We calculate the one-loop electroweak corrections to $e^{+}{e}^{-}\to W^{+}{W}^{-}Z$ and $e^{+}{e}^{-}\to ZZZ$ and analyze their impacts on both the total cross section and some key distributions. These processes are important for the measurements of the quartic couplings of the massive gauge bosons which can be a window on the mechanism of spontaneous symmetry breaking. We find that even after subtracting the leading QED corrections, the electroweak corrections can still be large, especially as the energy increases. We compare and implement different methods of dealing with potential instabilities in the routines pertaining to the loop integrals. For the real corrections we apply a dipole subtraction formalism and compare it to a phase-space slicing method.

• Received 8 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.073007