Vorticity and Polarization in Heavy Ion Collisions: Hydrodynamic Models

Abstract

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 $\Lambda$ 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 polarization of spin 1/2 fermions in the relativistic fluid. The latter is directly applied to compute the spin polarization of the $\Lambda$ hyperons, which are produced from the hot and dense medium, described with fluid dynamics. It is followed by a review of the existing calculations of global or local polarization of $\Lambda$ hyperons in different hydrodynamic models of relativistic heavy-ion collisions. We particularly focus on the explanations of the collision energy dependence of the global $\Lambda$ polarization from the different hydrodynamic models, the polarization component in the beam direction as well as on the origins of the global and local $\Lambda$ polarization.

arXiv comment39 pages; to appear in "Strongly Interacting Matter under Rotation", edited by F. Becattini, J. Liao and M. Lisa, Lecture Notes in Physics series. Due to the nature of the review, there is a text overlap with arXiv:1501.04468, arXiv:1610.04717, arXiv:1610.02506, arXiv:1707.07984, arXiv:1810.02706

References in corpus (28)

• Energy and system size dependence of chemical freeze-out in relativistic nuclear collisions
• Relativistic distribution function for particles with spin at local thermodynamical equilibrium
• Global polarization of $\Lambda$ hyperons in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Study of Lambda polarization in relativistic nuclear collisions at sqrt{s}_NN = 7.7-200 GeV
• Polarization of $\Lambda$ ($\bar{\Lambda }$) hyperons along the beam direction in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Vorticity in Heavy-Ion Collisions
• A study of vorticity formation in high energy nuclear collisions
• Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy
• A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions
• Vortical fluid and $\Lambda$ spin correlations in high-energy heavy-ion collisions
• Particlization in hybrid models
• Lambda Polarization in Peripheral Heavy Ion Collisions
• Polarization of massive fermions in a vortical fluid
• Estimation of the shear viscosity at finite net-baryon density from A+A collision data at $\sqrt{s_{\mathrm{NN}}}=7.7-200$ GeV
• Relativistic Heavy-Ion Collisions within 3-Fluid Hydrodynamics: Hadronic Scenario
• Global $\Lambda$ Polarization in high energy collisions
• Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid
• An effective chiral Hadron-Quark Equation of State
• Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP
• Covariant statistical mechanics and the stress-energy tensor
• Local spin polarization in high energy heavy ion collisions
• Transverse-momentum fluctuations in relativistic heavy-ion collisions from event-by-event viscous hydrodynamics
• Longitudinal spin polarization in a thermal model
• Estimates of hyperon polarization in heavy-ion collisions at collision energies $\sqrt{s_{NN}}=$ 4--40 GeV
• The initial state of ultra-relativistic heavy ion collision
• Correlation between global polarization, angular momentum and flow in heavy-ion collisions
• Lambda polarization in heavy ion collisions: from RHIC BES to LHC energies
• Fluid Dynamics Study of the $\Lambda$ Polarization for Au+Au Collisions at $\sqrt{s_{NN}}=200$ GeV

Cited by in corpus (5)

• Hyperon Polarization from the Vortical Fluid in Low Energy Nuclear Collisions
• Lambda polarization in ${}^{108}$Ag +${}^{108}$Ag and ${}^{197}$Au +${}^{197}$Au collisions around a few GeV
• Λ polarization from thermalized jet energy
• Evolution of global polarization in relativistic heavy-ion collisions within a perturbative approach
• Probing early-time longitudinal dynamics with the $\Lambda$ hyperon's spin polarization in relativistic heavy-ion collisions