Spin Polarization Formula for Dirac Fermions at Local Equilibrium

TL;DR

This paper derives a formula linking local thermal equilibrium parameters to observable spin polarization in Dirac fermions, aiding interpretation of experimental data in relativistic heavy-ion collisions.

Contribution

It introduces a novel Cooper-Frye type spin polarization formula for Dirac fermions at local equilibrium, connecting theoretical spin potentials to measurable polarization.

Findings

Provides a new formula for spin polarization in Dirac fermions.

Clarifies physical contributions to spin polarization.

Enables conversion of spin potentials to experimental observables.

Abstract

We derive a Cooper-Frye type spin polarization formula for Dirac fermions at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, chemical potential, and spin potential. We discuss the physical meaning of different contributions to spin polarization and compare them with previous works. The present formula provides machinery to convert the spin potential computed in, e.g., relativistic spin hydrodynamics to the spin polarization observable in, e.g., heavy-ion collisions.