${ϵ}_b$ Constraints on the Minimal $SU(5)$ and $SU(5)\times U(1)$ Supergravity Models

Abstract

We have performed a systematic analysis to compute the one-loop electroweak corrections to the Z->b b-bar vertex in terms of ${ϵ}_b$ and $R_b$ in the context of the minimal $SU(5)$ and no-scale $SU(5)\times U(1)$ supergravity models. With the measured top mass, $m_t=174\pm 10_{-12}^{+13}$ $\text{GeV}$ , recently announced by CDF, we use the latest LEP data on ${ϵ}_b$ and $R_b$ ($\equiv \Gamma (Z->bb-bar)/\Gamma (Z->hadrons)$) in order to constrain further the two models. We find that the present LEP data on ${ϵ}_b$ and $R_b$ constrain the two models rather severely. Especially, the low-$\tan \beta$ region is constrained more severely. $\tan \beta \text{lsim}2.5$ $(4.0)$ is excluded by ${ϵ}_b$ at $90\%$ C.~L. for $m_t\text{gsim}170$ $(180)$ $\text{GeV}$ in the minimal $SU(5)$ (no-scale $SU(5)\times U(1)$) supergravity. Even more stringent constraint comes from $R_b$. It excludes $\tan \beta \text{lsim}4.0$ at $90\%$ C.~L. for $m_t\text{gsim}160$ $(170)$ $\text{GeV}$ in the minimal $SU(5)$ (no-scale $SU(5)\times U(1)$) supergravity. We also find that the sign on $\mu$ in the two models can be determined from ${ϵ}_b$ and $R_b$ at $90\%$ C.~L.

Comments: RevTeX 3.0, 15 Pages+2 figures(not included but available as a uuencoded file from gtpark@phyb.snu.ac.kr), SNUTP-94-66