Corrections to quarkonium 1S energy level at O(alpha_S^4 m) from non-instantaneous Coulomb vacuum polarization

Abstract

We calculate O(alpha_S^4 m) and O(alpha_S^4 m log(alpha_S)) corrections to the quarkonium 1S energy level analytically, which have been overlooked in recent studies. These are the contributions from one Coulomb-gluon exchange with the 1-loop vacuum polarization insertion. A part of the corrections was computed numerically some time ago; we correct its error.

Comments: RevTeX4, 4 pages, 2 figures; (v2) A crucial reference is included; we correct its error