Spin polarization of fermions at local equilibrium: Second-order gradient expansion

TL;DR

This paper calculates the second-order gradient expansion of spin polarization for relativistic fermions at local equilibrium, highlighting the potential impact of non-trivial freeze-out hypersurface structures on polarization.

Contribution

It introduces a second-order gradient expansion approach to evaluate spin polarization in relativistic fluids, accounting for complex space-time structures.

Findings

Second-order derivatives vanish on hyperplanes t=const in the collision frame.

Non-trivial freeze-out hypersurfaces can produce non-zero polarization contributions.

Numerical assessments are needed for the magnitude of these effects.

Abstract

We present a calculation of the spin polarization of spin-1/2 fermions in a relativistic fluid at local thermodynamic equilibrium at the second order in the gradient expansion, including second-order derivatives. The second-order derivative terms vanish if the local equilibrium hypersurface is the hyperplane $t=const$ in the collision center-of-mass frame. However, since the freeze-out hypersurface has a non-trivial space-time structure, these terms may result in a non-vanishing contribution to the spin polarization, whose magnitude needs to be assessed with numerical computations.