Supersymmetric contribution to the electroweakρparameter

Contributions to the electroweak $\rho$ parameter, the ratio of the neutral- and charged-current strengths at zero-momentum transfer, are studied in the minimal extension of the standard model (SM) with softly broken sypersymmetry. The effects of the extended Higgs sector, the gaugino-Higgsino sector, the light-squark-slepton sector and that of the stop-sbottom sector are studied separately, and the role of the custodial ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_V$ symmetry in each sector is clarified. The stop-sbottom sector is found to give potentially a most significant contribution to $\delta \rho$ which can double the standard-model contribution from the top-bottom sector, whereas all the remaining sectors contribute to $\delta \rho$ at the level of at most a few × ${10}^{-3\mathrm{}}$. In the supergravity model with radiative electroweak gauge symmetry breaking there are no extra sources of the ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_V$ breaking at the grand unification scale other than those present already in the SM, and the resulting $\delta \rho$ is found to be significantly smaller than in the general case. Constraints on the allowed range of $\delta \rho$ in the supergravity models are given by taking account of existing and prospective experimental mass limits of additional particles at CERN LEP and $\mathrm{S}p\overline{p}\mathrm{S}$ and Fermilab Tevatron.