Hydrodynamic approach to spin relaxation in quark-gluon plasma*

The recent experimental observation of the spin polarization of hadrons in off-central relativistic heavy-ion collisions at RHIC and LHC has strongly motivated theoretical and phenomenological study of the dynamical evolution of spin polarization in a finite temperature plasma. Unlike nonrelativistic systems where spin-orbit coupling is suppressed, relativistic systems exhibit non-conservation of the spin angular momentum, which can be transferred to the orbital angular momentum. As a result, the spin density in relativistic systems, in general, exhibits a relaxation behavior toward its local equilibrium value in hydrodynamics. Therefore, it is essential to establish a theoretical framework that describes spin dynamics in quark-gluon plasma, providing a solid foundation for the analysis of the spin polarization observed in heavy-ion collision experiments.

In this presentation, I will give a brief overview of theoretical investigations of the spin dynamics in quark-gluon plasma. In particular, I will introduce a theoretical framework to desribe the spin relaxation in hydrodynamics based on our work [1-3], which rely on the second law of local thermodynamics and linear response theory. While the relaxation behavior of the spin density is model-independent, it exhibits parametrically slow relaxation in the heavy quark limit. Based on our formulation, I will also demonstrate the perturbative QCD evaluation of the spin relaxation rate for heavy quarks up to leading-log order in the coupling constant.