New Precision Electroweak Tests of SU(5) x U(1) Supergravity

Abstract

We explore the one-loop electroweak radiative corrections in $SU(5)\times U(1)$ supergravity via explicit calculation of vacuum-polarization and vertex-correction contributions to the ${ϵ}_1$ and ${ϵ}_b$ parameters. Experimentally, these parameters are obtained from a global fit to the set of observables ${\Gamma }_l,{\Gamma }_b,A_{FB}^l$, and $M_W/M_Z$. We include $q^2$-dependent effects, which induce a large systematic negative shift on ${ϵ}_1$ for light chargino masses ($m_{{\chi }_1^{\pm }}\text{lsim}70\text{GeV}$). The (non-oblique) supersymmetric vertex corrections to $\text{Zbb}$, which define the ${ϵ}_b$ parameter, show a significant positive shift for light chargino masses, which for $\tan \beta \approx 2$ can be nearly compensated by a negative shift from the charged Higgs contribution. We conclude that at the 90\%CL, for $m_t\text{lsim}160\text{GeV}$ the present experimental values of ${ϵ}_1$ and ${ϵ}_b$ do not constrain in any way $SU(5)\times U(1)$ supergravity in both no-scale and dilaton scenarios. On the other hand, for $m_t\text{gsim}160\text{GeV}$ the constraints on the parameter space become increasingly stricter. We demonstrate this trend with a study of the $m_t=170\text{GeV}$ case, where only a small region of parameter space, with $\tan \beta \text{gsim}4$, remains allowed and corresponds to light chargino masses ($m_{{\chi }_1^{\pm }}\text{lsim}70\text{GeV}$). Thus $SU(5)\times U(1)$ supergravity combined with high-precision LEP data would suggest the presence of light charginos if the top quark is not detected at the Tevatron.

Comments: LaTeX, 11 Pages+4 Figures(not included), the figures available upon request as an uuencoded file(0.4MB) or 4 PS files from park@tac.harc.edu, CERN-TH.7078/93, CTP-TAMU-68/93, ACT-24/93