Trilinear Gauge Boson Vertices in the MSSM

We study the $C$ and $P$ even $WW\gamma$ and $WWZ$ trilinear gauge boson vertices (TGV's), in the context of the MSSM as functions of the soft SUSY breaking parameters $A_0, m_0, M_{1/2}$ and the momentum $q$ carried by $\gamma, Z$, assuming the external $W$'s are on their mass shell. We follow a complete renormalization group analysis taking into account all constraints imposed by the radiative breaking of the electroweak symmetry. It is found that for energies ${\sqrt{s}} \equiv q^2 \le 200 \; GeV$ squark and slepton contributions to the aforementioned couplings are two orders of magnitude smaller than those of the Standard Model (SM). In the same energy range the bulk of the supersymmetric Higgs corrections to the TGV's is due to the lightest neutral Higgs, $h_0$, whose contribution is like that of a Standard Model Higgs of the same mass. The rest have negligible effect due to their heaviness. The contributions of the Neutralinos and Charginos are sensitive to the input value for the soft gaugino mass $M_{1/2}$ being more pronounced for values $M_{1/2} < 100 \; GeV$. In this case and in the unphysical region, $0 < \sqrt{s} < 2 M_W $ their contributions are substantially enhanced resulting to large corrections to the static quantities of the $W$ boson. However such an enhancement is not observed in the physical region and their corrections to the TGV's are rather small. In general for $2 M_W < \sqrt{s} < 200 \; GeV $ the MSSM predictions differ from those of the SM but they are of the same order of magnitude. Deviations from the SM predictions to be detectable require sensitivities reaching the per mille level and hence unlikely to be observed at LEP200. For higher energies SM and MSSM predictions exhibit a fast fall off behaviour, in accord with unitarity requirements, getting smaller by almost an