On the Feasibility of a Stop NLSP in Gravitino Dark Matter Scenarios

We analyze the possibility that the lighter stop {\tilde t_1} could be the next-to-lightest supersymmetric particle (NLSP) in models where the gravitino is the lightest supersymmetric particle (LSP). We do not find any possibility for a stop NLSP in the constrained MSSM with universal input soft supersymmetry-breaking masses at the GUT scale (CMSSM), but do find small allowed regions in models with non-universal Higgs masses (NUHM). We discuss the cosmological evolution of stop hadrons. Most {\tilde t_1}qq `sbaryons' and the corresponding `antisbaryons' annihilate with conventional antibaryons and baryons into {\tilde t_1}{\bar q} `mesinos' and the corresponding `antimesinos', respectively, shortly after the quark-hadron transition in the early Universe, and most mesinos and antimesinos subsequently annihilate. As a result, insufficient metastable charged stop hadrons survive to alter Big Bang nucleosynthesis.