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

Abstract

A modification of perturbation theory, known as the 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 the variationally improved perturbation technique appropriate to renormalizable asymptotically free theories, we show that the large expansion orders of certain physical quantities are similarly improved, and prove the Borel convergence of the corresponding series for $m_{\mathrm {v}} \lessim 0$ , with $m_{\mathrm {v}}$ the new (arbitrary) mass perturbation parameter. We argue that non-ambiguous estimates of quantities relevant to dynamical (chiral) symmetry breaking in QCD are possible in this resummation framework.