Three-loop static QCD potential in heavy quarkonia

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 χ² test. This approach results in more accurate descriptions of the hyperfine splittings in both the bb^¯ and cc^¯ systems