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 |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.

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

References in corpus (4)

• Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin
• Heavy Quarkonium Spectrum and Production/Annihilation Rates to order ${\beta }_0^3{\alpha }_s^3$
• Ultrasoft contribution to quarkonium production and annihilation
• Fermionic Corrections to the Three-Loop Matching Coefficient of the Vector Current

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