Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant $g$. The spin relaxation rate $\Gamma_s$ in spin hydrodynamics is shown to be $\Gamma_s\sim g^4\log(1/g)T (T/M)^2$ in the heavy-quark limit $T/M\ll 1$, which is smaller than the relaxation rate of other non-hydrodynamic modes by additional powers of $T/M$. We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, and 3) quantum kinetic theory of the spin distribution function in momentum space. We highlight the interesting differences between these methods, while they are ultimately connected to each other by the underlying Ward-Takahashi identity for the non-conserved spin density.