PION LIFETIME, RHOPI AND SIGMAPI INTERMEDIATE STATES, AND SUM RULES

The pion lifetime is calculated assuming an unsubtracted dispersion relation for the axial-vector matrix element and using ρπ and σπ intermediate states as well as the N̄N intermediate state. By imposing convergence conditions, a series of sum rules is obtained, including the generalized Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation and modified Goldberger-Treiman relations. By assuming that the NNπ, ρππ, and σππ vertex functions are dominated by a three-pion resonance with I=1 and JP=0-, it is found possible to make the Goldberger-Treiman relations agree with experiment if the resonance mass is MR2 GeV. This resonance is tentatively identified with the N̄N resonance structure observed around 2 GeV. © 1969 The American Physical Society.