One-loop contributions of charginos and neutralinos to W-pair production   in E+ E- collisions
  We study the one-loop effects of charginos and neutralinos on the helicity amplitudes for $\eeww$ in the minimal supersymmetric standard model. The calculation is tested by using two methods. First, the sum rule for the form factors between $\eeww$ and the process where the external $W^\pm$ bosons are replaced by the corresponding Goldstone bosons $\omega^\pm$ is employed to test the analytic expression and the accuracy of the numerical program. Second, the decoupling property in the large mass limit is used to test the overall normalization of the amplitudes. These two tests are most effectively carried out when the amplitudes are expanded in terms of the modified minimal subtraction ($\bar{\rm MS}$) couplings of the standard model. The resulting perturbation expansion is valid at collider energies below and around the threshold of the light supersymmetric particles. We find that the corrections to the cross section of the longitudinally polarized $W$-pair production can be as large as -1.4% at the threshold of the light chargino-pair production for large scattering angles. We also study the effects of the CP-violating phase in the chargino and neutralino sectors on the helicity amplitudes. We find that the resulting CP-violating asymmetries can be at most 0.1%. 
Kaoru Hagiwara, Shinya Kanemura, Michael Klasen and Yoshiaki Umeda