Third-order non-Coulomb correction to the S-wave quarkonium wave functions at the origin

Abstract

We compute the third-order correction to the S-wave quarkonium wave functions |\psi_n(0)|^2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultrasoft correction computed in a companion paper, this completes the third-order calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given.

Comments: 12 pages, v2: matches published version, missing factors in eq. (9), (29) added