CP4 miracle: shaping Yukawa sector with CP symmetry of order four

Abstract

We explore the phenomenology of a unique three-Higgs-doublet model based on the single CP symmetry of order 4 (CP4) without any accidental symmetries. The CP4 symmetry is imposed on the scalar potential and Yukawa interactions, strongly shaping both sectors of the model and leading to a very characteristic phenomenology. The scalar sector is analyzed in detail, and in the Yukawa sector we list all possible CP4-symmetric structures which do not run into immediate conflict with experiment, namely, do not lead to massless or mass-degenerate quarks nor to insufficient mixing or CP-violation in the CKM matrix. We show that the parameter space of the model, although very constrained by CP4, is large enough to comply with the electroweak precision data and the LHC results for the 125 GeV Higgs boson phenomenology, as well as to perfectly reproduce all fermion masses, mixing, and CP violation. Despite the presence of flavor changing neutral currents mediated by heavy Higgs scalars, we find through a parameter space scan many points which accurately reproduce the kaon CP-violating parameter ${\epsilon }_K$ as well as oscillation parameters in K and $B_{(s)}$ mesons. Thus, CP4 offers a novel minimalistic framework for building models with very few assumptions, sufficient predictive power, and rich phenomenology yet to be explored.

arXiv comment39 pages, 8 figures, 1 table; v2: expanded discussion, extra references, matches published version

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• Symmetries and Mass Degeneracies in the Scalar Sector
• Universal Inverse seesaw mechanism as a source of the SM fermion mass hierarchy
• Basis-invariant conditions for CP symmetry of order 4
• A renormalizable left-right symmetric model with low scale seesaw mechanisms
• Exploring multi-Higgs models with softly broken large discrete symmetry groups
• Solving the strong CP problem with non-conventional CP
• Beyond basis invariants
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• Complex $S_3$-symmetric 3HDM
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• $U(1)$-charged Dark Matter in three-Higgs-doublet models
• Dark matter from CP symmetry of order 4: evolution in the asymmetric regime
• Systematic analysis of 3HDM symmetries
• An extended 3-3-1 model with two scalar triplets and linear seesaw mechanism
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• Telling compositeness at a distance with outer automorphisms and CP
• Fitting the $Zb\bar{b}$ vertex in the two-Higgs-doublet model and in the three-Higgs-doublet model
• Tridiagonal scalar mass matrix in the CP4 3HDM and its implications
• A three Higgs doublet model with symmetry-suppressed flavour changing neutral currents
• Constraining the CP4-invariant three-Higgs-doublet model via top quark decays