From QCD to the low-energy effective action through composite fields: Goldstone's theorem and f/sub π/

We elaborate upon a formal derivation from QCD of a composite-field (bilocal) effective chiral Lagrangian which we presented in a previous work. We give here a detailed treatment of the transition to the local form of the chiral Lagrangian in the low-energy limit, when chiral symmetry is spontaneously broken. We find an explicit form of the Goldstone-boson mode wave function and use it to derive expressions for the pion decay constant in terms of the quark dynamical mass Σ by two different methods. Using several models for Σ appropriate to QCD and one appropriate to technicolor, we compare the values given by our two different f/sub π/ expressions with each other and with the values for f/sub π/ given by an expression due to Pagels and Stokar. We find good agreement among the various methods of calculating f/sub π/, and the agreement with the experimental value is satisfactory for a condensate mass scale in the range 0.5--1.0 GeV