The top-quark mass in SU(5)xU(1) supergravity

Abstract

We show that the currently experimentally preferred values of the top-quark mass (\ie, $130\lsim m_t\lsim180\GeV$) are naturally understood in the context of string models, where the top-quark Yukawa coupling at the string scale is generically given by $λ_t={\cal O}(g)$, with $g$ the unified gauge coupling. A detailed study of the Yukawa sector of $SU(5)\times U(1)$ supergravity shows that the ratio of the bottom-quark to tau-lepton Yukawa couplings at the string scale is required to be in the range $0.7\lsimλ_b/λ_τ\lsim1$, depending on the values of $m_t$ and $m_b$. This result is consistent with $SU(5)\times U(1)$ symmetry, which does {\em not} require the equality of these Yukawa couplings in the unbroken symmetry phase of the theory. As a means of possibly predicting the value of $m_t$, we propose a procedure whereby the size of the allowed parameter space is determined as a function of $m_t$, since all sparticle and Higgs-boson masses and couplings depend non-trivially on $m_t$. At present, no significant preference for particular values of $m_t$ in $SU(5)\times U(1)$ supergravity is observed, except that high-precision LEP data requires $m_t\lsim180\GeV$.