Supersymmetric benchmarks with non-universal scalar masses or gravitino dark matter

We motivate, propose and examine a new set of benchmark supersymmetric scenarios, some of which have non-universal Higgs scalar masses (NUHM) and others have gravitino dark matter (GDM). The scalar masses in these proposed models are either considerably larger or smaller than the narrow range allowed for the same gaugino mass m_1/2 in the constrained MSSM (CMSSM) with universal scalar masses m₀ and neutralino dark matter. Unlike the CMSSM, the proposed NUHM and GDM models with larger m₀ may have large branching ratios for Higgs and/or Z production in the cascade decays of heavier sparticles, whose detection we discuss. The novel phenomenology of the GDM models depends on the nature of the next-to-lightest supersymmetric particle (NLSP), which has a lifetime exceeding 10⁴ s in the proposed benchmark scenarios. In one GDM scenario the NLSP is the lightest neutralino χ, and the supersymmetric collider signatures are similar to those in previous CMSSM benchmarks, but with a distinctive spectrum that would be challenging for the LHC and ILC. In the other GDM scenarios based on minimal supergravity (mSUGRA), the NLSP is the lighter stau slepton Τ₁, with a lifetime between ∼ 10⁴ and 3 × 10⁶ s. Every supersymmetric cascade would end in a Τ₁, which would have a distinctive time-of-flight signature. Slow-moving Τ₁ 's might be trapped in a collider detector or outside it, and the preferred detection strategy would depend on the Τ₁ lifetime. We discuss the extent to which these mSUGRA GDM scenarios could be distinguished from gauge-mediated models.