Chiral Symmetry Breaking in QCD: A Variational Approach

Abstract

We develop a &#34;variational mass&#34; expansion approach, recently introduced in the Gross--Neveu model, to evaluate some of the order parameters of chiral symmetry breakdown in QCD. The method relies on a reorganization of the usual perturbation theory with the addition of an &#34;arbitrary quark mass $m$, whose non-perturbative behaviour is inferred partly from renormalization group properties, and from analytic continuation in $m$ properties. The resulting ansatz can be optimized, and in the chiral limit $m \to 0$ we estimate the dynamical contribution to the &#34;constituent&#34; masses of the light quarks $M_{u,d,s}$; the pion decay constant $F_π$ and the quark condensate $< \bar q q >$.