Three-loop Static QCD Potential in Heavy Quarkonia

TL;DR

This paper incorporates the full three-loop QCD correction into the static potential to improve the accuracy of heavy quarkonium spectroscopy and decay predictions, especially hyperfine splittings.

Contribution

It introduces a variational method using the complete three-loop corrected potential for heavy quarkonia, enhancing the precision of spectral and decay calculations.

Findings

More accurate hyperfine splitting predictions in bottomonium and charmonium.

Improved fit to experimental spectra using three-loop corrected potential.

Enhanced understanding of QCD effects at short distances.

Abstract

We investigate the effects of including the full three-loop QCD correction to the static short distance $1/r$ potential on the spectroscopy and decays in the charmonium and upsilon systems. We use a variational technique with the full three-loop corrected potential to determine a set of unperturbed trial wave functions and treat the relativistic and one-loop corrections as perturbations. The perturbed results are compared to the subset of the charmonium and upsilon spectra using a $\chi^2$ test. This approach results in more accurate descriptions of the hyperfine splittings in both the $b\bar{b}$ and $c\bar{c}$ systems.