We investigate in some detail a "variational mass" expansion approach,
generalized from a similar construction developed in the Gross-Neveu model, to
evaluate the basic order parameters of the dynamical breaking of the SU(2)L×SU(2)R and SU(3)L×SU(3)R chiral symmetries in QCD. The
method starts with a reorganization of the ordinary perturbation theory with
the addition of an arbitrary quark mass m. The new perturbative series can be
summed to all orders thanks to renormalization group properties, with specific
boundary conditions, and advocated analytic continuation in m properties. In
the approximation where the explicit breakdown of the chiral symmetries due to
small current quark masses is neglected, we derive ansatzes for the dynamical
contribution to the "constituent" masses Mq of the u,d,s quarks; the pion
decay constant Fπ; and the quark condensate in terms of
the basic QCD scale ΛMSˉ. Those ansatzes are then optimized,
in a sense to be specified, and also explicit symmetry breaking mass terms can
be consistently introduced in the framework. The obtained values of Fπ and
Mq are roughly in agreement with what is expected from other
non-perturbative methods. In contrast we obtain quite a small value of ∣<qˉq>∣ within our approach. The possible interpretation of the latter results
is briefly discussed.Comment: 40 pages, LaTex, 2 PS figures. Additions in section 2.2 to better
explain the relation between the current mass and the dynamical mass ansatz.
Minor misprints corrected. Version to appear in Phys. Rev.