Implications of Vector-Meson Field Theory and Partially Conserved Axial-Vector Current on Electron-Positron Annihilation into Hadrons

The total cross section for electron-positron annihilation into hadrons is examined under the assumption that the hadron electromagnetic current is a linear combination of vector-meson fields. A sum rule is found which implies that the cross section must fall off faster than $E^{-4\mathrm{}}{\left(\ln E\right)}^{-1\mathrm{}}$, where $E$ is the center-of-mass energy.