Spin Polarization of $Λ$ hyperons from Dissipative Spin Hydrodynamics

TL;DR

This work develops and solves a fully dynamical, dissipative spin-hydrodynamics framework for relativistic heavy-ion collisions, deriving spin evolution from quantum kinetic theory with nonlocal collisions in the small-polarization limit. The spin degrees of freedom (\\omega_0^{\\mu},\\kappa_0^{\\mu},\\mathfrak{t}^{\\mu\\nu}) evolve alongside the background hydrodynamics and relax toward the thermal vorticity, with the spin-shear tensor introducing dissipative effects. Applying the model to Au+Au collisions at \\sqrt{s_{NN}}=200 GeV, the authors reproduce the sign and qualitative momentum/rapidity dependence of \\Lambda polarization, with $I_{SP}$ providing best agreement for the local polarization. The framework highlights the nontrivial impact of microscopic interactions on local polarization and demonstrates predictive power with the only free parameter in the spin sector being the particle mass, while also indicating potential extensions to lower energies where non-equilibrium spin dynamics are more pronounced.

Abstract

We present a framework for spin dynamics in the quark-gluon plasma created in relativistic heavy-ion collisions. Under the approximation of small polarization, macroscopic spin degrees of freedom decouple from the background, and their evolution equations and transport coefficients have been computed using quantum kinetic theory of massive particles with nonlocal collisions. Employing this theory, we numerically solve dissipative relativistic spin hydrodynamics. We explore three interaction scenarios between constituent particles and apply this framework to compute both global and local spin polarization of $Λ$ hyperons in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Our results show that the initially vanishing spin potential relaxes toward thermal vorticity, driving global polarization. Furthermore, we demonstrate that the sign of longitudinal polarization is sensitive to the interaction type, emphasizing the need for a consistent treatment of dissipative effects in spin hydrodynamics to describe experimental data.

Figures (11)

• Figure 1: Time evolution of the energy-weighted space-averaged (left) $xz$ component of the spin potential, and (right) $zz$ component of the spin-shear stress, for three different interactions. Due to the symmetry of our initial condition model, the spatial average of all other components of the spin potential is zero.
• Figure 2: Comparison of results from dissipative spin hydrodynamics with experimental data for three interaction scenarios for Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. The simulations are performed with fixed impact parameter, $b=8.4$ fm, corresponding to 20-50% centrality. The top panel shows the (left) pseudorapidity and (right) transverse momentum dependence of the $y$ component of $\Lambda$ polarization. The bottom panel shows the (left) azimuthal and (right) transverse momentum dependence of the $z$ component of $\Lambda$ polarization. Experimental data are taken from Refs. STAR200_PjSTAR:2019erd with the updated decay parameter ($\alpha_\Lambda = 0.732$).
• Figure 3: Bulk observables for Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. Different symbols correspond to experimental data taken from Refs. STAR2003_pTBRAHMS2002_dNdetaSTAR200_v2.
• Figure 4: Relaxation times ($\tau_\omega$, $\tau_\kappa$, $\tau_{\mathfrak{t}}$) and the transport coefficient $\mathfrak{d}$ are shown as functions of $z=m/T$ for three different interactions.
• Figure 5: Time evolution of energy-weighted space-averaged $m/T$, for $m=300$ MeV, and $\mu_B/T$ for Au+Au collision at $\sqrt{s_{NN}}=200$ GeV, $b=8.4$ fm, and $\varepsilon_{\text{cut}}=0.5$ GeV/fm$^3$.