CP and Discrete Flavour Symmetries

Abstract

We give a consistent definition of generalised CP transformations in the context of discrete flavour symmetries. Non-trivial consistency conditions imply that every generalised CP transformation can be interpreted as a representation of an automorphism of the discrete group. This allows us to give consistent generalised CP transformations of popular flavour groups. We are able to clear up issues concerning recent claims about geometrical CP violation in models based on T', clarify the origin of 'calculable phases' in Delta(27) and explain why apparently CP violating scalar potentials of A4 result in a CP conserving ground state.

31 pages; v2: references added, discussion of T' models extended and clarified; v3: discussion of generalised CP as well as examples Z3 and A4 extended, version published in JHEP; v4: typos corrected, clarifying footnote added

References in corpus (9)

• Observation of electron-antineutrino disappearance at Daya Bay
• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• The Flavor Group Delta(3n^2)
• Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
• The Flavor Group Delta(6n^2)
• A common origin of fermion mixing and geometrical CP violation, and its test through Higgs physics at the LHC
• Geometric minimization of highly symmetric potentials
• Three-Higgs-doublet model with $A_4$ symmetry

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