Very constrained minimal supersymmetric standard models

Abstract

We consider very constrained versions of the minimal supersymmetric extension of the standard model (VCMSSMs) which, in addition to constraining the scalar masses ${m}_{0}$ and gaugino masses ${m}_{1/2}$ to be universal at some input scale, impose relations between the trilinear and bilinear soft supersymmetry-breaking parameters ${A}_{0}$ and ${B}_{0}$. These relations may be linear, as in simple minimal supergravity models, or nonlinear, as in the Giudice-Masiero mechanism for generating the Higgs-mixing $\ensuremath{\mu}$ term. We discuss the application of the electroweak vacuum conditions in VCMSSMs, which may be used to make a prediction for $\mathrm{tan}\ensuremath{\beta}$ 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 $\mathrm{tan}\ensuremath{\beta}$ with no relation between ${A}_{0}$ and ${B}_{0}$ assumed a priori, displaying contours of ${B}_{0}$ for a fixed input value of ${A}_{0}$, incorporating the latest CDF/D0 measurement of ${m}_{t}$ and the latest BNL measurement of ${g}_{\ensuremath{\mu}}\ensuremath{-}2$. We emphasize that phenomenological studies of the CMSSM are frequently not applicable to specific VCMSSMs, notably those based on minimal supergravity, which require ${m}_{0}={m}_{3/2}$ as well as ${A}_{0}={B}_{0}+{m}_{0}$. We then display $({m}_{1/2},{m}_{0})$ 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.