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 $Λ$ 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 $Λ$ 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 $Λ$ hyperons in different hydrodynamic models of relativistic heavy-ion collisions. We particularly focus on the explanations of the collision energy dependence of the global $Λ$ polarization from the different hydrodynamic models, the polarization component in the beam direction as well as on the origins of the global and local $Λ$ polarization.