Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions

TL;DR

This paper investigates local spin polarization in relativistic heavy ion collisions using an extended hydrodynamic model, revealing complex dependencies on various physical factors and highlighting the importance of shear viscosity and thermal vorticity.

Contribution

It generalizes the Wigner function approach to include massive particles and multiple physical contributions, providing a more comprehensive model of local spin polarization.

Findings

Shear correction aligns with experimental azimuthal-angle dependence.

Thermal vorticity and other terms often oppose shear effects.

Total polarization is highly sensitive to model parameters.

Abstract

We study local spin polarization in the relativistic hydrodynamic model. Generalizing the Wigner functions previously obtained from chiral kinetic theory by Y. Hidaka et al. [Phys. Rev. D 97, 016004 (2018)] to the massive case, we present the possible contributions up to the order of $\hbar$ from thermal vorticity, shear viscous tensor, other terms associated with the temperature and chemical-potential gradients, and electromagnetic fields to the local spin polarization. We then implement the (3+1)-dimensional viscous hydrodynamic model to study the spin polarizations from these sources with a small chemical potential and ignorance of electromagnetic fields by adopting an equation of state different from those in other recent studies. Although the shear correction alone upon the local polarization results in a sign and azimuthal-angle dependence more consistent with experimental observations, as also discovered in other recent studies, it is mostly suppressed by the contributions from thermal vorticity and other terms that yield an opposite trend. It is found that the total local spin polarization can be very sensitive to the equation of states, the ratio of shear viscosity to entropy density, and the freeze-out temperature.