Vector Currents and Current Algebra. III. Dual-Resonance Model with Universally Coupled Vector Mesons

Abstract

We extend the model for conserved vector currents in the dual-resonance model to include the infinite set of universally coupled vector mesons. One- and two-current amplitudes satisfying current algebra and factorizing on the $M$ highest trajectories are constructed for a form factor falling like ${\left(q^2\right)}^{-M}$. Physically acceptable completely factorized amplitudes are not obtained in the limit $M\to \infty$, however. Complete factorization and unsubtracted dispersion relations in $q^2$ for single-current amplitudes are shown to indeed imply exponentially falling form factors. However, we then prove that no acceptable completely factorized two-current amplitudes can be constructed from a current coupling only to the universal vector mesons.