Polarization of Λ (Λ[over ¯]) Hyperons along the Beam Direction in Au+Au Collisions at sqrt[s_{NN}]=200 GeV

Hyperon Polarization along the Beam Direction Relative to the Second and Third Harmonic Event Planes in Isobar Collisions at sqrt[s_{NN}]=200 GeV

The polarization of Λ and Λ[over ¯] hyperons along the beam direction has been measured relative to the second and third harmonic event planes in isobar Ru+Ru and Zr+Zr collisions at sqrt[s_{NN}]=200  GeV. This is the first experimental evidence of the hyperon polarization by the triangular flow originating from the initial density fluctuations. The amplitudes of the sine modulation for the second and third harmonic results are comparable in magnitude, increase from central to peripheral collisions, and show a mild p_{T} dependence. The azimuthal angle dependence of the polarization follows the vorticity pattern expected due to elliptic and triangular anisotropic flow, and qualitatively disagrees with most hydrodynamic model calculations based on thermal vorticity and shear induced contributions. The model results based on one of existing implementations of the shear contribution lead to a correct azimuthal angle dependence, but predict centrality and p_{T} dependence that still disagree with experimental measurements. Thus, our results provide stringent constraints on the thermal vorticity and shear-induced contributions to hyperon polarization. Comparison to previous measurements at RHIC and the LHC for the second-order harmonic results shows little dependence on the collision system size and collision energy.

Spin polarization and alignment in heavy-ion collisions

We report the measurements of global spin polarization of hyperons (PΛ) from FAIR, RHIC and LHC energies. The PΛ continues to follow an increasing trend at √SNN < 7.7 GeV indicating that enormous vorticity prevails even in hadronic dominant region. New measurements of local spin polarization (Pz,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 (Pz,2net), show a negative value in Au+Au collisions at √SNN = 19.6 and 27 GeV. The first Pz measurement with respect to third order harmonic in 200 GeV RHIC isobar collisions shows a non-zero sine modulation, indicating the presence of complex vortical structure in the medium. Surprising new patterns of spin alignment (ρ00) for various vector mesons (K*0, K*±, ϕ and J/ψ emerged at both RHIC and LHC energies. The large deviation in ρ00 of several species poses challenge to the theory.

Measurements of global and local polarization of hyperons in isobar collisions at 200 GeV from STAR

In heavy-ion collisions, the observation of the global and local polarization of hyperons has revealed the existence of large vorticities perpendicular to reaction plane due to system’s orbital angular momentum and along beam direction due to collective velocity field, respectively. With the high-statistics data from isobar collisions of Ru+Ru and Zr+Zr at √SNN = 200 GeV collected by the STAR experiment, we present differential measurements of global polarization for Λ/Λ¯ as a function of centrality. These measurements allow us to study the possible magnetic field driven effects through the polarization difference between Ru+Ru and Zr+Zr, owing to a larger magnetic field in the former. Furthermore, the first measurements of Λ hyperon local polarization along beam direction relative to the third-order event plane as well as the second-order event plane are presented. A comparison of results from isobar and Au+Au collisions provides important new insights into the collision system size dependence of the vorticities in heavy-ion collisions.

Polarization in heavy ion collisions: A theoretical review

In these proceedings I discuss the recent progress in the theory of spin polarization in relativistic fluids. To date, a number of studies have begun to examine the impact of the shear tensor on the local spin polarization and whether this contribution can restore agreement between the measurements and the predictions obtained from a polarization induced by the gradients of the plasma. I present the derivation of the spin polarization vector of a fermion at local thermal equilibrium and I discuss the role of pseudo-gauge transformations and of dissipative effects. I list what we can learn from the polarization measured at lower energies. Finally, I discuss possible applications of spin polarization measurements in relativistic heavy ion collisions.

Local equilibrium and Lambda polarization in high energy heavy ion collisions

The polarization of the Λ hyperon has become an important probe of the Quark-Gluon Plasma produced in relativistic heavy-ion collisions. Recently, it has been found that polarization receives a substantial contribution from a local equilibrium term proportional to the symmetric derivative of the four-temperature vector, the thermal shear tensor. We show that, at very high energies, this term can restore the agreement between the experimental measurements and the predictions of the hydrodynamic model, provided that the hadronization hypersurface is isothermal. We review the theoretical derivation of this new term, discuss numerical computations at RHIC and LHC energies, and compare them with the experimental data. We also present the effect of feed-down corrections.

