Supersymmetric Models With Tanβ Close to Unity

Within the framework of supersymmetric grand unification, estimates of the b quark mass based on the asymptotic relation mb ≃ mτ single out the region with tanβ close to unity, particularly if mt(mt) < ∼ 170 GeV . We explore the radiative breaking of the electroweak symmetry and the associated sparticle and higgs spectroscopy in models with 1 < tanβ < ∼ 1.6. The lightest scalar higgs is expected to have a mass below 100 GeV , while the remaining four higgs masses exceed 300 GeV . The lower bounds on some of the sparticle masses are within the range of LEP 200. 7 (1) Institut de Physique Théorique, Université de Lausanne, CH 1015, Lausanne, Switzerland (2) Bartol Research Institute, University of Delaware, Newark, DE 19716, USA Recent improvements in the determination of the three standard model gauge couplings has renewed interest in the exciting possibility that they do indeed converge to the same value at some superheavy scale ∼ 10 GeV [1]. Within the framework of standard grand unification (GUT), compatibility with the available data requires an intermediate mass scale, on the order of 10 GeV in some schemes. Perhaps a somewhat more elegant possibility is provided by supersymmetric grand unification (SUSY GUT), with SUSY broken at a scale MS ∼ 100 GeV to a few TeV. Among other things, this latter approach offers the prospects of resolving the formidable gauge hierarchy problem[2]. One could also hope that SUSY GUTs can shed light on at least some of the many parameters appearing in the minimal supersymmetric SU(3) × SU(2) × U(1) model (MSSM). A particularly important example is offered by the well known asymptotic relation mb ≈ m 0 τ [3]. It has become clear in recent years[4] that the determination of the b-quark mass from this relation depends in a rather interesting way on mt(mt), αS(MZ) and tan β. In particular, and we verify this in the first part of the paper, for αS(MZ) near 0.12 and mt(mt) < ∼ 170 GeV , the two regions, tan β close to unity (1 < ∼ tanβ < ∼ 1.6), and tanβ ≫ 1 are singled out. The large tanβ case can arise naturally in minimal SO(10) type GUTs[5] and has been the subject of several investigations[6]. However, weak-scale radiative corrections to the b mass through gluino exchange[7] can be quite substantial in this case. With tanβ near unity and a top mass in the range of 150 170 GeV (favored by precision electroweak measurements), the top–quark Yukawa coupling ht is near the infrared quasi–fixed point ht(mt) ≃ 1.1 [8]. This may be an appealing feature in that a wide range of initial values ht(MX) near the GUT scale will be mapped to essentially the same value of ht(mt) thereby making it insensitive to the initial conditions. Furthermore, with tanβ close to unity, the weak-scale radiative corrections to the b mass can be quite small (< ∼ 1− 2%). Some investigations have recently appeared in which tanβ close to unity has been considered, although not exclusively so [9]. In this paper we primarily focus on this possibility and, where appropriate, offer comparisons with the large tanβ case. It turns