CERN LHC signatures of resonant $CP$ violation in a minimal supersymmetric Higgs sector

We present the general formalism for studying CP-violating phenomena in the production, mixing and decay of a coupled system of CP-violating neutral Higgs bosons at high-energy colliders. Considering the Minimal Supersymmetric Standard Model (MSSM) Higgs sector in which CP violation is radiatively induced by phases in the soft supersymmetry-breaking third-generation trilinear squark couplings and gaugino masses, we apply our formalism to neutral Higgs production via {\bar b}b, gg and W^+ W^- collisions at the LHC. We discuss CP asymmetries in the longitudinal and transverse polarizations of \tau^+ \tau^- pairs. The signatures of CP violation are more prominent in the production via gg and W^+ W^- than via {\bar b}b, and are resonantly enhanced when two (or all three) neutral Higgs bosons are nearly degenerate with mass differences comparable to their decay widths. Such scenarios occur naturally in the MSSM for values of \tan\beta >~ 5 (30) and large (small) charged Higgs-boson masses. We analyze representative examples with large mixing between the three neutral Higgs bosons weighing about 120 GeV, that may exhibit observable CP asymmetries even as large as 80%.