Supersymmetric Benchmarks with Non-Universal Scalar Masses or Gravitino Dark Matter

We 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 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 m_0 and neutralino dark matter. The NUHM and GDM models with larger m_0 may have large branching ratios for Higgs and/or $Z$ production in the cascade decays of heavier sparticles, whose detection we discuss. The phenomenology of the GDM models depends on the nature of the next-to-lightest supersymmetric particle (NLSP), which has a lifetime exceeding 10^4 seconds in the proposed benchmark scenarios. In one GDM scenario the NLSP is the lightest neutralino \chi, and the supersymmetric collider signatures are similar to those in previous CMSSM benchmarks, but with a distinctive spectrum. In the other GDM scenarios based on minimal supergravity (mSUGRA), the NLSP is the lighter stau slepton {\tilde \tau}_1, with a lifetime between ~ 10^4 and 3 X 10^6 seconds. Every supersymmetric cascade would end in a {\tilde \tau}_1, which would have a distinctive time-of-flight signature. Slow-moving {\tilde \tau}_1's might be trapped in a collider detector or outside it, and the preferred detection strategy would depend on the {\tilde \tau}_1 lifetime. We discuss the extent to which these mSUGRA GDM scenarios could be distinguished from gauge-mediated models.