. With the feed-down effect taken into account, the global polarizations of $\Lambda$ and $\Xi^-$ are clearly separated, and the final global polarizations are in the ordering: $P_{\Omega^-}>P_{\Xi^-}>P_\Lambda$. Such a relation can be tested in experiments, which will provide us more information about the global polarization mechanism., Comment: 6 pages, 3 figures. v2: discussion added

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 spin polarization. Finally we give a brief overview of recent theoretical results for both the global and local spin polarization of $\Lambda$ and $\bar\Lambda$ hyperons., Comment: V2: 29 pages, 15 figures, published in Lecture Notes in Physics vol.987, "Strongly Interacting Matter under Rotation", page 281-308

We investigate the spin alignment of vector mesons arising from locally polarized quarks and anti-quarks (local spin alignment) in heavy-ion collisions. We find that $\rho_{00}\neq 1/3$ does not necessarily signal the global polarization of quarks and anti-quarks along the orbital angular momentum of the system, but may also originate from their local spin polarization. Such local spin polarization could be induced by local vorticity arising from the anisotropic expansion of the fireball. We further propose experimental observables that can distinguish between the local and the global spin alignments. Measurements of these observables in heavy-ion collisions can probe the vorticity pattern and shed light on the puzzles of $\phi$ and $K^{*0}$ spin alignments., Comment: 7 pages, 3 figures; version accepted by PLB

We develop a theoretical framework to study the feed-down effect of higher-lying strange baryons on the spin polarization of the $\Lambda$ hyperon. In this framework, we consider two-body decays through strong, electromagnetic, and weak processes and derive general formulas for the angular distribution and spin polarization of the daughter particle by adopting the helicity formalism. Using the realistic experimental data as input, we explore the feed-down contribution to the global and the local $\Lambda$ polarizations and find that such a contribution suppresses the primordial $\Lambda$ polarization, which is not strong enough to resolve the discrepancy between the current theoretical and the experimental results on the azimuthal-angle dependence of $\Lambda$ polarization. Our paper may also be useful for the measurement of spin polarization of baryons heavier than $\Lambda$ (e.g., $\Xi^-$) in future experiments., Comment: 12 pages, 9 figures

We study the local structure of the vorticity field and the $\Lambda$ polarization in Au+Au collisions in the energy range $\sqrt{s_{\mathrm{NN}}}=7.7$--$200$ GeV and Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2760$ GeV using A Multi-Phase Transport (AMPT) model. We focus on the vorticity field arising from the non-uniform expansion of the fireball, which gives the circular structure of the transverse vorticity $\boldsymbol{\omega}_{\perp}=(\omega_{x},\omega_{y})$ around the $z$ direction as well as the quadrupole pattern of the longitudinal vorticity $\omega_{z}$ in the transverse plane. As a consequence, the three components of the polarization vector $\mathbf{P}=(P_{x},P_{y},P_{z})$ for $\Lambda$ hyperons show harmonic behaviors as $\mathrm{sgn}(Y)\sin\phi_{p}$, $-\mathrm{sgn}(Y)\cos\phi_{p}$, and $-\sin(2\phi_{p})$, where $\phi_{p}$ and $Y$ are the azimuthal angle and rapidity in momentum space. These patterns of the local $\Lambda$ polarization are expected to be tested in future experiments., Comment: 8 pages, 7 figures. One table, one figure and references added. Discussions in Sec III and IV improved. To appear in Phys. Rev. C

Large orbital angular momentum can be generated in non-central heavy-ion collisions, and part of it is expected to be converted into final particle's polarization due to the spin-orbit coupling. Within the framework of A Multi-Phase Transport (AMPT) model, we studied the vorticity-induced polarization of $\Lambda$ hyperons at the midrapidity region $|\eta|<1$ in Au-Au collisions at energies $\sqrt{s_{NN}}=7.7\sim200$ GeV. Our results show that the global polarization decreases with the collisional energies and is consistent with the recent STAR measurements. This behavior can be understood by less asymmetry of participant matter in the midrapidity region due to faster expansion of fireball at higher energies. As another evidence, we discuss how much the angular momentum is deposited in different rapidity region. The result supports our asymmetry argument., Comment: 6 pages, 4 figures, CPOD 2017 proceeding

We compute the fermion spin distribution in the vortical fluid created in off-central high-energy heavy-ion collisions. We employ the event-by-event (3+1)D viscous hydrodynamic model. The spin polarization density is proportional to the local fluid vorticity in quantum kinetic theory. As a result of strong collectivity, the spatial distribution of the local vorticity on the freeze-out hyper-surface strongly correlates to the rapidity and azimuthal angle distribution of fermion spins. We investigate the sensitivity of the local polarization to the initial fluid velocity in the hydrodynamic model and compute the global polarization of {\Lambda} hyperons by the AMPT model. The energy dependence of the global polarization agrees with the STAR data., Comment: 4 pages, 4 figures, Quark Matter 2017 proceeding

The polarizations of $\Lambda$ and $\bar{\Lambda}$ hyperons are important quantities in extracting the fluid vorticity of the strongly coupled quark gluon plasma and the magnitude of the magnetic field created in off-central heavy-ion collisions, through the spin-vorticity and spin-magnetic coupling. We computed the energy dependence of the global $\Lambda$ polarization in off-central Au+Au collisions in the energy range $\sqrt{s_{NN}}=7.7-200$ GeV using a multiphase transport model. The observed polarizations with two different impact parameters agree quantitatively with recent STAR measurements. The energy dependence of the global $\Lambda$ polarization is decomposed as energy dependence of the $\Lambda$ distribution at hadronization and the space-time distribution of the fluid-vorticity field. The visualization of both the $\Lambda$ distribution and the fluid-vorticity field show a smaller tilt at higher collisional energies, which indicates that the smaller global polarization at higher collisional energies is caused by a smaller angular momentum deposition at midrapidity., Comment: RevTex 4-1, 7 pages, 6 figures, to appear in Phys. Rev. C

We study the time evolution of the magnetic field in a plasma with a chiral magnetic current. The Vector Spherical Harmonic functions (VSH) are used to expand all fields. We define a measure for the Chandrasekhar-Kendall-Woltjer (CKW) state, which has a simple form in VSH expansion. We propose the conditions for a general class of initial momentum spectra that will evolve into the CKW state. For this class of initial conditions, to approach the CKW state, (i) a non-vanishing chiral magnetic conductivity is necessary, and (ii) the time integration of the product of the electric resistivity and chiral magnetic conductivity must grow faster than the time integration of the resistivity. We give a few examples to test these conditions numerically which work very well., Comment: RevTex 4, 15 pages, 6 figures. Typos in paragraph 1 and 2 in the introduction of the published version are corrected. These typos have no effects on the result of the paper. The typos in paragraph 2 are in Eq. (1) and in the inline formula in the second to last line