Observing a light $\mathrm{CP}$-violating Higgs boson in diffraction

Light $\mathrm{CP}$-violating Higgs bosons with a mass lower than 70 GeV might have escaped detection in direct searches at the CERN LEP collider. They may remain undetected in conventional search channels at the Fermilab Tevatron and CERN LHC. In this paper we show that exclusive diffractive reactions may be able to probe for the existence of these otherwise elusive Higgs particles. As a prototype example, we calculate diffractive production cross sections of the lightest Higgs boson within the framework of the minimal supersymmetric standard model with explicit $\mathrm{CP}$ violation. Our analysis shows that the challenging regions of parameter space corresponding to a light $\mathrm{CP}$-violating Higgs boson might be accessible at the LHC provided suitable proton tagging detectors are installed.