Automatic Calculation of Complete $O(\alpha )$ Corrections to $e^{+}{e}^{-}\to W^{+}\mu {\bar{\nu }}_{\mu }$

Using the automatic system GRACE-LOOP, the full $O(\alpha )$ electroweak corrections has been calculated for the process $e^+e^- \to W^+\mu \bar{\nu}_{\mu}$. The total correction to the cross section is found to be typically -6.4% at $\sqrt{s}=190$ GeV with ${10}^{\circ }$ cut on the muon angle from the beam, including the correction from the hard photon emission. It is observed that the correction is rather sensitive to the physical parameters. With the same conditions the correction corresponding to the real W-boson pair is -4.1% and hence the deviation is not negligible.