Large orders of perturbation theory versus energy

The computation of the large orders of perturbation theory in gauge theories with spontaneous symmetry breaking is re-examined in the light of the recent studies on instanton-induced scattering at high energies. We obtain a more transparent physical interpretation of well known results. We examine the energy dependence of the large order coefficients for energies of order of the sphaleron mass, and we argue that it is determined by the same function which governs the fermion number violating cross section.