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

We compute the third-order correction to the S-wave quarkonium wave functions |ψ_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.

preprint2008arXivOpen access
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