Large-order estimates for perturbation theory of a Yang-Mills field coupled to a scalar field

Using an iteration procedure we have found the six possible forms of classical solutions to coupled Yang-Mills and isodoublet scalar fields which are needed to learn the high-order behavior of the perturbation series of that field theory. For some of these solutions we have obtained solutions in closed form; for others we numerically estimate their contribution to the asymptotic behavior of the perturbation-theory coefficients. It turns out that in the limit of a pure Yang-Mills theory, the most important contribution comes from an instanton---anti-instanton configuration and leads to the conclusion that the perturbation theory is not definable by a Borel summation technique.