Speaker
Description
Summary
First, i will give a very brief review showing how CP symmetries have to act in order to warrant physical CP conservation in the flavor sector. It is clear that true, physcial CP transformations have to guarantee that CP violating invariants, most prominently the Jarlskog invariant, vanish. Therefore, i will argue that CP transformations, in general, have to map all present representations of a symmetry to their corresponding complex conjugate representations. As a consequence of that, physical CP transformations are special outer automorphisms of all present symmetry groups. This is in particular true and important for discrete flavor symmetries. In this context, i will explain that having generalized CP symmetries is not some additional exotic feature, but that in fact all CP symmetries are generalized CP symmetries. In particular, the notion of a canonical CP transformation is basis dependent. Having this established, one can ask whether all groups can co-exist in consistency with CP symmetries. I will show that for a large class of discrete symmetry groups this is not the case and discuss new mathematical tools to decide whether or not a given group is of this kind. We will see that this is tightly related to whether or not groups allow for bases with real Clebsch-Gordan coefficients. If a group cannot consistently co-exist with CP symmetries, that is if it does not allow for the corresponding outer automorphisms, the presence of the group itself signals physical CP violation in a generic setup. Since the group fixes all relevant couplings, the magnitude of CP violation can be predicted from group theory. I will base this discussion on an explicit toy model example.