Diffraction as a CP and Lineshape Analyzer for MSSM Higgs Bosons at the LHC

We study the production and decay of a coupled system of mixed neutral MSSM Higgs bosons in exclusive double-diffractive processes at the LHC, including non-vanishing 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 three-way mixing scenario which we also term tri-mixing. A resolution in the Higgs mass of \sim 1 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.