Higgs boson decays to $\mathrm{CP}$-odd scalars at the Fermilab Tevatron and beyond

In extended Higgs models, the Higgs boson may decay into a pair of light $\mathrm{CP}$-odd scalars, with distinctive collider signatures. We study the ensuing Higgs signals at the upgraded Fermilab Tevatron, considering the subsequent decays of the scalars into pairs of gluons or photons. For $\mathrm{CP}$-odd scalars lighter than a few GeV, the Higgs boson manifests itself as a diphoton resonance and can be discovered up to masses of a few hundred GeV. For heavier $\mathrm{CP}$-odd scalars the reach extends at most up to $M_h\sim 120\mathrm{GeV}.$ We also discuss the capabilities of the CERN LHC and lepton colliders in these channels.