Strong-interaction contributions to one-loop leptonic processes.

Abstract

We classify all strong-interaction contributions to all four-lepton processes through one loop in electroweak ${\mathrm{SU}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{U}}_{1}$ and to all orders in strong interactions. We show that those parts which are not reliably calculated in perturbative QCD are all related to a certain integral over the total cross section for ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}hadrons at low energies. We evaluate this integral for the most recent data and find that, for most four-lepton processes of interest, it is dominated by the timelike \ensuremath{\Vert}q${\mathcal{'}}^{2}$\ensuremath{\Vert} region from 1 to 100 ${\mathrm{GeV}}^{2}$. We show that the associated theoretical strong-interaction uncertainty is a factor of \ensuremath{\sim}2 smaller than previously published estimates. We give the strong-interaction contribution and associated theoretical uncertainty for future SLAC, CERN, and Fermilab precision experiments and show that the theoretical uncertainty is quite small, thus allowing precision tests of the electroweak theory at the one-loop level.