The NMSSM Solution to the Fine-Tuning Problem, Precision Electroweak Constraints and the Largest 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 $100\text{gev}$, as beautifully consistent with precision electroweak data, while escaping LEP constraints due to the dominance of $h\to aa$ decays with $m_a<2m_b$ so that $a\to \text{tauptaum}$ or jets. The residual $\sim 10$ branching ratio for $h\to b\anti b$explainsperfectlythewell-knownLEPexcessat$\mh\sim 100\gev$. 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 $m_a>30\text{gev}$, and decays primarily to $\text{gam}\text{gam}$ leading to an $h\to aa\to 4\text{gam}$ Higgs signal.