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, $\delta\mathcal{P}^{\mu}$, 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.