Relativistic distribution function for particles with spin at local thermodynamical equilibrium

TL;DR

This paper extends the relativistic distribution function to include spin for particles at local thermodynamical equilibrium, predicting polarization effects due to vorticity and temperature gradients in heavy ion collisions.

Contribution

It introduces a spin-inclusive distribution function at local equilibrium, generalizing the Cooper-Frye formula for polarized particles in relativistic settings.

Findings

Particles acquire polarization proportional to vorticity.

Temperature gradients induce orthogonal polarization.

The formula predicts polarization in heavy ion collision freeze-out.

Abstract

We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of the global equilibrium case, that at local thermodynamical equilibrium particles acquire a net polarization proportional to the vorticity of the inverse temperature four-vector field. The obtained formula for polarization also implies that a steady gradient of temperature entails a polarization orthogonal to particle momentum. The single-particle distribution function in momentum space extends the so-called Cooper-Frye formula to particles with spin 1/2 and allows to predict their polarization in relativistic heavy ion collisions at the freeze-out.