Ultrasoft NLL running of the nonrelativistic O(v) QCD quark potential

Using the nonrelativistic effective field theory vNRQCD, we determine the contribution to the next-to-leading logarithmic (NLL) running of the effective quark-antiquark potential at order upsilon (1/m|k|) from diagrams with one potential and two ultrasoft loops, upsilon being the velocity of the quarks in the c. m. frame. The results are numerically important and complete the description of ultrasoft next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair production and annihilation close to threshold.