Relativistic Spin Magnetohydrodynamics

Starting from the kinetic theory description of massive spin-1/2 particles in the presence of a magnetic field, equations for relativistic dissipative nonresistive magnetohydrodynamics are obtained in the small polarization limit. We use a relaxation-time approximation for the collision kernel in the relativistic Boltzmann equation and calculate nonequilibrium corrections to the phase-space distribution function of spin-polarizable particles. We demonstrate that our framework naturally leads to emergence of the well-known Einstein-de Haas and Barnett effects. We obtain multiple transport coefficients and show, for the first time, that the coupling between spin and magnetic field appear at gradient order in the hydrodynamic equation.

Spin and polarization: a new direction in relativistic heavy ion physics

Since the first evidence of a global polarization of Λ hyperons in relativistic nuclear collisions in 2017, spin has opened a new window in the field, both at experimental and theoretical level, and an exciting perspective. The current state of the field is reviewed with regard to the theoretical understanding of the data, reporting on the most recent achievements and envisioning possible developments. The intriguing connections of spin physics in relativistic matter with fundamental questions in quantum field theory and applications in the non-relativistic domain are discussed.

Precise Measurements of Decay Parameters and CP Asymmetry with Entangled Λ-Λ[over ¯] Pairs

Based on 10 billion J/ψ events collected at the BESIII experiment, a search for CP violation in Λ decay is performed in the difference between CP-odd decay parameters α_{-} for Λ→pπ^{-} and α_{+} for Λ[over ¯]→p[over ¯]π^{+} by using the process e^{+}e^{-}→J/ψ→ΛΛ[over ¯]. With a five-dimensional fit to the full angular distributions of the daughter baryon, the most precise values for the decay parameters are determined to be α_{-}=0.7519±0.0036±0.0024 and α_{+}=-0.7559±0.0036±0.0030, respectively. The Λ and Λ[over ¯] averaged value of the decay parameter is extracted to be α_{avg}=0.7542±0.0010±0.0024 with unprecedented accuracy. The CP asymmetry A_{CP}=(α_{-}+α_{+})/(α_{-}-α_{+}) is determined to be -0.0025±0.0046±0.0012, which is one of the most precise measurements in the baryon sector. The reported results for the decay parameter will play an important role in the studies of the polarizations and CP violations for the strange, charmed and beauty baryons.

Probing CP symmetry and weak phases with entangled double-strange baryons

Though immensely successful, the standard model of particle physics does not offer any explanation as to why our Universe contains so much more matter than antimatter. A key to a dynamically generated matter-antimatter asymmetry is the existence of processes that violate the combined charge conjugation and parity (CP) symmetry1. As such, precision tests of CP symmetry may be used to search for physics beyond the standard model. However, hadrons decay through an interplay of strong and weak processes, quantified in terms of relative phases between the amplitudes. Although previous experiments constructed CP observables that depend on both strong and weak phases, we present an approach where sequential two-body decays of entangled multi-strange baryon-antibaryon pairs provide a separation between these phases. Our method, exploiting spin entanglement between the double-strange Ξ- baryon and its antiparticle2 [Formula: see text], has enabled a direct determination of the weak-phase difference, (ξP - ξS) = (1.2 ± 3.4 ± 0.8) × 10-2 rad. Furthermore, three independent CP observables can be constructed from our measured parameters. The precision in the estimated parameters for a given data sample size is several orders of magnitude greater than achieved with previous methods3. Finally, we provide an independent measurement of the recently debated Λ decay parameter αΛ (refs. 4,5). The [Formula: see text] asymmetry is in agreement with and compatible in precision to the most precise previous measurement4.

