The NMSSM Close to the R-symmetry Limit and Naturalness in h→aah \to aa Decays for m_a<2\mb

Dominant decay of a SM-like Higgs boson into particles beyond those contained in the minimal supersymmetric standard model has been identified as a natural scenario to avoid fine tuning in electroweak symmetry breaking while satisfying all LEP limits. In the simplest such extension, the next-to-minimal supersymmetric model, the lightest CP-even Higgs boson can decay into two pseudoscalars. In the scenario with least fine tuning the lightest CP-even Higgs boson has mass of order 100 GeV. In order to escape LEP limits it must decay to a pair of the lightest CP-odd Higgs bosons with Br(h -> aa)>.7 and m_a \tau^+ \tau^- or light quarks and gluons). The mass of the lightest CP-odd Higgs boson is controlled by the soft-trilinear couplings, A_\lambda(m_Z) and A_\kappa(m_Z). We identify the region of parameter space where this situation occurs and discuss how natural this scenario is. It turns out that in order to achieve m_a < 2 m_b with A_\lambda(m_Z), A_\kappa(m_Z) of order the typical radiative corrections, the required tuning of trilinear couplings need not be larger than 5-10 %. Further, the necessity for this tuning can be eliminated in specific SUSY breaking scenarios. Quite interestingly, Br(h -> aa) is typically above 70 % in this region of parameter space and thus an appropriately large value requires no additional tuning.Comment: 33 pages, 25 figure

Physics at a Muon Collider

I discuss the exciting prospects for exploring a wide range of new physics at a low-energy muon collider.Comment: 21 pages, full postscript file is also available via anonymous ftp at ftp://ucdhep.ucdavis.edu/gunion/fnalmumuplenary.p

Do precision electroweak constraints guarantee \epem collider discovery of at least one Higgs boson of a type-II two-Higgs-doublet model?

The manner in which the parameters of a two-Higgs-doublet model can be chosen so that no Higgs boson is discovered at a \sqrt{s}\leq 800\gev \epem collider, while maintaining consistency with current precision electroweak measurements, is described. The importance of a Giga-$Z$ factory and higher collider energies for such a scenario is emphasized.Comment: 6 pages, 3 figure