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

摘要

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