Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

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