Toward convergence of the variational mass expansion and Chiral Symmetry Breaking parameters

We re-examine a modification of perturbative expansions, valid for asymptot ically free theories, producing "variationally improved" expansions of phys ical quantities relevant to dynamical (chiral) symmetry breaking. The large order behaviour of this expansion is drastically improved, with respect to the original perturbative expansion (making the series at least Borel summ able, in a certain range of renormalization scheme parameters). We argue th at non-perturbative estimates of the order parameters of QCD chiral symmetr y breaking are therefore possible in this framework.