Asymptotic Limit ofσ(e++e−→hadrons)σ(e++e−→μ+μ−)

Abstract

Combining the low-energy theorem by Crewther and by Chanowitz and Ellis on the anomalous vertex function for partially conserved dilation current and a new result from the most conventional vector-meson dominance, we predict the asymptotic limit of the ratio $\frac{\sigma (e^{+}+e^{-}\to \mathrm{hadrons})}{\sigma (e^{+}+e^{-}\to {\mu }^{+}{\mu }^{-})}$ to be $R\cong \frac{16{\pi }^2}{f_0^{}{}_{}{}^2}=5.7\mathrm{}\pm 0.9$, which is in remarkable agreement with the preliminary data from the Cambridge Electron Accelerator $e^{+}-e^{-}$ colliding-beam experiment but in strong contradiction with the other predictions $R=\frac{2}{3}$ and $R=2\mathrm{}$ in the single- and three-triplet fractionally charged quark models.