Spectral function sum rules from current algebra, unitarity and analyticity

Abstract

With the assumptions of SU(2) × SU(2) current algebra, conservation of the vector currents, PCAC and finiteness of the Schwinger terms C V and C A , some restrictions of unitarity and analyticity on hard pion current algebra models are obtained for the specific case of the pion form factor. Among the results are a representation for the proper vertex of the vector current between pion states, the Kawarabayashi-Suzuki-Fayyazuddin-Riazuddin relation and other spectral function sum rules. In the case of polynomial models for the proper vertices, a lower bound on C V and an upper bound for the ϱ width are derived, and estimates are made of corrections to ϱ pole dominance of the vector current spectral function.