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Generalized CP Invariance and the Yukawa sector of Two-Higgs Models

We analyze generalized CP symmetries of two-Higgs doublet models, extending them from the scalar to the fermion sector of the theory. We show that, with a single exception, those symmetries imply massless fermions. The single model which accommodates a fermionic mass spectrum compatible with experimental data possesses a remarkable feature. It displays a new type of spontaneous CP violation, which occurs not in the scalar sector responsible for the symmetry breaking mechanism but, rather, in the fermion sector.