Basis-invariant conditions for CP symmetry of order 4

Abstract

Three-Higgs-doublet models (3HDM) allow for a novel, physically distinct form of CP invariance: CP symmetry of order 4 (CP4). Due to the large basis change freedom in 3HDM, it is imperative to recognize the presence of a possibly hidden CP4 in a basis-invariant way. In the present work, we solve this problem and establish basis-invariant necessary and sufficient conditions for a 3HDM to possess a CP4 symmetry. We also derive a basis-invariant criterion to decide whether or not a CP4 symmetric 3HDM possesses any additional CP symmetry, as well as a criterion to decide whether or not CP4 is spontaneously broken.

arXiv comment32 pages

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Cited by in corpus (13)

• Systematic construction of basis invariants in the 2HDM
• Recognizing symmetries in 3HDM in basis-independent way
• Exploring multi-Higgs models with softly broken large discrete symmetry groups
• Solving the strong CP problem with non-conventional CP
• Beyond basis invariants
• Complex $S_3$-symmetric 3HDM
• Softly-broken $A_4$ or $S_4$ 3HDMs with stable states
• Global Symmetries and Effective Potential of 2HDM in Orbit Space
• Systematic analysis of 3HDM symmetries
• Computable conditions for order-2 $CP$ symmetry in NHDM potentials
• Discriminating between $CP$ and family transformations in the bilinear space of NHDM
• Representation-theoretical characterization of canonical custodial symmetry in NHDM potentials
• The Hilbert Series and the Flavor Invariants of the 3HDM