Full formula for heavy quarkonium energy levels at next-to-next-to-next-to-leading order

We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers n, l, s and j, up to O(alpha(5)(S)m) and O(alpha(5)(S)m log alpha(S)) in perturbative QCD. The QCD Bethe logarithm is given in a one-parameter integral form. The rest of the formula is given as a combination of rational numbers, transcendental numbers (pi, zeta(3), zeta(5)) and finite sums (besides the 3-loop constant (alpha) over bar (3) of the static potential whose full analytic form is still unknown). A derivation of the formula is given. (C) 2014 The Authors. Published by Elsevier B.V.