Second-order effects in chiral-invariant pion Lagrangians and the use of superpropagators

We examine the second-order corrections to the scattering amplitude and to the vector currents for chiral-invariant Lagrangians of massless pions. Standard renormalization theory leads to three undetermined parameters. We discuss the possibility of choosing definite values for these parameters by applying the technique of superpropagators. In an appendix we investigate the restrictions which follow if localizability of the perturbation expansion in powers of the interaction Lagrangian is required. It is shown that this condition determines the pion-field coordinates uniquely.