Quantum kinetic theory for spin transport: General formalism for collisional effects

We systematically derive the collision term for the axial kinetic theory a quantum kinetic theory delineating the coupled dynamics of the vector/axial charges and spin transport carried by the massive spin-1/2 fermions traversing a medium. We employ the Wigner-function approach and propose a consistent power-counting scheme where the axial-charge distribution function, a non-conserved quantity for massive particles, is accounted as the first-order quantity in the h expansion, while the vector-charge distribution function the zeroth-order quantity Among the terms generally expressed with the fermion self-energies, we identify the crucial terms which are responsible for the spin-diffusion effect and the quantum effects inducing the spin polarization. We also confirm that the obtained collisional axial kinetic theory smoothly reduces to the chiral kinetic theory in the massless limit. Our general expression also reduces to a particularly simple form when the spin frame vector is fixed to the specific Lorentz frame, i.e., the rest frame of a massive fermion. As an application to the weakly coupled quark-gluon plasma at high temperature, we compute the spin-diffusion term for massive quarks up to the leading logarithmic order.