The static quark self-energy at O($\alpha^{20}$) in perturbation theory

In Refs. [1,2] we determined 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 $\alpha^{20}$. We used numerical stochastic perturbation theory [3], where we employed a new second order integrator and twisted boundary conditions. The expansions were obtained in lattice regularization with the Wilson action and two different discretizations of the covariant time derivative within the Polyakov loop. Overall, we obtained four different perturbative series. For all of them the high order coefficients displayed the factorial growth predicted by the conjectured renormalon picture, based on the operator product expansion. This enabled us to determine the normalization constants of the leading infrared renormalons of heavy quark and heavy gluino pole masses. Here we present improved determinations of the normalization constants and the perturbative coefficients by incorporating the four-loop beta-function coefficient (which we also determine) in the fit function.