A Simple Born-Form Approximation for $e^{+} e^{-}\rightarrow W^{+}W^{-}$ at One Loop

A simple Born-form approximation at the one-loop level for e^+e^- to W^+ W^- at high energies is given in analytic form. The different contributions to the three invariant one-loop amplitudes, S_I^{(-)}(s,t) and S_Q^{(\pm)}(s,t), determining the Born-form helicity amplitudes are thoroughly investigated analytically and numerically. At energies above 500 GeV, the accuracy of the simple Born-form approximation for the differential production cross section is better than 1% for almost all W^+W^- production angles, independently of whether the W^+W^- polarization is summed over, or whether a longitudinal or a transverse polarization is selected for both the W^+ and the W^-.