Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory

Abstract

We determine the infinite volume coefficients of the perturbative expansions of the self-energies of static sources in the fundamental and adjoint representations in SU(3) gluodynamics to order ${\ensuremath{\alpha}}^{20}$ in the strong coupling parameter $\ensuremath{\alpha}$. We use numerical stochastic perturbation theory, where we employ a new second order integrator and twisted boundary conditions. The expansions are obtained in lattice regularization with the Wilson action and two different discretizations of the covariant time derivative within the Polyakov loop. Overall, we obtain four different perturbative series. For all of them the high order coefficients display the factorial growth predicted by the conjectured renormalon picture, based on the operator product expansion. This enables us to determine the normalization constants of the leading infrared renormalons of heavy quark and heavy gluino pole masses and to translate these into the modified minimal subtraction scheme ($\overline{\mathrm{MS}}$). We also estimate the four-loop $\ensuremath{\beta}$-function coefficient of the lattice scheme.