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

Abstract

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.

44 pages, 11 figures; v2: 45 pages. Minor changes in the text. Small modifications in Figs. 1 and 10. Eqs. 74 and 75 modified. Conclusions unchanged. Journal version