Wayne W. Repko, Marco D. Santia, Stanley F. Radford
We investigate the effects of including the two-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 two-loop corrected potential to determine a set of unperturbed trial wave functions and treat the relativistic and one-loop corrections as perturbations. This approach results in more accurate descriptions of the hyperfine splittings in both the $b\bar{b}$ and $c\bar{c}$ systems.
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http://arxiv.org/abs/1211.6373
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