In the NMSSM it is well possible to find an additional Higgs boson with a mass below 125 GeV which remains invisible in standard Higgs boson search channels. We study the Higgs pair production cross sections times branching fractions in this scenario, focussing on gluon fusion and the bb̄ + τ + τ − and bb̄ + γγ final states. Summing over the SM-like and the lighter Higgs states, the production cross sections times branching fractions are never below the ones for SM Higgs pair production. Sizeable enhancements of the signal rates are also possible, notably if a lighter Higgs state is produced. However, the rates involving at least one lighter Higgs boson are not always sufficiently large to guarantee its discovery.
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Ulrich Ellwanger (2013) studied this question.
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