PION MASS AND DECAY CONSTANT

Independent of assumptions about the form of the quark-antiquark scatt ering kernel we derive the explicit relation between the pion Bethe-Sa lpeter amplitude, Gamma(pi), and the quark propagator in the chiral li mit; Gamma(pi), necessarily involves a non-negligible gamma(5) gamma.P term (P is the pion four-momentum). We also obtain exact expressions for the pion decay constant, f(pi), and mass, both of which depend on Gamma(pi); and demonstrate the equivalence between f(pi) and the pion Bethe-Salpeter normalisation constant in the chiral limit. We stress t he importance of preserving the axial-vector Ward-Takahashi identity i n any study of the pion itself, and in any study whose goal is a unifi ed understanding of the properties of the pion and other hadronic boun d states. (C) 1998 Published by Elsevier Science B.V.