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

Understand

We obtain the Potential NRQCD Lagrangian relevant for S-wave states with next-next-to-next-to-leading logarithmic (NNNLL) accuracy.

• We compute the heavy quarkonium mass of spin-averaged $l= 0$ (angular momentum) states, with otherwise arbitrary quantum numbers, with NNNLL accuracy.
• These results are complete up to a missing contribution of the two-loop soft running.