Very constrained minimal supersymmetric standard models

We consider very constrained versions of the minimal supersymmetric extension of the standard model (VCMSSMs) which, in addition to constraining the scalar masses m₀ and gaugino masses m_1/2 to be universal at some input scale, impose relations between the trilinear and bilinear soft supersymmetry-breaking parameters A₀ and B₀. These relations may be linear, as in simple minimal supergravity models, or nonlinear, as in the Giudice-Masiero mechanism for generating the Higgs-mixing μ term. We discuss the application of the electroweak vacuum conditions in VCMSSMs, which may be used to make a prediction for tanβ as a function of m ₀ and m_1/2 that is usually unique. We baseline the discussion of the parameter spaces allowed in VCMSSMs by updating the parameter space allowed in the CMSSM for fixed values of tanβ with no relation between A₀ and B₀ assumed a priori, displaying contours of B₀ for a fixed input value of A₀, incorporating the latest CDF/DO measurement of m_t and the latest BNL measurement of g_μ - 2. We emphasize that phenomenological studies of the CMSSM are frequently not applicable to specific VCMSSMs, notably those based on minimal supergravity, which require m₀ = m_3/2 as well as A₀ = B₀ + m₀. We then display (m_1/2, m₀) planes for selected VCMSSMs, treating in a unified way the parameter regions where either a neutralino or the gravitino is the lightest supersymmetric particle. In particular, we examine in detail the allowed parameter space for the Giudice-Masiero model.