Borel convergence of the variationally improved mass expansion and dynamical symmetry breaking

A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D = 1 models (oscillator energy levels) with factorially divergent ordinary perturbative expansions. In a generalization of variationally improved perturbation appropriate to renormalizable, asymptotically free theories, we show that the large expansion orders of certain physical quantities are similarly drastically improved, and prove the (Borel) convergence of the corresponding series. We argue in particular that non-ambiguous estimates of quantities relevant to dynamical (chiral) symmetry breaking in QCD, are possible in this resummation framework.