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We compute the relaxation rate of the spin density of heavy quarks in aperturbative QCD plasma to leading-log order in the coupling constant $g$. Thespin 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 $T/M\ll 1$, whichis smaller than the relaxation rate of other non-hydrodynamic modes byadditional powers of $T/M$. We demonstrate three different methods to evaluatethe spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamicregime, 2) the spin density correlation function in the strict hydrodynamiclimit, and 3) quantum kinetic theory of the spin distribution function inmomentum space. We highlight the interesting differences between these methods,while they are ultimately connected to each other by the underlyingWard-Takahashi identity for the non-conserved spin density.

Spin relaxation rate for heavy quarks in weakly coupled QCD plasma