Supersymmetric Contributions to Electroweak Precision Observables: QCD Corrections

We calculate the two-loop QCD correction to the scalar quark contributions to the electroweak gauge-boson self-energies at zero momentum transfer in the supersymmetric extension of the standard model (SM) and derive the associated $O\left({\alpha }_s\right)$ correction to the $\rho$ parameter. The two-loop corrections modify the one-loop contribution by up to 30%; the gluino decouples for large masses. Contrary to the SM case where the QCD corrections are negative and screen the one-loop value, the corresponding corrections in the supersymmetric case are in general positive, increasing the sensitivity in the search for scalar quarks through their virtual effects in high-precision electroweak observables.