The presence of a new singlet scalar particle a can open up new decay channels for the Higgs boson, through cascades of the form h→2a→X, possibly making discovery through standard model channels impossible. If a is $CP$ odd, its decays are particularly sensitive to new physics. Quantum effects from heavy fields can naturally make h→4g the dominant decay which is difficult to observe at hadron colliders, and is allowed by CERN LEP for mₕ>82 GeV. However, there are usually associated decays, either h→2g2γ or h→4γ, which are more promising. The decay h→4γ is a clean channel that can discover both a and h. At the CERN LHC with 300 fb^-1 of luminosity, a branching ratio of order 10^-4 is sufficient for discovery for a large range of Higgs boson masses. With total luminosity of ~8 fb^-1, discovery at the Fermilab Tevatron requires more than 5×10^-3 in branching ratio.
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Chang et al. (2007) studied this question.
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