We study the central diffractive production of the (three neutral) Higgs bosons, with a rapidity gap on either side, in an MSSM scenario with CP-violation. We consider the \documentclass[12pt]{minimal}
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\begin{document}$b\bar{b}$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$\tau\bar{\tau}$\end{document} decay for the light H1 boson and the four b-jet final state for the heavy H2 and H3 bosons, and discuss the corresponding backgrounds. A direct indication of the existence of CP-violation can come from the observation of either an azimuthal asymmetry in the angular distribution of the tagged forward protons (for the exclusive \documentclass[12pt]{minimal}
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\begin{document}$pp\to p + H + p$\end{document} process) or of a \documentclass[12pt]{minimal}
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\begin{document}$\sin 2\varphi$\end{document} contribution in the azimuthal correlation between the transverse energy flows in the proton fragmentation regions for the process with the diffractive dissociation of both incoming protons (\documentclass[12pt]{minimal}
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\begin{document}$pp\to X + H + Y$\end{document}). We emphasise the advantage of reactions with the rapidity gaps (that is, production by pomeron-pomeron fusion) to probe CP-parity and to determine the quantum numbers of the produced central object.
