Towards a No-Lose Theorem for NMSSM Higgs Discovery at the LHC

We scan the parameter space of the NMSSM for the observability of a Higgs boson at the LHC with $300 {\rm fb}^{-1}$ integrated luminosity per detector, taking the present LEP constraints into account. We focus on the regions of parameter space for which none of the usually considered LHC detection modes are viable due to the fact that the only light non-singlet (and, therefore, potentially visible) Higgs boson, $h$, decays mainly to two CP-odd light Higgs bosons, $h\to a a$. We simulate the $WW\to h \to aa$ detection mode. We find that this signal may be detectable at the LHC as a signal/background $\sim 600/600$ bump in the tail of a rapidly falling mass distribution. If further study gives us confidence that the shape of the background tail is predictable, then we can conclude that NMSSM Higgs detection at the LHC will be possible throughout all of parameter space by combining this signal with the usual detection modes previously simulated by ATLAS and CMS. We also show that this $WW\to h\to aa$ signal will be highly visible at the LC due to its cleaner environment and high luminosity. We present a study of the production modes and decay channels of interest at the LC.