Radiative Corrections to $\gamma\gamma\to W^+ W^-$ in the Electroweak Standard Model

The cross-section for $\gamma\gamma\to W^+ W^-$ with arbitrary polarized photons and W bosons is calculated within the electroweak Standard Model including the complete virtual and soft-photonic ${\cal O}(\alpha)$ corrections. We present a detailed numerical discussion of the complete radiative corrections and an analytical investigation of the leading corrections. It turns out that in the on-shell renormalization scheme for fixed $M_W$ no leading corrections associated with the running of $\alpha$ or heavy top-quark and Higgs-boson masses occur. The corrections are typically of the order of 10\%. They reach, however, larger values where the lowest-order cross-sections are suppressed.