Spin polarization induced by the hydrodynamic gradients

TL;DR

This paper investigates how hydrodynamic gradients influence spin polarization in phase space, revealing new effects like shear-induced polarization that can aid in interpreting heavy-ion collision experiments.

Contribution

It systematically analyzes all first-order hydrodynamic gradient effects on spin polarization, identifying a novel shear-induced polarization effect previously overlooked.

Findings

Shear strength induces a quadrupole in spin polarization.

Reproduction of known effects from temperature gradient and vorticity.

Identification of new significant contributions to spin polarization.

Abstract

We systematically analyze the effects of the derivatives of the hydrodynamic fields on axial Wigner function that describes the spin polarization vector in phase space. We have included all possible first-order derivative contributions that are allowed by symmetry and compute the associated transport functions at one-loop using the linear response theory. In addition to reproducing known effects due to the temperature gradient and vorticity, we have identified a number of potentially significant contributions that are overlooked previously. In particular, we find that the shear strength, the symmetric and traceless part of the flow gradient, will induce a quadrupole for spin polarization in the phase space. We refer to this novel effect as the shear-induced polarization (SIP). Our results, together with hydrodynamic gradients obtained from hydrodynamic simulations, can be employed as a basis for the interpretation of the $\Lambda$ (anti-$\Lambda$) spin polarization measurement in heavy-ion collisions.