computations for top threshold observables is non-relativistic QCD (NRQCD).[^1] It provides an economic and systematic treatment for the non-relativistic expansion and for QCD radiative corrections coming from high and low energies. It has also become evident that it is advantageous to use renormalization group methods [@LMR] to resum logarithms of the top quark velocity $v$ to all orders of QCD perturbation theory in order to avoid large normalization uncertainties of at least $20$ % that are obtained in fixed-order predictions [@synopsis]. Concerning QCD effects at next-to-leading-logarithmic (NLL) order for the total cross section only the $t\bar t$ production current has a non-trivial running, which is fully known[@LMR; @HoangStewartultra; @Manohar1; @Pineda1]. At next-to-next-to-leading-logarithmic (NNLL) order for the total cross section the QCD evolution of almost all required couplings is known [@HoangStewartultra; @Pineda2; @Hoang3loop; @Peninc1] except for missing subleading mixing effects in the running of the heavy quark pair production current. Theoretical analyses for the total cross section at NNLL order were given in [@hmst; @hmst1; @HoangEpiphany]. Currently the normalization uncertainties of the total cross section from QCD effects are estimated to be around $6\%$ [@HoangEpiphany].

While the major focus in recent work was directed on a better understanding of QCD corrections 