High order perturbative expansions rom lattice QCD

Due to the dynamical generation of a mass gap in non-Abelian quantum field theories, in general observables will receive contributions from perturbative series as well as from non-perturbative matrix elements. The general structure of such an expansion is that of a trans-series. In particular this means that perturbative expansions can at best be asymptotic. So far only model calculations and conjectures based on various approximations existed, regarding the positions and normalizations of the singularities of such series in the Borel plane. Using lattice regularization, we expand observables in four-dimensional pure gauge QCD to order α35 in the strong coupling parameter. This enables us to verify predictions on the large order behaviour, which are based on the operator product expansion. I also comment on implications for expansions performed in dimensional regularization, using the modified minimal subtraction scheme. Some introduction into the subject area will be provided.