S -wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy

© 2018 authors. Published by the American Physical Society. We obtain the potential nonrelativistic quantum chromodynamics Lagrangian relevant for S-wave states with next-to-next-to-next-to-leading logarithmic accuracy. We compute the heavy quarkonium mass of spin-averaged l=0 (angular momentum) states, with otherwise arbitrary quantum numbers, with next-to-next-to-next-to-leading logarithmic accuracy. These results are complete up to a missing contribution of the two-loop soft running.