Two loop mass effects in the static position space QCD-potential

Abstract

The perturbatively calculable short distance QCD potential is known to two loops including the effect of massive quarks. Recently, a simple approximate solution in momentum space was utilized to obtain the potential in coordinate space. The latter is important in several respects. A comparison with non-perturbative lattice results is feasible in the overlap regime using light $\bar{MS}$ masses. This might be even more promising employing the concept of the force between the heavy color singlet sources, which can be easily derived from the potential. In addition, the better than two percent accuracy bottom mass determination from $Υ$-mesons is sensitive to massive charm loops at the two loop order. We summarize recent results using exact one loop functions and explicit decoupling parametrizations.