Polarization of Λ and Λ[over ¯] Hyperons along the Beam Direction in Pb-Pb Collisions at sqrt[s]_{NN}=5.02 TeV

The polarization of the Λ and Λ[over ¯] hyperons along the beam (z) direction, P_{z}, has been measured in Pb-Pb collisions at sqrt[s_{NN}]=5.02  TeV recorded with ALICE at the Large Hadron Collider (LHC). The main contribution to P_{z} comes from elliptic flow-induced vorticity and can be characterized by the second Fourier sine coefficient P_{z,s2}=⟨P_{z}sin(2φ-2Ψ_{2})⟩, where φ is the hyperon azimuthal emission angle and Ψ_{2} is the elliptic flow plane angle. We report the measurement of P_{z,s2} for different collision centralities and in the 30%-50% centrality interval as a function of the hyperon transverse momentum and rapidity. The P_{z,s2} is positive similarly as measured by the STAR Collaboration in Au-Au collisions at sqrt[s_{NN}]=200  GeV, with somewhat smaller amplitude in the semicentral collisions. This is the first experimental evidence of a nonzero hyperon P_{z} in Pb-Pb collisions at the LHC. The comparison of the measured P_{z,s2} with the hydrodynamic model calculations shows sensitivity to the competing contributions from thermal and the recently found shear-induced vorticity, as well as to whether the polarization is acquired at the quark-gluon plasma or the hadronic phase.

Recent progress on global and local polarization of hyperons in heavy-ion collisions

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.

Local Polarization and Isothermal Local Equilibrium in Relativistic Heavy Ion Collisions

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_{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 this finding are discussed.

Shear-Induced Spin Polarization in Heavy-Ion Collisions

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 z[over ^] and the out-plane direction y[over ^] in noncentral 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 a strange quark, SIP wins the competition, and the resulting azimuthal angle dependent spin polarization P_{y} and P_{z} agree qualitatively with the experimental data.

Generating Spin Polarization from Vorticity through Nonlocal Collisions

We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in ℏ, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.

Global Polarization of Ξ and Ω Hyperons in Au+Au Collisions at sqrt[s_{NN}]=200 GeV

Global polarization of Ξ and Ω hyperons has been measured for the first time in Au+Au collisions at sqrt[s_{NN}]=200  GeV. The measurements of the Ξ^{-} and Ξ[over ¯]^{+} hyperon polarization have been performed by two independent methods, via analysis of the angular distribution of the daughter particles in the parity violating weak decay Ξ→Λ+π, as well as by measuring the polarization of the daughter Λ hyperon, polarized via polarization transfer from its parent. The polarization, obtained by combining the results from the two methods and averaged over Ξ^{-} and Ξ[over ¯]^{+}, is measured to be ⟨P_{Ξ}⟩=0.47±0.10(stat)±0.23(syst)% for the collision centrality 20%-80%. The ⟨P_{Ξ}⟩ is found to be slightly larger than the inclusive Λ polarization and in reasonable agreement with a multiphase transport model. The ⟨P_{Ξ}⟩ is found to follow the centrality dependence of the vorticity predicted in the model, increasing toward more peripheral collisions. The global polarization of Ω, ⟨P_{Ω}⟩=1.11±0.87(stat)±1.97(syst)% was obtained by measuring the polarization of daughter Λ in the decay Ω→Λ+K, assuming the polarization transfer factor C_{ΩΛ}=1.

Spin Polarizations in a Covariant Angular-Momentum-Conserved Chiral Transport Model

Using a covariant and angular-momentum-conserved chiral transport model, which takes into account the spin-orbit interactions of chiral fermions in their scatterings via the side jumps, we study the quark spin polarization in quark matter. For a system of rotating and unpolarized massless quarks in an expanding box, we find that side jumps can dynamically polarize the quark spin and result in a final quark spin polarization consistent with that of thermally equilibrated massless quarks in a self-consistent vorticity field. For the quark matter produced in noncentral relativistic heavy ion collisions, we find that in the medium rest frame both the quark local spin polarizations in the direction perpendicular to the reaction plane and along the longitudinal beam direction show an azimuthal angle dependence in the transverse plane similar to those observed in experiments for the Lambda hyperon.

Recent STAR Results from Heavy-Ion and Polarized Proton Programs

We present recent physics results from the STAR experiment at Relativistic Heavy Ion Collider (RHIC). The proceedings cover studies of azimuthal anisotropy in small and large systems, global and local hyperon polarization, correlation femtoscopy, antideuteron and J/ψ production from heavyion program as well as the measurements of longitudinal spin asymmetry from polarized proton program.