  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 improved, and prove the Borel convergence of the corresponding series
for $m_v \lsim 0$, with $m_v$ 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.
