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

TL;DR

This paper calculates the third-order non-Coulomb correction to S-wave quarkonium wave functions at the origin, completing the third-order analysis with implications for bottomonium and toponium.

Contribution

It introduces the third-order correction from non-Coulomb potentials, advancing the precision of quarkonium wave function calculations.

Findings

Numerical estimates for bottomonium and toponium.

Completion of third-order corrections including non-Coulomb effects.

Enhanced accuracy in quarkonium wave function predictions.

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.