Title:Difficult Scenarios for NMSSM Higgs Discovery at the LHC

Abstract: We identify scenarios not ruled out by LEP data in which NMSSM Higgs detection at the LHC will be particularly challenging. We first review the `no-lose' theorem for Higgs discovery at the LHC that applies if Higgs bosons do not decay to other Higgs bosons - namely, with L=300 fb^-1, there is always one or more `standard' Higgs detection channel with at least a 5 sigma signal. However, we provide examples of no-Higgs-to-Higgs cases for which all the standard signals are no larger than 7 sigma implying that if the available L is smaller or the simulations performed by ATLAS and CMS turn out to be overly optimistic, all standard Higgs signals could fall below 5 sigma even in the no-Higgs-to-Higgs part of NMSSM parameter space. In the vast bulk of NMSSM parameter space, there will be Higgs-to-Higgs decays. We show that when such decays are present it is possible for all the standard detection channels to have very small significance. In most such cases, the only strongly produced Higgs boson is one with fairly SM-like couplings that decays to two lighter Higgs bosons (either a pair of the lightest CP-even Higgs bosons, or, in the largest part of parameter space, a pair of the lightest CP-odd Higgs bosons). A number of representative bench-mark scenarios of this type are delineated in detail and implications for Higgs discovery at various colliders are discussed.