ON THE MINIMAL SUSY SO ( 10 ) MODEL FROM COSMOLOGY AND THE b → sγ DECAY

It is shown that the minimal supersymmetric SO(10) model with electroweak radiative breaking and universal soft mass terms at the GUT scale is strongly disfavoured by the combination of constraints from the b → sγ decay and the condition Ωh < 1 for the lightest (stable) neutralino. The constraints are, however, easily satisfied for certain class of supersymmetric SO(10) models with non–universal scalar masses which gives small supersymmetric corrections to the bottom quark mass and light higgsino–like neutralinos. CERN-TH.7515/94 December 1994 on leave from Institute for Theoretical Physics, Warsaw University, Warsaw, Poland In the minimal supersymmetric SO(10) (SUSY–SO(10)) models the Yukawa couplings of the tau lepton and of the bottom and top quarks unify at the scale of grand unification. The consequence of such an exact unification of couplings is that the top quark mass, mt and the ratio of the two vacuum expectation values present in the model, tan β, are determined, once the bottom quark mass, mb, the tau lepton mass, mτ , and the strong gauge coupling, αS, are fixed [1, 2, 3]. Large values of tanβ are naturally obtained in this case, leading to a proper bottom–top mass hierarchy [4]. In this context, an interesting question is the issue of the compatibility of this exact Yukawa coupling unification with the possibility of breaking the electroweak gauge symmetry through radiative effects. This question has been investigated in a number of papers in the minimal SUSY–SO(10) models with universal [5, 2] and non–universal [6, 7] soft supersymmetry breaking parameters at the GUT scale. Moreover, it has been recently observed that for these large values of tanβ, potentially large corrections to mb may be induced through the supersymmetry breaking sector of the theory [3, 2]. These corrections are decisive in obtaining acceptable predictions for mt, when the supersymmetric parameter space is constrained by the mechanism of radiative breaking. A systematic and complete determination of the GUT scale parameter space of the minimal SUSY–SO(10) models with universal soft breaking terms has been carried out in [2]. The approach used in this study is the bottom–up approach discussed in [8]. It was found that the requirement of radiative electroweak breaking implies strong correlations between the soft supersymmetry breaking parameters and, as a consequence, distinct features of the sparticle spectrum. In addition, the supersymmetry corrections to mb were found to be almost constant for fixed tanβ and to imply an upper bound on mt of the order of (160–170) GeV. A study of SUSY–SO(10) models with non-universal boundary values for the soft breaking terms, which uses the same bottom-up approach, was performed in [7]. This work is a supplement to the studies presented in [2, 7]. We investigate here the constraints due to the requirement that the relic abundance of the lightest neutralino, which is the lightest supersymmetric particle (LSP) in these models, does not overclose the Universe. Furthermore, we study the restrictions imposed by the recent observation of the inclusive decay b → sγ by the CLEO II Collaboration [9]. The measured branching ratio has the value: BR(b → sγ) = (2.32± 0.51± 0.29± 0.32) · 10, (1) where the errors are statistical, experimental systematics and theoretical systematics (due to the extrapolation from the observed part of the photon spectrum). This measurement implies a 95% c.l. upper and lower limits on this branching ratio of 3.4·10 and 1.2·10, respectively [10]. Both constraints turn out to be important for SUSY–SO(10) models, given the correlations present in their parameter spaces. We start our discussion with the SUSY–SO(10) model with universal soft breaking terms. In order to set the terms of our discussion, we give a brief summary of the main properties of the parameter space and of the spectra characteristic of this model. We list