Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion

TL;DR

This paper analytically solves the evolution of spin density and chemical potential in a relativistic dissipative fluid undergoing Bjorken expansion, revealing their decay behaviors and implications for spin polarization in heavy-ion collisions.

Contribution

It provides the first analytic solutions for spin density and chemical potential evolution with viscosity and relaxation corrections in relativistic hydrodynamics.

Findings

Spin density decays as ~τ^{-1}

Spin chemical potential decays as ~τ^{-1/3}

Initial spin density may not survive at freezeout

Abstract

We have studied analytically the longitudinally boost-invariant motion of a relativistic dissipative fluid with spin. We have derived the analytic solutions of spin density and spin chemical potential as a function of proper time $\tau$ in the presence of viscous tensor and the second order relaxation time corrections for spin. Interestingly, analogous to the ordinary particle number density and chemical potential, we find that the spin density and spin chemical potential decay as $\sim\tau^{-1}$ and $\sim\tau^{-1/3}$, respectively. It implies that the initial spin density may not survive at the freezeout hyper-surface. These solutions can serve both to gain insight on the dynamics of spin polarization in relativistic heavy-ion collisions and as testbeds for further numerical codes.