Naturalness and Higgs decays in the MSSM with a singlet

The simplest extension of the supersymmetric standard model - the addition of one singlet superfield - can have a profound impact on the Higgs and its decays. We perform a general operator analysis of this scenario, focusing on the phenomenologically distinct scenarios that can arise, and not restricting the scope to the narrow framework of the NMSSM. We reexamine decays to four b quarks and four tau's, finding that they are still generally viable, but at the edge of LEP limits. We find a broad set of Higgs decay modes, some new, including those with four gluon final states, as well as more general six and eight parton final states. We find the phenomenology of these scenarios is dramatically impacted by operators typically ignored, specifically those arising from D-terms in the hidden sector, and those arising from weak-scale colored fields. In addition to sensitivity of mZ, there are potential tunings of other aspects of the spectrum. In spite of this, these models can be very natural, with light stops and a Higgs as light as 82GeV. These scenarios motivate further analyses of LEP data as well as studies of the detection capabilities of future colliders to the new decay channels presented.