Renormalization group study of the standard model and its extensions: The minimal supersymmetric standard model

In this paper we summarize the minimal supersymmetric standard model as well as the renormalization group equations of its parameters. We proceed to examine the feasibility of the model when the breaking of supersymmetry is parametrized by the soft terms suggested by supergravity theories. In such models, the electroweak symmetry is exact at the tree level and is broken spontaneously at one-loop order. We make the additional assumption that the GUT-inspired relation $m_b=m_{\tau }$ be valid at the scale where the gauge coupling constants unify, which constrains the value of the top quark mass. For all types of soft breaking terms expected in supergravity theories, we present the results of numerical runs which yield electroweak breaking at the required scale. These yield not only the allowed ranges for the soft supersymmetry breaking parameters, but also the value of the supersymmetric partners' masses. Taking $m_b=m_{\tau }$ at the unification scale, $m_b=4.9\mathrm{}$ GeV, and ${\alpha }_3\left(M_Z\right)=0.118\mathrm{}$, we find that for models in which global supersymmetry breaking arises solely from soft gaugino masses and bilinear mixing between the two Higgs scalars the top quark mass can be no lighter than ∼ 180 GeV.