CP-odd invariants for multi-Higgs models and applications with discrete symmetry

Abstract

CP-odd invariants are useful for studying the CP properties of Lagrangians in any basis. We explain how to build basis invariants for the scalar sector, and how to distinguish CP-odd invariants from CP-even invariants. Up to a certain order, we use these methods to systematically build all the CP-odd invariants. The CP-odd invariants signal either explicit or spontaneous violation of CP. Making use of the CP-odd invariants, we determine the CP properties of potentials with 3 and with 6 Higgs fields arranged as triplets of specific discrete symmetries in the $\Delta (3n^2)$ or $\Delta (6n^2)$ series (inlcuding $A_4$, $S_4$, $\Delta (27)$ and $\Delta (54)$ as well as the cases for $n>3$).

9 pages. Contribution to the proceedings of DISCRETE 2016, Warsaw

References in corpus (14)

• Towards a complete $A_4\times SU(5)$ SUSY GUT
• Symmetry breaking patterns in 3HDM
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
• Lepton Mixing Predictions including Majorana Phases from $\Delta (6n^2)$ Flavour Symmetry and Generalised CP
• Lepton Mixing Parameters from $\Delta (48)$ Family Symmetry and Generalised CP
• Dark Matter with Two Inert Doublets plus One Higgs Doublet
• Properties of the general NHDM. II. Higgs potential and its symmetries
• Lepton Mixing Predictions from Infinite Group Series $D_{9n,3n}^{(1)}$ with Generalized CP
• Spontaneous symmetry breaking in the $S_3$-symmetric scalar sector
• Symmetries of symmetries and geometrical CP violation
• Geometrical CP violation in the N-Higgs-doublet model
• Compatible abelian symmetries in N-Higgs-Doublet Models
• Neutrino Mixing from $\Delta (6n^2)$ Groups

Cited by in corpus (1)

• The Hilbert Series and the Flavor Invariants of the 3HDM