Many light Higgs bosons in the next-to-minimal supersymmetric model

The next-to-minimal supersymmetric model with a light doubletlike CP-odd Higgs boson and small tan beta can satisfy all experimental limits on Higgs bosons even with light superpartners. In these scenarios, the two lightest CP-even Higgs bosons, h(1) and h(2), and the charged Higgs boson, h(+), can all be light enough to be produced at CERN LEP and yet have decays that have not been looked for or are poorly constrained by existing collider experiments. The channel h(1) -> a(1)a(1) with a(1) -> tau(+)tau(-) or 2j is still awaiting LEP constraints for m(h1) > 86 or 82 GeV, respectively. LEP data may also contain e(+)e(-) -> h(2)a(1) events where h(2) -> Za(1) is the dominant decay, a channel that was never examined. Decays of the charged Higgs bosons are often dominated by H-+/- -> W-+/-(*())a(1) with a(1) -> gg, c (c) over bar, and tau(+)tau(-). This is a channel that has so far been ignored in the search for t -> h(+)b decays at the Tevatron. A specialized analysis might reveal a signal. The light a(1) might be within the reach of B factories via Gamma -> gamma a(1) decays. We study typical mass ranges and branching ratios of Higgs bosons in this scenario and compare these scenarios where the a(1) has a large doublet component to the more general scenarios with arbitrary singlet component for the a(1).