Optimized-Variational Quark Mass Expansion and Dynamical Chiral Symmetry Breakdown

Abstract

A recently proposed variational mass expansion approach to dynamical chiral symmetry breakdown is reviewed. We briefly explain how a specific integral ansatz over the analytically continued, arbitrary Lagrangian mass parameter, resums the usual variational mass expansion (``delta-expansion".) The construction is then generalized to obtain non-perturbative expressions for the order parameters of the $SU(n_f)_L \times SU(n_f)_R$ breakdown ($n_f =$ 2 or 3), in QCD. Emphasis is put on some general aspects as well as possible limitations of this approach.