CP violation from dimensional reduction: a simple example

CP is a symmetry of pure gauge theories, that is without scalar interactions. Actually its violation originates in the Standard Model from the completely arbitrary Yukawa couplings. Thus, as the unification principle would wash out the arbitrariness of these couplings possibly relating them to the gauge interactions, the resulting theory should be expected as CP-invariant. According to this, a breaking mechanism of CP should then take place. We will explore here the possibility of CP breaking through the dimensional reduction process.