One-loop sfermion corrections toe−e+→W−W+in the MSSM

We study one-loop effects of sfermions on helicity amplitudes for $e^{-}{e}^{+}\to W^{-}{W}^{+}$ in the minimal supersymmetric standard model. The one-loop contributions are calculated in the modified minimal subtraction scheme $\left(\overline{\mathrm{MS}}\right)$ renormalization scheme. In order to verify the validity of the analytic calculation and the numerical program, the following tests are performed. (i) The Becchi-Rouet-Stora sum rules hold exactly among the analytic expressions of the form factors of the $e^{-}{e}^{+}\to W^{-}{W}^{+}$ amplitude and those of the amplitudes where the external $W^{\pm }$ bosons are replaced by the corresponding Goldstone bosons ${\chi }^{\pm };$ hence, they hold within the expected accuracy of the numerical program. (ii) The one-loop sfermion contribution to the amplitudes decouple in the heavy mass limit. This property is used to test the overall normalization of the amplitudes. In order to observe the analytically exact decoupling, the amplitudes are expanded by the $\overline{\mathrm{MS}}$ couplings of the standard model. (iii) The high-energy analytic formulas of the helicity amplitudes, which are verified by using the equivalence theorem analytically, are used for the numerical test of the high-energy behavior of the amplitudes. We then investigate the magnitude of the one-loop effects on each helicity amplitude which may be measured by experiments at future linear colliders. Under the constraint from available precision data, the one-loop corrections to a few helicity amplitudes (for example, the longitudinal-W-pair production) can be at most from -0.8% to +0.6% in magnitude in the observables. The corrections in the helicity-summed cross sections are smaller, typically a few times ±0.1% at large scattering angles.