Chiral symmetry breaking in QCD: a variational approach

We develop a “variational mass” 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 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 → 0 we estimate the dynamical contribution to the “constituent” masses of the light quarks Mu,d,s; the pion decay constant Fπ and the quark condensate 〈qq〉.