Degeneracy on a two-Higgs CP non-invariant Higgs sector

Many models with extended Higgs sectors have states where masses are quasidegenerate at tree-level. Higher order corrections may separate this masses, but they may also bring them closer, opening the possibility of total or near degeneracy of the physical masses. If, in addition, the Higgs sector does not conserve CP symmetry, then the neutral Higgs physical states are no longer defined with a CP charge, they would be a mixture of CP defined states given at tree level. Near degeneracy in the heavy neutral Higgs system with CP violation could imply mixing of coherent overlapping states, which at exact degeneracy will show up as a double pole in the propagator matrix of the neutral Higgs sector. This possibility has consequences on the phenomenology and in the type of expected experimental signatures for the nearly and exact Higgs degeneracy, for example, the lineshape will be different than expected for the fermion scattering amplitude via Higgs, . (paper)