# Can the divergence of perturbation series hinting the solution is not an analytic function of the parameter?

In QFT, the perturbation series of some amplitudes diverge. As far as I know, perturbation series assume the solution is an analytic function of the small parameter. However this assumption can be wrong. Does that hint that the amplitudes in the consideration are not analytic functions of small parameters? i.e non-perturbative effects exist?

Edit

The thing I want to ask is if non-perturbative effects are the cause of divergent perturbation series in QFT, which also includes QED.