CP violating supersymmetric contributions to the electroweak $\rho$ parameter

Abstract

Effects of CP violation on the supersymmetric electroweak correction to the $\rho$ parameter are investigated. To avoid the EDM constraints, we require that arg$(\mu )<10^{-2}$ and the non-universal trilinear couplings $A_f=(0,0,A_0)$ and also assume that gluinos are heavier than 400 GeV. The CP phase ${\varphi }_t=$ arg($A_0$) leads to large enhancement of the relative mass splittings between ${\tilde{t}}_2$ and ${\tilde{b}}_L({\tilde{t}}_1)$, which in turn reduces the one-loop contribution of the stop and sbottom to $\Delta \rho$. For small $\tan \beta$, such a CP violating effect is prominent. We also study how much the two-loop gluon and gluino contributions are affected by the CP phase. Possible contributions to the $\rho$ parameter arising from the Higgs sector with CP violation are discussed.

Comments: 14 pages, Revtex, 4 eps figures, to appear in Phys. Rev. D (Rapid Comm.)