Three-loop Static QCD Potential in Heavy Quarkonia

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.