Spin dynamics and polarization in relativistic systems: recent developments

TL;DR

This review covers recent advances in understanding spin polarization and dynamics in relativistic heavy-ion collisions, emphasizing theoretical frameworks, experimental observations, and the role of vorticity and magnetic fields.

Contribution

It synthesizes recent theoretical and experimental progress, highlighting the impact of pseudo-gauge freedom, spin hydrodynamics formulations, and stochastic spin evolution in relativistic systems.

Findings

Vorticity induces observable spin polarization of emitted hadrons.

Different formulations of spin hydrodynamics influence polarization predictions.

Spin dynamics in heavy flavor particles reveal stochastic relaxation processes.

Abstract

We review recent theoretical and experimental developments in spin dynamics and polarization phenomena in relativistic systems, with a particular focus on heavy-ion collisions. The large angular momentum and magnetic field generated in non-central collisions induce vorticity in the quark-gluon plasma, leading to observable spin polarization of emitted hadrons. We discuss the theoretical foundations of spin polarization arising from spin-vorticity coupling, including formulations based on relativistic hydrodynamics, kinetic theory, and quantum statistical approaches such as the Zubarev density operator. A central theme of the review is the role of pseudo-gauge freedom and its implications for defining energy-momentum and spin tensors, which can influence theoretical predictions of polarization observables. We further examine different formulations of spin hydrodynamics, emphasizing the impact of gradient expansions, spin chemical potential, and entropy-current analysis on the structure of the theory and associated transport coefficients. In addition, we discuss the recent developments in heavy flavor spin dynamics within the framework of rotational Brownian motion, where spin degrees of freedom undergo stochastic evolution due to interactions with the medium. This framework provides a complementary perspective on spin relaxation and diffusion by incorporating the effects of strong initial magnetic fields and establishes connections between spin polarization and the initial geometry through the definition of polarization harmonics. This review provides a comprehensive overview of relativistic spin hydrodynamics as well as non-equilibrium spin dynamics, and outlines future directions toward a consistent and predictive description of spin phenomena in strongly interacting matter.