Construction of Three- and Four-Point Functions of Currents for Arbitrary Spin-One Spectral Functions

Abstract

A model is presented for three- and four-point functions of currents which satisfies the Ward identities implied by chiral $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ for arbitrary vector and axial-vector spectral functions. In the limit in which the spectral functions are single-particle dominated, the three- and four-point functions of the usual hard-pion approach are recovered. However, this limit is not forced upon us by the assumption of smoothness of primitive vertices, since the singularity structure is extracted in a manner somewhat different from the hard-pion approach.