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

Abstract

We have investigated the collisional corrections to the spin polarization pseudo-vector, $\hat{I}´{\mathcal{P}}^{\hat{I}}¼$, using quantum kinetic theory in Chapman-Enskog expansion. We derive the spin Boltzmann equation incorporating Møller 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 $\hat{I}´{\mathcal{P}}_{}^{\hat{I}}¼$ 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 $\hat{I}´{\mathcal{P}}_{}^{\hat{I}}¼$ in this scenario are at $\mathcal{O}({\hslash }^2{\partial }^2)$. Additionally, we evaluate the $\hat{I}´{\mathcal{P}}^{\hat{I}}¼$ 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.

32 pages, 1 figure; version accepted for publication of PRD