A Simple Approximation of the One-Loop Corrected Cross Section for $e^{+}{e}^{-}\to W^{+}{W}^{-}$ at LEP 2

Abstract

Using the SU(2) gauge coupling, $g_{W^{\pm }}(M_{W^{\pm }}^2)$, at the high-energy scale of $M_{W^{\pm }}$, defined by the (theoretical value of the) leptonic W-width, rather than using the low-energy value, defined via the Fermi coupling, $G_{\mu }$, in the Born approximation, and supplementing with Coulomb corrections and initial state radiation, errors with respect to the exact one-loop results for the differential cross section of $e^{+}{e}^{-}\to W^{+}{W}^{-}$ are below 1% at LEP 2 energies at all $W^{+}{W}^{-}$ production angles. A similar procedure is suggested to incorporate leading bosonic loop effects into four-fermion production in the fermion-loop scheme. The resulting accuracy below 1% is sufficient for LEP 2 experiments.

12 pages, LaTeX including 1 postscript figure, submitted to Phys. Lett. B