  In two-Higgs doublet models (and particularly in the MSSM) the CP-even (H)
and CP-odd (A) neutral scalars are nearly degenerate in mass, and their
s-channel production would lead to nearly overlapping resonances. CP-violating
effects may connect these two Higgs bosons, giving origin to one-loop particle
mixing, which, due to their mass proximity, can be resonantly enhanced,
altering their lineshape significantly. We show that, in general, the effect of
such a CP-violating mixing cannot be mimicked by (or be re-absorbed into) a
simple redefinition of the H and A masses in the context of a CP-conserving
model. Specifically, the effects of the CP-mixing are such that, either the
mass-splitting of the H and A bosons lies outside the range allowed by the
theory in the absence of CP-mixing, and/or the detailed energy dependence of
the produced lineshape is clearly different from the one obtained by redefining
the masses, but not allowing any mixing.
