We study the production and decay of a coupled system of mixed neutral minimal supersymmetric extension of the Standard Model (MSSM) Higgs bosons in exclusive double-diffractive processes at the LHC, including nonvanishing $CP$ phases in the soft supersymmetry-breaking gaugino masses and third-generation trilinear squark couplings. The three neutral Higgs bosons are naturally nearly degenerate, for large values of $\tan \beta$, when the charged Higgs boson weighs around 150 GeV. Large mixing between all three neutral Higgs bosons is possible when $CP$ is violated, a threeway mixing scenario which we also term trimixing. A resolution in the Higgs mass of $\sim 1\mathrm{GeV}$, which may be achievable using the missing-mass method, would allow one to distinguish nearly degenerate Higgs bosons by studying the production lineshape. Measurements of the polarizations of the tau leptons coming from the Higgs-boson decays could offer a direct and observable signal of $CP$ violation in the Higgs sector.

• Received 7 March 2005

DOI:https://doi.org/10.1103/PhysRevD.71.075007