Collisional corrections to spin polarization from quantum kinetic theory using Chapman-Enskog expansion

TL;DR

This paper develops a quantum kinetic theory framework to analyze collisional corrections to spin polarization, considering different scenarios and approximations, providing a basis for future numerical studies on spin dynamics.

Contribution

The paper derives a spin Boltzmann equation with Møller scattering and explores collisional corrections under various assumptions, including off-equilibrium and local thermal equilibrium scenarios.

Findings

Polarization corrections are modified by gradients of chemical potential and shear viscosity.

In one scenario, corrections are independent of coupling constant.

In another, corrections are of order .

Abstract

We have investigated the collisional corrections to the spin polarization pseudo-vector, $\delta\mathcal{P}^{\mu}$, using quantum kinetic theory in Chapman-Enskog expansion. We derive the spin Boltzmann equation incorporating M{\o}ller scattering process. We further consider two distinct scenarios using hard thermal loop approximations for simplification. In scenario (I), the vector charge distribution function is treated as off-equilibrium under the validity domain of gradient expansion. Remarkably, the polarization induced by gradients of thermal chemical potential and shear viscous tensors are modified, but $\delta\mathcal{P}_{\textrm{ }}^{\mu}$ in this scenario does not depend on the coupling constant. In scenario (II), the vector charge distribution function is assumed to be in local thermal equilibrium. Then collisional corrections $\delta\mathcal{P}_{\textrm{ }}^{\mu}$ in this scenario are at $\mathcal{O}(\hbar^{2}\partial^{2})$. Additionally, we evaluate the $\delta\mathcal{P}^{\mu}$ using relaxation time approach for comparative analysis. Our results establish the theoretical framework necessary for the future numerical investigations on the interaction corrections to spin polarization.