Abstract

In QCD it is not always trivial to combine perturbative short distance results with non-perturbative long-distance matrix elements in a consistent way. Since the subject is rather technical, we will provide an introduction into the convergence of perturbative expansions in an effective field theory context. We suggest a way to account for renormalon ambiguities in perturbative expansions, within effective field theories and in particular within potential non-relativistic QCD (pNRQCD). The renormalon contribution is estimated and explicitly subtracted from short distance matching coefficients and added to low energy matrix elements. In doing so we find excellent agreement between non-perturbative continuum limit lattice results on static potentials and perturbation theory. Similar methods can also be applied to results obtained at finite lattice spacing, in which case the renormalon can be traded in against a power term. We are able to predict the b quark mass and to relate bound state glueballino masses to gluino masses. The methods presented are readily applicable to quarkonium and gluinonium physics.