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 m1/2 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 m0 and m1/2 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/D0 measurement of mt and the latest BNL measurement of gμ-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=m3/2 as well as A0=B0+m0. We then display (m1/2,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