$R_b$ in supersymmetric models

Abstract

We compute the supersymmetric contribution to $R_b\equiv \Gamma (Z\to b\bar{b})/\Gamma (Z\to \mathrm{hadrons})$ in a variety of supersymmetric models. In the context of supergravity models with universal soft-supersymmetry-breaking and radiative electroweak breaking we find $R^{\rm susy}_b\lsim0.0004$, which does not shift significantly the Standard Model prediction ($R_b^{\mathrm{SM}}=0.2157$ for $m_t=175\GeV$; $R_b^{\exp }=0.2204\pm 0.0020$). We also compute $R_b$ in the minimal supersymmetric standard model (MSSM), and delineate the region of parameter space which yields interestingly large values of $R_b$. This region entails light charginos and top-squarks, but is {\em strongly} restricted by the {\em combined} constraints from $B(b\to s\gamma )$ and a not-too-large invisible top-quark branching ratio: only a few percent of the points with $R_b^{\mathrm{susy}}>0.0020(1\sigma )$ are allowed.

20 pages (LaTeX), 10 figures (included)

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