Perturbative expansion of the plaquette to $\mathcal{O}({\alpha }^{35})$ in four-dimensional SU(3) gauge theory

Abstract

Using numerical stochastic perturbation theory, we determine the first 35 infinite volume coefficients of the perturbative expansion in powers of the strong coupling constant $\alpha$ of the plaquette in SU(3) gluodynamics. These coefficients are obtained in lattice regularization with the standard Wilson gauge action. The on-set of the dominance of the dimension four renormalon associated to the gluon condensate is clearly observed. We determine the normalization of the corresponding singularity in the Borel plane and convert this into the $\overline{\mathrm{MS}}$ scheme. We also comment on the impact of the renormalon on non-perturbative determinations of the gluon condensate.

Comments: 52 pages, 9 figures. Minor changes. One reference added. To meet journal version