Consistency of LEP $Z+b$-jets excess with an {\boldmath $h\to aa$} Decay Scenario and Low-Fine-Tuning NMSSM Models

We examine the LEP limits for the $Zh\to Z+b$'s final state and find that the excess of observed events for $\mh\sim 100\gev$ correlates well with there being an $\mh\sim 100\gev$ Higgs boson with SM-like $ZZh$ coupling that decays partly via $h\to b\anti b+\tauptaum$ [with $\br(h\to b\anti b)\sim 0.08$] but dominantly via $h\to aa$ [with $\br(h\to aa)\sim 0.9$], where $\ma<2\mb$ so that $a\to \tauptaum$ (or light quarks and gluons) decays are dominant. Scenarios of precisely this type arise in the Next-to-Minimal Supersymmetric Model for parameter choices yielding the lowest possible fine-tuning.