Next-to-minimal supersymmetric model solution to the fine-tuning problem, precision electroweak constraints, and the largest CERN LEP Higgs event excess

We present an extended study of how the next-to-minimal supersymmetric model easily avoids fine-tuning in electroweak symmetry breaking for a SM-like light Higgs with mass in the vicinity of 100 GeV, as beautifully consistent with precision electroweak data, while escaping LEP constraints due to the dominance of h -> aa decays with m(a)< 2m(b) so that a ->tau(+)tau(-) or jets. The residual similar to 10% branching ratio for h -> bb explains perfectly the well-known LEP excess at m(h)similar to 100 GeV. Details of model parameter correlations and requirements are discussed as a function tan beta. Comparisons of fine-tuning in the NMSSM to that in the MSSM are presented. We also discuss fine-tuning associated with scenarios in which the a is essentially pure singlet, has mass m(a)> 30 GeV, and decays primarily to gamma gamma leading to an h -> aa -> 4 gamma Higgs signal.