Supersymmetric contributions to electroweak precision observables: QCD corrections

Abstract

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. We then derive the $O(α_s)$ correction to the contribution of the scalar top and bottom quark loops to the rho parameter, which is the most sizable supersymmetric contribution to the electroweak mixing angle and the W-boson mass. 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.

Figures (5)

• Figure 1: Feynman diagrams for the contribution of scalar quark loops to the gauge boson self--energies at one--loop.
• Figure 2: One--loop contribution of the $(\tilde{t}, \tilde{b})$ doublet to $\Delta \rho$ as a function of the common mass $m_{\tilde{q}}$, for $\theta_{\tilde{t}} =0$ and $\theta_{\tilde{t}} \sim-\pi/4$ [with $\tan \beta=1.6$ and $m_{\rm LR}=0$ and 200 GeV, respectively, where $m_{\rm LR}$ is the off--diagonal term in the $\tilde{t}$ mass matrix].
• Figure 3: Typical Feynman diagrams for the contribution of scalar quarks and gluinos to the $W/Z$--boson self--energies at the two--loop level.
• Figure 4: Gluon exchange contribution to the $\rho$ parameter at two--loop as a function of $m_{\tilde{q}}$ for the scenarios of Fig. 2.
• Figure 5: Contribution of the gluino exchange diagrams to $\Delta \rho_1^ {\rm SUSY}$ for two values of $m_{\tilde{g}}$ in the scenarios of Fig. 2.