Abstract
Motivated by arguments in favour of spontaneous CP violation, we investigate the general conditions imposed by P and CP invariance on the Yukawa couplings in SU(2) L × SU(2) R × U(1) gauge theories. A complete discussion of these constraints is presented for two minimal Higgs sectors. In addition to the standard case of manifest CP invariance, we find two phenomenologically interesting models where the P and CP transformations are non-aligned in flavour and Higgs spaces. To a certain extent, P and CP invariance may be responsible for the existence of horizontal symmetries. An intimate connection between CP violation and the general flavour problem emerges.
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